mirror of
https://github.com/krahets/hello-algo.git
synced 2026-08-17 22:10:59 +00:00
deploy
This commit is contained in:
krahets
@@ -4720,7 +4720,80 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">graph_adjacency_matrix.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">GraphAdjMat</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
|
||||
<div class="highlight"><span class="filename">graph_adjacency_matrix.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 基於鄰接矩陣實現的無向圖類別 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="c1">### 建構子 ###</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 頂點串列，元素代表“頂點值”，索引代表“頂點索引”</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="vi">@vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 鄰接矩陣，行列索引對應“頂點索引”</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="vi">@adj_mat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="c1"># 新增頂點</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="n">vertices</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">val</span><span class="o">|</span><span class="w"> </span><span class="n">add_vertex</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="c1"># 新增邊</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="c1"># 請注意，edges 元素代表頂點索引，即對應 vertices 元素索引</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">edges</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">e</span><span class="o">|</span><span class="w"> </span><span class="n">add_edge</span><span class="p">(</span><span class="n">e</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">e</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="c1">### 獲取頂點數量 ###</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="vi">@vertices</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
|
||||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="c1">### 新增頂點 ###</span>
|
||||
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span>
|
||||
<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w"> </span><span class="c1"># 向頂點串列中新增新頂點的值</span>
|
||||
<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w"> </span><span class="vi">@vertices</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">val</span>
|
||||
<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w"> </span><span class="c1"># 在鄰接矩陣中新增一行</span>
|
||||
<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w"> </span><span class="n">new_row</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w"> </span><span class="vi">@adj_mat</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">new_row</span>
|
||||
<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w"> </span><span class="c1"># 在鄰接矩陣中新增一列</span>
|
||||
<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w"> </span><span class="vi">@adj_mat</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">row</span><span class="o">|</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a>
|
||||
<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w"> </span><span class="c1">### 刪除頂點 ###</span>
|
||||
<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span>
|
||||
<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a>
|
||||
<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="w"> </span><span class="c1"># 在頂點串列中移除索引 index 的頂點</span>
|
||||
<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w"> </span><span class="vi">@vertices</span><span class="o">.</span><span class="n">delete_at</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="w"> </span><span class="c1"># 在鄰接矩陣中刪除索引 index 的行</span>
|
||||
<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a><span class="w"> </span><span class="vi">@adj_mat</span><span class="o">.</span><span class="n">delete_at</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="w"> </span><span class="c1"># 在鄰接矩陣中刪除索引 index 的列</span>
|
||||
<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a><span class="w"> </span><span class="vi">@adj_mat</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">row</span><span class="o">|</span><span class="w"> </span><span class="n">row</span><span class="o">.</span><span class="n">delete_at</span><span class="p">(</span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a>
|
||||
<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a><span class="w"> </span><span class="c1">### 新增邊 ###</span>
|
||||
<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="w"> </span><span class="c1"># 參數 i, j 對應 vertices 元素索引</span>
|
||||
<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a><span class="w"> </span><span class="c1"># 索引越界與相等處理</span>
|
||||
<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span>
|
||||
<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span>
|
||||
<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-52" name="__codelineno-12-52" href="#__codelineno-12-52"></a><span class="w"> </span><span class="c1"># 在無向圖中，鄰接矩陣關於主對角線對稱，即滿足 (i, j) == (j, i)</span>
|
||||
<a id="__codelineno-12-53" name="__codelineno-12-53" href="#__codelineno-12-53"></a><span class="w"> </span><span class="vi">@adj_mat</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-12-54" name="__codelineno-12-54" href="#__codelineno-12-54"></a><span class="w"> </span><span class="vi">@adj_mat</span><span class="o">[</span><span class="n">j</span><span class="o">][</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-12-55" name="__codelineno-12-55" href="#__codelineno-12-55"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-56" name="__codelineno-12-56" href="#__codelineno-12-56"></a>
|
||||
<a id="__codelineno-12-57" name="__codelineno-12-57" href="#__codelineno-12-57"></a><span class="w"> </span><span class="c1">### 刪除邊 ###</span>
|
||||
<a id="__codelineno-12-58" name="__codelineno-12-58" href="#__codelineno-12-58"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-59" name="__codelineno-12-59" href="#__codelineno-12-59"></a><span class="w"> </span><span class="c1"># 參數 i, j 對應 vertices 元素索引</span>
|
||||
<a id="__codelineno-12-60" name="__codelineno-12-60" href="#__codelineno-12-60"></a><span class="w"> </span><span class="c1"># 索引越界與相等處理</span>
|
||||
<a id="__codelineno-12-61" name="__codelineno-12-61" href="#__codelineno-12-61"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span>
|
||||
<a id="__codelineno-12-62" name="__codelineno-12-62" href="#__codelineno-12-62"></a><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="no">IndexError</span>
|
||||
<a id="__codelineno-12-63" name="__codelineno-12-63" href="#__codelineno-12-63"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-64" name="__codelineno-12-64" href="#__codelineno-12-64"></a><span class="w"> </span><span class="vi">@adj_mat</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-65" name="__codelineno-12-65" href="#__codelineno-12-65"></a><span class="w"> </span><span class="vi">@adj_mat</span><span class="o">[</span><span class="n">j</span><span class="o">][</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-66" name="__codelineno-12-66" href="#__codelineno-12-66"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-67" name="__codelineno-12-67" href="#__codelineno-12-67"></a>
|
||||
<a id="__codelineno-12-68" name="__codelineno-12-68" href="#__codelineno-12-68"></a><span class="w"> </span><span class="c1">### 列印鄰接矩陣 ###</span>
|
||||
<a id="__codelineno-12-69" name="__codelineno-12-69" href="#__codelineno-12-69"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="n">__print__</span>
|
||||
<a id="__codelineno-12-70" name="__codelineno-12-70" href="#__codelineno-12-70"></a><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="s2">"頂點串列 = </span><span class="si">#{</span><span class="vi">@vertices</span><span class="si">}</span><span class="s2">"</span>
|
||||
<a id="__codelineno-12-71" name="__codelineno-12-71" href="#__codelineno-12-71"></a><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="s1">'鄰接矩陣 ='</span>
|
||||
<a id="__codelineno-12-72" name="__codelineno-12-72" href="#__codelineno-12-72"></a><span class="w"> </span><span class="n">print_matrix</span><span class="p">(</span><span class="vi">@adj_mat</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-73" name="__codelineno-12-73" href="#__codelineno-12-73"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-74" name="__codelineno-12-74" href="#__codelineno-12-74"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -5801,7 +5874,73 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">graph_adjacency_list.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">GraphAdjList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
|
||||
<div class="highlight"><span class="filename">graph_adjacency_list.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 基於鄰接表實現的無向圖類別 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjList</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="kp">attr_reader</span><span class="w"> </span><span class="ss">:adj_list</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1">### 建構子 ###</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">edges</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 鄰接表，key：頂點，value：該頂點的所有鄰接頂點</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="vi">@adj_list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{}</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 新增所有頂點和邊</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">edge</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">edges</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="n">add_edge</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">edge</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>
|
||||
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="c1">### 獲取頂點數量 ###</span>
|
||||
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
|
||||
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">length</span>
|
||||
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a>
|
||||
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w"> </span><span class="c1">### 新增邊 ###</span>
|
||||
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="no">ArgumentError</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>
|
||||
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet1</span><span class="o">]</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">vet2</span>
|
||||
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet2</span><span class="o">]</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">vet1</span>
|
||||
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a>
|
||||
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a><span class="w"> </span><span class="c1">### 刪除邊 ###</span>
|
||||
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="no">ArgumentError</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a>
|
||||
<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w"> </span><span class="c1"># 刪除邊 vet1 - vet2</span>
|
||||
<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet1</span><span class="o">].</span><span class="n">delete</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet2</span><span class="o">].</span><span class="n">delete</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a>
|
||||
<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a><span class="w"> </span><span class="c1">### 新增頂點 ###</span>
|
||||
<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a>
|
||||
<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a><span class="w"> </span><span class="c1"># 在鄰接表中新增一個新鏈結串列</span>
|
||||
<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vet</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
|
||||
<a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a>
|
||||
<a id="__codelineno-26-47" name="__codelineno-26-47" href="#__codelineno-26-47"></a><span class="w"> </span><span class="c1">### 刪除頂點 ###</span>
|
||||
<a id="__codelineno-26-48" name="__codelineno-26-48" href="#__codelineno-26-48"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-49" name="__codelineno-26-49" href="#__codelineno-26-49"></a><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="no">ArgumentError</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-50" name="__codelineno-26-50" href="#__codelineno-26-50"></a>
|
||||
<a id="__codelineno-26-51" name="__codelineno-26-51" href="#__codelineno-26-51"></a><span class="w"> </span><span class="c1"># 在鄰接表中刪除頂點 vet 對應的鏈結串列</span>
|
||||
<a id="__codelineno-26-52" name="__codelineno-26-52" href="#__codelineno-26-52"></a><span class="w"> </span><span class="vi">@adj_list</span><span class="o">.</span><span class="n">delete</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-53" name="__codelineno-26-53" href="#__codelineno-26-53"></a><span class="w"> </span><span class="c1"># 走訪其他頂點的鏈結串列，刪除所有包含 vet 的邊</span>
|
||||
<a id="__codelineno-26-54" name="__codelineno-26-54" href="#__codelineno-26-54"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">vertex</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="vi">@adj_list</span>
|
||||
<a id="__codelineno-26-55" name="__codelineno-26-55" href="#__codelineno-26-55"></a><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vertex</span><span class="o">.</span><span class="n">first</span><span class="o">].</span><span class="n">delete</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vertex</span><span class="o">.</span><span class="n">first</span><span class="o">].</span><span class="n">include?</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-56" name="__codelineno-26-56" href="#__codelineno-26-56"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-57" name="__codelineno-26-57" href="#__codelineno-26-57"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-58" name="__codelineno-26-58" href="#__codelineno-26-58"></a>
|
||||
<a id="__codelineno-26-59" name="__codelineno-26-59" href="#__codelineno-26-59"></a><span class="w"> </span><span class="c1">### 列印鄰接表 ###</span>
|
||||
<a id="__codelineno-26-60" name="__codelineno-26-60" href="#__codelineno-26-60"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="n">__print__</span>
|
||||
<a id="__codelineno-26-61" name="__codelineno-26-61" href="#__codelineno-26-61"></a><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="s1">'鄰接表 ='</span>
|
||||
<a id="__codelineno-26-62" name="__codelineno-26-62" href="#__codelineno-26-62"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">vertex</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="vi">@adj_list</span>
|
||||
<a id="__codelineno-26-63" name="__codelineno-26-63" href="#__codelineno-26-63"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@adj_list</span><span class="o">[</span><span class="n">vertex</span><span class="o">.</span><span class="n">first</span><span class="o">].</span><span class="n">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">v</span><span class="o">|</span><span class="w"> </span><span class="n">v</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-26-64" name="__codelineno-26-64" href="#__codelineno-26-64"></a><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="s2">"</span><span class="si">#{</span><span class="n">vertex</span><span class="o">.</span><span class="n">first</span><span class="o">.</span><span class="n">val</span><span class="si">}</span><span class="s2">: </span><span class="si">#{</span><span class="n">tmp</span><span class="si">}</span><span class="s2">,"</span>
|
||||
<a id="__codelineno-26-65" name="__codelineno-26-65" href="#__codelineno-26-65"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-66" name="__codelineno-26-66" href="#__codelineno-26-66"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-67" name="__codelineno-26-67" href="#__codelineno-26-67"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
|
||||
@@ -3709,7 +3709,11 @@
|
||||
<li>在迴圈的每輪迭代中，彈出佇列首頂點並記錄訪問，然後將該頂點的所有鄰接頂點加入到佇列尾部。</li>
|
||||
<li>迴圈步驟 <code>2.</code> ，直到所有頂點被訪問完畢後結束。</li>
|
||||
</ol>
|
||||
<p>為了防止重複走訪頂點，我們需要藉助一個雜湊表 <code>visited</code> 來記錄哪些節點已被訪問。</p>
|
||||
<p>為了防止重複走訪頂點，我們需要藉助一個雜湊集合 <code>visited</code> 來記錄哪些節點已被訪問。</p>
|
||||
<div class="admonition tip">
|
||||
<p class="admonition-title">Tip</p>
|
||||
<p>雜湊集合可以看作一個只儲存 <code>key</code> 而不儲存 <code>value</code> 的雜湊表，它可以在 <span class="arithmatex">\(O(1)\)</span> 時間複雜度下進行 <code>key</code> 的增刪查改操作。根據 <code>key</code> 的唯一性，雜湊集合通常用於資料去重等場景。</p>
|
||||
</div>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
@@ -3718,7 +3722,7 @@
|
||||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="c1"># 頂點走訪序列</span>
|
||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
|
||||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="c1"># 佇列用於實現 BFS</span>
|
||||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">que</span> <span class="o">=</span> <span class="n">deque</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
|
||||
@@ -3742,7 +3746,7 @@
|
||||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="n">unordered_set</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="n">startVet</span><span class="p">};</span>
|
||||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="n">queue</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">que</span><span class="p">;</span>
|
||||
@@ -3771,7 +3775,7 @@
|
||||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
||||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><></span><span class="p">();</span>
|
||||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||||
@@ -3800,7 +3804,7 @@
|
||||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">GraphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="n">startVet</span><span class="p">];</span>
|
||||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="n">Queue</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
|
||||
@@ -3829,7 +3833,7 @@
|
||||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">func</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="nx">Vertex</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{})</span>
|
||||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="nx">visited</span><span class="p">[</span><span class="nx">startVet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
|
||||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS, 使用切片模擬佇列</span>
|
||||
@@ -3863,7 +3867,7 @@
|
||||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">func</span> <span class="nf">graphBFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">startVet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">-></span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">{</span>
|
||||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a> <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
|
||||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a> <span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a> <span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a> <span class="kd">var</span> <span class="nv">visited</span><span class="p">:</span> <span class="n">Set</span><span class="p"><</span><span class="n">Vertex</span><span class="p">></span> <span class="p">=</span> <span class="p">[</span><span class="n">startVet</span><span class="p">]</span>
|
||||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a> <span class="c1">// 佇列用於實現 BFS</span>
|
||||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a> <span class="kd">var</span> <span class="nv">que</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">=</span> <span class="p">[</span><span class="n">startVet</span><span class="p">]</span>
|
||||
@@ -3891,7 +3895,7 @@
|
||||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
|
||||
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||||
@@ -3920,7 +3924,7 @@
|
||||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphBFS</span><span class="p">(</span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o"><</span><span class="nx">Vertex</span><span class="o">></span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
|
||||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="nx">visited</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||||
@@ -3949,7 +3953,7 @@
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="c1">// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
|
||||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||||
@@ -3979,7 +3983,7 @@
|
||||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="k">fn</span> <span class="nf">graph_bfs</span><span class="p">(</span><span class="n">graph</span>: <span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span>: <span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span>-> <span class="nb">Vec</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
|
||||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span>::<span class="n">new</span><span class="p">();</span>
|
||||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">start_vet</span><span class="p">);</span>
|
||||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||||
@@ -4083,7 +4087,7 @@
|
||||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex</span><span class="p">):</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">Vertex?></span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o"><</span><span class="n">Vertex?></span><span class="p">()</span>
|
||||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="p">()</span>
|
||||
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">)</span>
|
||||
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="c1">// 佇列用於實現 BFS</span>
|
||||
@@ -4107,7 +4111,29 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">graph_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graph_bfs</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">graph_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 廣度優先走訪 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">graph_bfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="c1"># 頂點走訪序列</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="c1"># 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Set</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="o">[</span><span class="n">start_vet</span><span class="o">]</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="c1"># 佇列用於實現 BFS</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">start_vet</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 以頂點 vet 為起點，迴圈直至訪問完所有頂點</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">que</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="o">.</span><span class="n">shift</span><span class="w"> </span><span class="c1"># 佇列首頂點出隊</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="c1"># 記錄訪問頂點</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="c1"># 走訪該頂點的所有鄰接頂點</span>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">adj_vet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="o">[</span><span class="n">vet</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="c1"># 跳過已被訪問的頂點</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">adj_vet</span><span class="w"> </span><span class="c1"># 只入列未訪問的頂點</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="c1"># 標記該頂點已被訪問</span>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="c1"># 返回頂點走訪序列</span>
|
||||
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="n">res</span>
|
||||
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -4167,14 +4193,14 @@
|
||||
</div>
|
||||
<h3 id="2">2. 複雜度分析<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||||
<p><strong>時間複雜度</strong>：所有頂點都會入列並出隊一次，使用 <span class="arithmatex">\(O(|V|)\)</span> 時間；在走訪鄰接頂點的過程中，由於是無向圖，因此所有邊都會被訪問 <span class="arithmatex">\(2\)</span> 次，使用 <span class="arithmatex">\(O(2|E|)\)</span> 時間；總體使用 <span class="arithmatex">\(O(|V| + |E|)\)</span> 時間。</p>
|
||||
<p><strong>空間複雜度</strong>：串列 <code>res</code> ，雜湊表 <code>visited</code> ，佇列 <code>que</code> 中的頂點數量最多為 <span class="arithmatex">\(|V|\)</span> ，使用 <span class="arithmatex">\(O(|V|)\)</span> 空間。</p>
|
||||
<p><strong>空間複雜度</strong>：串列 <code>res</code> ，雜湊集合 <code>visited</code> ，佇列 <code>que</code> 中的頂點數量最多為 <span class="arithmatex">\(|V|\)</span> ，使用 <span class="arithmatex">\(O(|V|)\)</span> 空間。</p>
|
||||
<h2 id="932">9.3.2 深度優先走訪<a class="headerlink" href="#932" title="Permanent link">¶</a></h2>
|
||||
<p><strong>深度優先走訪是一種優先走到底、無路可走再回頭的走訪方式</strong>。如圖 9-11 所示，從左上角頂點出發，訪問當前頂點的某個鄰接頂點，直到走到盡頭時返回，再繼續走到盡頭並返回，以此類推，直至所有頂點走訪完成。</p>
|
||||
<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="圖的深度優先走訪" class="animation-figure" src="../graph_traversal.assets/graph_dfs.png" /></a></p>
|
||||
<p align="center"> 圖 9-11 圖的深度優先走訪 </p>
|
||||
|
||||
<h3 id="1_1">1. 演算法實現<a class="headerlink" href="#1_1" title="Permanent link">¶</a></h3>
|
||||
<p>這種“走到盡頭再返回”的演算法範式通常基於遞迴來實現。與廣度優先走訪類似，在深度優先走訪中，我們也需要藉助一個雜湊表 <code>visited</code> 來記錄已被訪問的頂點，以避免重複訪問頂點。</p>
|
||||
<p>這種“走到盡頭再返回”的演算法範式通常基於遞迴來實現。與廣度優先走訪類似，在深度優先走訪中，我們也需要藉助一個雜湊集合 <code>visited</code> 來記錄已被訪問的頂點，以避免重複訪問頂點。</p>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
@@ -4194,7 +4220,7 @@
|
||||
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a> <span class="c1"># 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||||
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a> <span class="c1"># 頂點走訪序列</span>
|
||||
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a> <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a> <span class="c1"># 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a> <span class="c1"># 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a> <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]()</span>
|
||||
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a> <span class="k">return</span> <span class="n">res</span>
|
||||
@@ -4219,7 +4245,7 @@
|
||||
<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||||
<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w"> </span><span class="n">unordered_set</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">visited</span><span class="p">;</span>
|
||||
<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||||
@@ -4245,7 +4271,7 @@
|
||||
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
||||
<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><></span><span class="p">();</span>
|
||||
<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||||
@@ -4272,7 +4298,7 @@
|
||||
<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">GraphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||||
@@ -4300,7 +4326,7 @@
|
||||
<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="kd">func</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="nx">Vertex</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Vertex</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||||
<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">Vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{})</span>
|
||||
<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">g</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span>
|
||||
<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w"> </span><span class="c1">// 返回頂點走訪序列</span>
|
||||
@@ -4328,7 +4354,7 @@
|
||||
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="kd">func</span> <span class="nf">graphDFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">startVet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">-></span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">{</span>
|
||||
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a> <span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a> <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
|
||||
<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a> <span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a> <span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a> <span class="kd">var</span> <span class="nv">visited</span><span class="p">:</span> <span class="n">Set</span><span class="p"><</span><span class="n">Vertex</span><span class="p">></span> <span class="p">=</span> <span class="p">[]</span>
|
||||
<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">:</span> <span class="p">&</span><span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">,</span> <span class="n">vet</span><span class="p">:</span> <span class="n">startVet</span><span class="p">)</span>
|
||||
<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a> <span class="k">return</span> <span class="n">res</span>
|
||||
@@ -4356,7 +4382,7 @@
|
||||
<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
|
||||
<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
|
||||
@@ -4388,7 +4414,7 @@
|
||||
<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="kd">function</span><span class="w"> </span><span class="nx">graphDFS</span><span class="p">(</span><span class="nx">graph</span><span class="o">:</span><span class="w"> </span><span class="kt">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">Vertex</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">visited</span><span class="o">:</span><span class="w"> </span><span class="kt">Set</span><span class="o"><</span><span class="nx">Vertex</span><span class="o">></span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="p">();</span>
|
||||
<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">graph</span><span class="p">,</span><span class="w"> </span><span class="nx">visited</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
|
||||
@@ -4419,7 +4445,7 @@
|
||||
<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-22-23" name="__codelineno-22-23" href="#__codelineno-22-23"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-22-24" name="__codelineno-22-24" href="#__codelineno-22-24"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-22-25" name="__codelineno-22-25" href="#__codelineno-22-25"></a><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
|
||||
<a id="__codelineno-22-26" name="__codelineno-22-26" href="#__codelineno-22-26"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
|
||||
<a id="__codelineno-22-27" name="__codelineno-22-27" href="#__codelineno-22-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||||
@@ -4448,7 +4474,7 @@
|
||||
<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="k">fn</span> <span class="nf">graph_dfs</span><span class="p">(</span><span class="n">graph</span>: <span class="nc">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span>: <span class="nc">Vertex</span><span class="p">)</span><span class="w"> </span>-> <span class="nb">Vec</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[];</span>
|
||||
<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span>::<span class="n">new</span><span class="p">();</span>
|
||||
<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="o">&</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">);</span>
|
||||
<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a>
|
||||
@@ -4515,7 +4541,7 @@
|
||||
<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">:</span><span class="w"> </span><span class="n">Vertex?)</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o"><</span><span class="n">Vertex?></span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w"> </span><span class="c1">// 頂點走訪序列</span>
|
||||
<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o"><</span><span class="n">Vertex?></span><span class="p">()</span>
|
||||
<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w"> </span><span class="c1">// 雜湊表，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w"> </span><span class="c1">// 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><</span><span class="n">Vertex?></span><span class="p">()</span>
|
||||
<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span>
|
||||
<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
|
||||
@@ -4523,9 +4549,28 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">graph_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">graph_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 深度優先走訪輔助函式 ###</span>
|
||||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="c1"># 記錄訪問頂點</span>
|
||||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="c1"># 標記該頂點已被訪問</span>
|
||||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 走訪該頂點的所有鄰接頂點</span>
|
||||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">adj_vet</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="o">[</span><span class="n">vet</span><span class="o">]</span>
|
||||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="k">next</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">visited</span><span class="o">.</span><span class="n">include?</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span><span class="w"> </span><span class="c1"># 跳過已被訪問的頂點</span>
|
||||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="c1"># 遞迴訪問鄰接頂點</span>
|
||||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adj_vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="k">end</span>
|
||||
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>
|
||||
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="c1">### 深度優先走訪 ###</span>
|
||||
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="k">def</span><span class="w"> </span><span class="nf">graph_dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="c1"># 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點</span>
|
||||
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="c1"># 頂點走訪序列</span>
|
||||
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
|
||||
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="c1"># 雜湊集合，用於記錄已被訪問過的頂點</span>
|
||||
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Set</span><span class="o">.</span><span class="n">new</span>
|
||||
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">start_vet</span><span class="p">)</span>
|
||||
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w"> </span><span class="n">res</span>
|
||||
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
@@ -4593,7 +4638,7 @@
|
||||
</div>
|
||||
<h3 id="2_1">2. 複雜度分析<a class="headerlink" href="#2_1" title="Permanent link">¶</a></h3>
|
||||
<p><strong>時間複雜度</strong>：所有頂點都會被訪問 <span class="arithmatex">\(1\)</span> 次，使用 <span class="arithmatex">\(O(|V|)\)</span> 時間；所有邊都會被訪問 <span class="arithmatex">\(2\)</span> 次，使用 <span class="arithmatex">\(O(2|E|)\)</span> 時間；總體使用 <span class="arithmatex">\(O(|V| + |E|)\)</span> 時間。</p>
|
||||
<p><strong>空間複雜度</strong>：串列 <code>res</code> ，雜湊表 <code>visited</code> 頂點數量最多為 <span class="arithmatex">\(|V|\)</span> ，遞迴深度最大為 <span class="arithmatex">\(|V|\)</span> ，因此使用 <span class="arithmatex">\(O(|V|)\)</span> 空間。</p>
|
||||
<p><strong>空間複雜度</strong>：串列 <code>res</code> ，雜湊集合 <code>visited</code> 頂點數量最多為 <span class="arithmatex">\(|V|\)</span> ，遞迴深度最大為 <span class="arithmatex">\(|V|\)</span> ，因此使用 <span class="arithmatex">\(O(|V|)\)</span> 空間。</p>
|
||||
|
||||
<!-- Source file information -->
|
||||
|
||||
|
||||
Reference in New Issue
Block a user