build

en/docs/chapter_searching/binary_search.md

@@ -63,7 +63,7 @@ The code is as follows:
         # 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:
@@ -202,7 +202,7 @@ We can implement a binary search algorithm with the same functionality based on
         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/docs/chapter_searching/binary_search_insertion.md

@@ -35,7 +35,7 @@ Therefore, at the end of the binary, it is certain that: $i$ points to the first
         """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:
@@ -217,7 +217,7 @@ Even so, we can still keep the conditions expanded, as their logic is clearer an
         """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: