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/python/chapter_backtracking/permutations_i.py

@@ -8,7 +8,7 @@ Author: krahets (krahets@163.com)
 def backtrack(
     state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]
 ):
-    """Backtracking algorithm: Permutation I"""
+    """Backtracking algorithm: Permutations I"""
     # When the state length equals the number of elements, record the solution
     if len(state) == len(choices):
         res.append(list(state))
@@ -17,18 +17,18 @@ def backtrack(
     for i, choice in enumerate(choices):
         # Pruning: do not allow repeated selection of elements
         if not selected[i]:
-            # Attempt: make a choice, update the state
+            # Attempt: make choice, update state
             selected[i] = True
             state.append(choice)
             # Proceed to the next round of selection
             backtrack(state, choices, selected, res)
-            # Retract: undo the choice, restore to the previous state
+            # Backtrack: undo choice, restore to previous state
             selected[i] = False
             state.pop()
 
 
 def permutations_i(nums: list[int]) -> list[list[int]]:
-    """Permutation I"""
+    """Permutations I"""
     res = []
     backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)
     return res