[Rust] Normalize mid calculation in case overflow (#1363)

* Normalize mid calculate in case overflow

* Change ALL language

* Update merge_sort.py

* Update merge_sort.zig

* Update binary_search_tree.zig

* Update binary_search_recur.py

---------

Co-authored-by: Yudong Jin <krahets@163.com>

en/codes/python/chapter_searching/binary_search.py

@@ -12,7 +12,7 @@ def binary_search(nums: list[int], target: int) -> int:
     # Loop until the search interval is empty (when i > j, it is empty)
     while i <= j:
         # Theoretically, Python's numbers can be infinitely large (depending on memory size), so there is no need to consider large number overflow
-        m = (i + j) // 2  # Calculate midpoint index m
+        m = i + (j - i) // 2  # Calculate midpoint index m
         if nums[m] < target:
             i = m + 1  # This situation indicates that target is in the interval [m+1, j]
         elif nums[m] > target:
@@ -28,7 +28,7 @@ def binary_search_lcro(nums: list[int], target: int) -> int:
     i, j = 0, len(nums)
     # Loop until the search interval is empty (when i = j, it is empty)
     while i < j:
-        m = (i + j) // 2  # Calculate midpoint index m
+        m = i + (j - i) // 2  # Calculate midpoint index m
         if nums[m] < target:
             i = m + 1  # This situation indicates that target is in the interval [m+1, j)
         elif nums[m] > target:

en/codes/python/chapter_searching/binary_search_insertion.py

@@ -9,7 +9,7 @@ def binary_search_insertion_simple(nums: list[int], target: int) -> int:
     """Binary search for insertion point (no duplicate elements)"""
     i, j = 0, len(nums) - 1  # Initialize double closed interval [0, n-1]
     while i <= j:
-        m = (i + j) // 2  # Calculate midpoint index m
+        m = i + (j - i) // 2  # Calculate midpoint index m
         if nums[m] < target:
             i = m + 1  # Target is in interval [m+1, j]
         elif nums[m] > target:
@@ -24,7 +24,7 @@ def binary_search_insertion(nums: list[int], target: int) -> int:
     """Binary search for insertion point (with duplicate elements)"""
     i, j = 0, len(nums) - 1  # Initialize double closed interval [0, n-1]
     while i <= j:
-        m = (i + j) // 2  # Calculate midpoint index m
+        m = i + (j - i) // 2  # Calculate midpoint index m
         if nums[m] < target:
             i = m + 1  # Target is in interval [m+1, j]
         elif nums[m] > target:

en/codes/python/chapter_sorting/merge_sort.py

@@ -41,7 +41,7 @@ def merge_sort(nums: list[int], left: int, right: int):
     if left >= right:
         return  # Terminate recursion when subarray length is 1
     # Partition stage
-    mid = (left + right) // 2  # Calculate midpoint
+    mid = left + (right - left) // 2  # Calculate midpoint
     merge_sort(nums, left, mid)  # Recursively process the left subarray
     merge_sort(nums, mid + 1, right)  # Recursively process the right subarray
     # Merge stage