Translate all code to English (#1836)

* Review the EN heading format.

* Fix pythontutor headings.

* Fix pythontutor headings.

* bug fixes

* Fix headings in **/summary.md

* Revisit the CN-to-EN translation for Python code using Claude-4.5

* Revisit the CN-to-EN translation for Java code using Claude-4.5

* Revisit the CN-to-EN translation for Cpp code using Claude-4.5.

* Fix the dictionary.

* Fix cpp code translation for the multipart strings.

* Translate Go code to English.

* Update workflows to test EN code.

* Add EN translation for C.

* Add EN translation for CSharp.

* Add EN translation for Swift.

* Trigger the CI check.

* Revert.

* Update en/hash_map.md

* Add the EN version of Dart code.

* Add the EN version of Kotlin code.

* Add missing code files.

* Add the EN version of JavaScript code.

* Add the EN version of TypeScript code.

* Fix the workflows.

* Add the EN version of Ruby code.

* Add the EN version of Rust code.

* Update the CI check for the English version  code.

* Update Python CI check.

* Fix cmakelists for en/C code.

* Fix Ruby comments

en/codes/ruby/chapter_dynamic_programming/min_path_sum.rb

@@ -0,0 +1,93 @@
+=begin
+File: min_path_sum.rb
+Created Time: 2024-05-29
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### Minimum path sum: brute force search ###
+def min_path_sum_dfs(grid, i, j)
+  # If it's the top-left cell, terminate the search
+  return grid[i][j] if i == 0 && j == 0
+  # If row or column index is out of bounds, return +∞ cost
+  return Float::INFINITY if i < 0 || j < 0
+  # Calculate the minimum path cost from top-left to (i-1, j) and (i, j-1)
+  up = min_path_sum_dfs(grid, i - 1, j)
+  left = min_path_sum_dfs(grid, i, j - 1)
+  # Return the minimum path cost from top-left to (i, j)
+  [left, up].min + grid[i][j]
+end
+
+### Minimum path sum: memoization search ###
+def min_path_sum_dfs_mem(grid, mem, i, j)
+  # If it's the top-left cell, terminate the search
+  return grid[0][0] if i == 0 && j == 0
+  # If row or column index is out of bounds, return +∞ cost
+  return Float::INFINITY if i < 0 || j < 0
+  # If there's a record, return it directly
+  return mem[i][j] if mem[i][j] != -1
+  # Minimum path cost for left and upper cells
+  up = min_path_sum_dfs_mem(grid, mem, i - 1, j)
+  left = min_path_sum_dfs_mem(grid, mem, i, j - 1)
+  # Record and return the minimum path cost from top-left to (i, j)
+  mem[i][j] = [left, up].min + grid[i][j]
+end
+
+### Minimum path sum: dynamic programming ###
+def min_path_sum_dp(grid)
+  n, m = grid.length, grid.first.length
+  # Initialize dp table
+  dp = Array.new(n) { Array.new(m, 0) }
+  dp[0][0] = grid[0][0]
+  # State transition: first row
+  (1...m).each { |j| dp[0][j] = dp[0][j - 1] + grid[0][j] }
+  # State transition: first column
+  (1...n).each { |i| dp[i][0] = dp[i - 1][0] + grid[i][0] }
+  # State transition: rest of the rows and columns
+  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
+
+### Minimum path sum: space-optimized DP ###
+def min_path_sum_dp_comp(grid)
+  n, m = grid.length, grid.first.length
+  # Initialize dp table
+  dp = Array.new(m, 0)
+  # State transition: first row
+  dp[0] = grid[0][0]
+  (1...m).each { |j| dp[j] = dp[j - 1] + grid[0][j] }
+  # State transition: rest of the rows
+  for i in 1...n
+    # State transition: first column
+    dp[0] = dp[0] + grid[i][0]
+    # State transition: rest of the columns
+    (1...m).each { |j| dp[j] = [dp[j - 1], dp[j]].min + grid[i][j] }
+  end
+  dp[m - 1]
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  grid = [[1, 3, 1, 5], [2, 2, 4, 2], [5, 3, 2, 1], [4, 3, 5, 2]]
+  n, m = grid.length, grid.first.length
+
+  # Brute-force search
+  res = min_path_sum_dfs(grid, n - 1, m - 1)
+  puts "Minimum path sum from top-left to bottom-right is #{res}"
+
+  # Memoization search
+  mem = Array.new(n) { Array.new(m, - 1) }
+  res = min_path_sum_dfs_mem(grid, mem, n - 1, m -1)
+  puts "Minimum path sum from top-left to bottom-right is #{res}"
+
+  # Dynamic programming
+  res = min_path_sum_dp(grid)
+  puts "Minimum path sum from top-left to bottom-right is #{res}"
+
+  # Space-optimized dynamic programming
+  res = min_path_sum_dp_comp(grid)
+  puts "Minimum path sum from top-left to bottom-right is #{res}"
+end