build

zh-Hant/docs/chapter_dynamic_programming/dp_solution_pipeline.md

@@ -369,7 +369,18 @@ $$
 === "Ruby"
 
     ```ruby title="min_path_sum.rb"
-    [class]{}-[func]{min_path_sum_dfs}
+    ### 最小路徑和：暴力搜尋 ###
+    def min_path_sum_dfs(grid, i, j)
+      # 若為左上角單元格，則終止搜尋
+      return grid[i][j] if i == 0 && j == 0
+      # 若行列索引越界，則返回 +∞ 代價
+      return Float::INFINITY if i < 0 || j < 0
+      # 計算從左上角到 (i-1, j) 和 (i, j-1) 的最小路徑代價
+      up = min_path_sum_dfs(grid, i - 1, j)
+      left = min_path_sum_dfs(grid, i, j - 1)
+      # 返回從左上角到 (i, j) 的最小路徑代價
+      [left, up].min + grid[i][j]
+    end
     ```
 
 === "Zig"
@@ -736,7 +747,20 @@ $$
 === "Ruby"
 
     ```ruby title="min_path_sum.rb"
-    [class]{}-[func]{min_path_sum_dfs_mem}
+    ### 最小路徑和：記憶化搜尋 ###
+    def min_path_sum_dfs_mem(grid, mem, i, j)
+      # 若為左上角單元格，則終止搜尋
+      return grid[0][0] if i == 0 && j == 0
+      # 若行列索引越界，則返回 +∞ 代價
+      return Float::INFINITY if i < 0 || j < 0
+      # 若已有記錄，則直接返回
+      return mem[i][j] if mem[i][j] != -1
+      # 左邊和上邊單元格的最小路徑代價
+      up = min_path_sum_dfs_mem(grid, mem, i - 1, j)
+      left = min_path_sum_dfs_mem(grid, mem, i, j - 1)
+      # 記錄並返回左上角到 (i, j) 的最小路徑代價
+      mem[i][j] = [left, up].min + grid[i][j]
+    end
     ```
 
 === "Zig"
@@ -1121,7 +1145,24 @@ $$
 === "Ruby"
 
     ```ruby title="min_path_sum.rb"
-    [class]{}-[func]{min_path_sum_dp}
+    ### 最小路徑和：動態規劃 ###
+    def min_path_sum_dp(grid)
+      n, m = grid.length, grid.first.length
+      # 初始化 dp 表
+      dp = Array.new(n) { Array.new(m, 0) }
+      dp[0][0] = grid[0][0]
+      # 狀態轉移：首行
+      (1...m).each { |j| dp[0][j] = dp[0][j - 1] + grid[0][j] }
+      # 狀態轉移：首列
+      (1...n).each { |i| dp[i][0] = dp[i - 1][0] + grid[i][0] }
+      # 狀態轉移：其餘行和列
+      for i in 1...n
+        for j in 1...m
+          dp[i][j] = [dp[i][j - 1], dp[i - 1][j]].min + grid[i][j]
+        end
+      end
+      dp[n -1][m -1]
+    end
     ```
 
 === "Zig"
@@ -1521,7 +1562,23 @@ $$
 === "Ruby"
 
     ```ruby title="min_path_sum.rb"
-    [class]{}-[func]{min_path_sum_dp_comp}
+    ### 最小路徑和：空間最佳化後的動態規劃 ###
+    def min_path_sum_dp_comp(grid)
+      n, m = grid.length, grid.first.length
+      # 初始化 dp 表
+      dp = Array.new(m, 0)
+      # 狀態轉移：首行
+      dp[0] = grid[0][0]
+      (1...m).each { |j| dp[j] = dp[j - 1] + grid[0][j] }
+      # 狀態轉移：其餘行
+      for i in 1...n
+        # 狀態轉移：首列
+        dp[0] = dp[0] + grid[i][0]
+        # 狀態轉移：其餘列
+        (1...m).each { |j| dp[j] = [dp[j - 1], dp[j]].min + grid[i][j] }
+      end
+      dp[m - 1]
+    end
     ```
 
 === "Zig"