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en/chapter_searching/binary_search_insertion/index.html

@@ -4666,7 +4666,7 @@
 <p>The problem requires inserting <code>target</code> to the left of equal elements, which means the newly inserted <code>target</code> replaces the position of the original <code>target</code>. In other words, <strong>when the array contains <code>target</code>, the insertion point index is the index of that <code>target</code></strong>.</p>
 <p><strong>Question 2</strong>: When the array does not contain <code>target</code>, what is the insertion point index?</p>
 <p>To analyze this further, consider the binary search process: when <code>nums[m] &lt; target</code>, <span class="arithmatex">\(i\)</span> moves, meaning that pointer <span class="arithmatex">\(i\)</span> is approaching elements greater than or equal to <code>target</code>. Similarly, pointer <span class="arithmatex">\(j\)</span> is always approaching elements less than or equal to <code>target</code>.</p>
-<p>Therefore, when the binary search ends, <span class="arithmatex">\(i\)</span> must point to the first element greater than <code>target</code>, and <span class="arithmatex">\(j\)</span> must point to the first element less than <code>target</code>. <strong>It follows that when the array does not contain <code>target</code>, the insertion index is <span class="arithmatex">\(i\)</span></strong>. The code is shown below:</p>
+<p>Therefore, when the binary search ends, <span class="arithmatex">\(i\)</span> must point to the first element greater than <code>target</code>, and <span class="arithmatex">\(j\)</span> must point to the rightmost element less than <code>target</code>. <strong>It follows that when the array does not contain <code>target</code>, the insertion index is <span class="arithmatex">\(i\)</span></strong>. The code is shown below:</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:13"><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" /><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></div>
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@@ -4952,7 +4952,7 @@
 <li>When <code>nums[m] &lt; target</code> or <code>nums[m] &gt; target</code>, it means <code>target</code> has not been found yet, so use the standard interval-shrinking operation of binary search to <strong>move pointers <span class="arithmatex">\(i\)</span> and <span class="arithmatex">\(j\)</span> closer to <code>target</code></strong>.</li>
 <li>When <code>nums[m] == target</code>, it means elements less than <code>target</code> are in the interval <span class="arithmatex">\([i, m - 1]\)</span>, so use <span class="arithmatex">\(j = m - 1\)</span> to shrink the interval, thereby <strong>moving pointer <span class="arithmatex">\(j\)</span> closer to elements less than <code>target</code></strong>.</li>
 </ul>
-<p>After the loop completes, <span class="arithmatex">\(i\)</span> points to the leftmost <code>target</code>, and <span class="arithmatex">\(j\)</span> points to the first element less than <code>target</code>, <strong>so index <span class="arithmatex">\(i\)</span> is the insertion point</strong>.</p>
+<p>After the loop completes, <span class="arithmatex">\(i\)</span> points to the leftmost <code>target</code>, and <span class="arithmatex">\(j\)</span> points to the rightmost element less than <code>target</code>, <strong>so index <span class="arithmatex">\(i\)</span> is the insertion point</strong>.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:8"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label></div>
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@@ -4998,7 +4998,7 @@
 <a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
 <a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># target is in the interval [i, m-1]</span>
 <a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="k">else</span><span class="p">:</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="c1"># Return insertion point i</span>
 <a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>    <span class="k">return</span> <span class="n">i</span>
 </code></pre></div>
@@ -5014,7 +5014,7 @@
 <a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="c1">// Return insertion point i</span>
@@ -5033,7 +5033,7 @@
 <a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="c1">// Return insertion point i</span>
@@ -5052,7 +5052,7 @@
 <a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="c1">// Return insertion point i</span>
@@ -5075,7 +5075,7 @@
 <a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">            </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
 <a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">            </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">            </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
 <a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><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="p">}</span>
@@ -5097,7 +5097,7 @@
 <a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">    </span><span class="c1">// Return insertion point i</span>
@@ -5117,7 +5117,7 @@
 <a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="c1">// Return insertion point i</span>
@@ -5137,7 +5137,7 @@
 <a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">            </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="c1">// Return insertion point i</span>
@@ -5156,7 +5156,7 @@
 <a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="p">}</span>
 <a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">  </span><span class="c1">// Return insertion point i</span>
@@ -5175,7 +5175,7 @@
 <a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="c1">// Return insertion point i</span>
@@ -5194,7 +5194,7 @@
 <a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">    </span><span class="c1">// Return insertion point i</span>
@@ -5214,7 +5214,7 @@
 <a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// target is in the interval [i, m-1]</span>
 <a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="c1">// The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w">    </span><span class="c1">// Return insertion point i</span>
@@ -5237,7 +5237,7 @@
 <a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w">    </span><span class="k">elsif</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span>
 <a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># target is in the interval [i, m-1]</span>
 <a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">    </span><span class="k">else</span>
-<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># The first element less than target is in the interval [i, m-1]</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1"># The rightmost element less than target is in the interval [i, m-1]</span>
 <a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">    </span><span class="k">end</span>
 <a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">  </span><span class="k">end</span>
 <a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a>