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_searching/binary_search.rb

@@ -0,0 +1,63 @@
+=begin
+File: binary_search.rb
+Created Time: 2024-04-09
+Author: Blue Bean (lonnnnnnner@gmail.com)
+=end
+
+### Binary search (closed interval) ###
+def binary_search(nums, target)
+  # Initialize closed interval [0, n-1], i.e., i, j point to the first and last elements of the array
+  i, j = 0, nums.length - 1
+
+  # Loop, exit when the search interval is empty (empty when i > j)
+  while i <= j
+    # In theory, Ruby numbers can be infinitely large (limited by memory), no need to consider overflow
+    m = (i + j) / 2   # Calculate the midpoint index m
+  
+    if nums[m] < target
+      i = m + 1 # This means target is in the interval [m+1, j]
+    elsif nums[m] > target
+      j = m - 1 # This means target is in the interval [i, m-1]
+    else
+      return m  # Found the target element, return its index
+    end
+  end
+
+  -1  # Target element not found, return -1
+end
+
+### Binary search (left-closed right-open interval) ###
+def binary_search_lcro(nums, target)
+  # Initialize left-closed right-open interval [0, n), i.e., i, j point to the first element and last element+1
+  i, j = 0, nums.length
+
+  # Loop, exit when the search interval is empty (empty when i = j)
+  while i < j
+    # Calculate the midpoint index m
+    m = (i + j) / 2
+
+    if nums[m] < target
+      i = m + 1 # This means target is in the interval [m+1, j)
+    elsif nums[m] > target
+      j = m - 1 # This means target is in the interval [i, m)
+    else
+      return m  # Found the target element, return its index
+    end
+  end
+
+  -1  # Target element not found, return -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}"
+
+  # Binary search (left-closed right-open interval)
+  index = binary_search_lcro(nums, target)
+  puts "Index of target element 6 is #{index}"
+end