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_divide_and_conquer/binary_search_recur.rb

@@ -0,0 +1,42 @@
+=begin
+File: binary_search_recur.rb
+Created Time: 2024-05-13
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### Binary search: problem f(i, j) ###
+def dfs(nums, target, i, j)
+  # If the interval is empty, it means there is no target element, return -1
+  return -1 if i > j
+  
+  # Calculate the midpoint index m
+  m = (i + j) / 2
+
+  if nums[m] < target
+    # Recursion subproblem f(m+1, j)
+    return dfs(nums, target, m + 1, j)
+  elsif nums[m] > target
+    # Recursion subproblem f(i, m-1)
+    return dfs(nums, target, i, m - 1)
+  else
+    # Found the target element, return its index
+    return m
+  end
+end
+
+### Binary search ###
+def binary_search(nums, target)
+  n = nums.length
+  # Solve the problem f(0, n-1)
+  dfs(nums, target, 0, n - 1)
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  target = 6
+  nums = [1, 3, 6, 8, 12, 15, 23, 26, 31, 35]
+
+  # Binary search (closed interval on both sides)
+  index = binary_search(nums, target)
+  puts "Index of target element 6 is #{index}"
+end

en/codes/ruby/chapter_divide_and_conquer/build_tree.rb

@@ -0,0 +1,46 @@
+=begin
+File: build_tree.rb
+Created Time: 2024-05-13
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+require_relative '../utils/tree_node'
+require_relative '../utils/print_util'
+
+### Build binary tree: divide and conquer ###
+def dfs(preorder, inorder_map, i, l, r)
+  # Terminate when the subtree interval is empty
+  return if r - l < 0
+
+  # Initialize the root node
+  root = TreeNode.new(preorder[i])
+  # Query m to divide the left and right subtrees
+  m = inorder_map[preorder[i]]
+  # Subproblem: build the left subtree
+  root.left = dfs(preorder, inorder_map, i + 1, l, m - 1)
+  # Subproblem: build the right subtree
+  root.right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r)
+
+  # Return the root node
+  root
+end
+
+### Build binary tree ###
+def build_tree(preorder, inorder)
+  # Initialize hash map, storing the mapping from inorder elements to indices
+  inorder_map = {}
+  inorder.each_with_index { |val, i| inorder_map[val] = i }
+  dfs(preorder, inorder_map, 0, 0, inorder.length - 1)
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  preorder = [3, 9, 2, 1, 7]
+  inorder = [9, 3, 1, 2, 7]
+  puts "Pre-order traversal = #{preorder}"
+  puts "In-order traversal = #{inorder}"
+
+  root = build_tree(preorder, inorder)
+  puts "The constructed binary tree is:"
+  print_tree(root)
+end

en/codes/ruby/chapter_divide_and_conquer/hanota.rb

@@ -0,0 +1,55 @@
+=begin
+File: hanota.rb
+Created Time: 2024-05-13
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### Move one disk ###
+def move(src, tar)
+  # Take out a disk from the top of src
+  pan = src.pop
+  # Place the disk on top of tar
+  tar << pan
+end
+
+### Solve Tower of Hanoi f(i) ###
+def dfs(i, src, buf, tar)
+  # If there is only one disk left in src, move it directly to tar
+  if i == 1
+    move(src, tar)
+    return
+  end
+
+  # Subproblem f(i-1): move the top i-1 disks from src to buf using tar
+  dfs(i - 1, src, tar, buf)
+  # Subproblem f(1): move the remaining disk from src to tar
+  move(src, tar)
+  # Subproblem f(i-1): move the top i-1 disks from buf to tar using src
+  dfs(i - 1, buf, src, tar)
+end
+
+### Solve Tower of Hanoi ###
+def solve_hanota(_A, _B, _C)
+  n = _A.length
+  # Move the top n disks from A to C using B
+  dfs(n, _A, _B, _C)
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  # The tail of the list is the top of the rod
+  A = [5, 4, 3, 2, 1]
+  B = []
+  C = []
+  puts "In initial state:"
+  puts "A = #{A}"
+  puts "B = #{B}"
+  puts "C = #{C}"
+
+  solve_hanota(A, B, C)
+
+  puts "After disk movement is complete:"
+  puts "A = #{A}"
+  puts "B = #{B}"
+  puts "C = #{C}"
+end