Retranslate the complete English edition from Simplified Chinese (#2010)

* Retranslate the complete English edition from Simplified Chinese

* Polish three English explanations after reader-focused review

en/codes/python/chapter_sorting/bubble_sort.py

@@ -8,9 +8,9 @@ Author: timi (xisunyy@163.com)
 def bubble_sort(nums: list[int]):
     """Bubble sort"""
     n = len(nums)
-    # Outer loop: unsorted interval is [0, i]
+    # Outer loop: the unsorted range is [0, i]
     for i in range(n - 1, 0, -1):
-        # Inner loop: swap the largest element in the unsorted interval [0, i] to the rightmost end of the interval
+        # Inner loop: move the largest element in the unsorted range [0, i] to its right end through swaps
         for j in range(i):
             if nums[j] > nums[j + 1]:
                 # Swap nums[j] and nums[j + 1]
@@ -20,25 +20,25 @@ def bubble_sort(nums: list[int]):
 def bubble_sort_with_flag(nums: list[int]):
     """Bubble sort (flag optimization)"""
     n = len(nums)
-    # Outer loop: unsorted interval is [0, i]
+    # Outer loop: the unsorted range is [0, i]
     for i in range(n - 1, 0, -1):
-        flag = False  # Initialize flag
-        # Inner loop: swap the largest element in the unsorted interval [0, i] to the rightmost end of the interval
+        flag = False  # Initialize the flag
+        # Inner loop: move the largest element in the unsorted range [0, i] to its right end through swaps
         for j in range(i):
             if nums[j] > nums[j + 1]:
                 # Swap nums[j] and nums[j + 1]
                 nums[j], nums[j + 1] = nums[j + 1], nums[j]
-                flag = True  # Record element swap
+                flag = True  # Record that a swap occurred
         if not flag:
-            break  # No elements were swapped in this round of "bubbling", exit directly
+            break  # Exit immediately if this pass made no swaps
 
 
-"""Driver Code"""
+"""Driver code"""
 if __name__ == "__main__":
     nums = [4, 1, 3, 1, 5, 2]
     bubble_sort(nums)
-    print("After bubble sort, nums =", nums)
+    print("After bubble sort, array =", nums)
 
     nums1 = [4, 1, 3, 1, 5, 2]
     bubble_sort_with_flag(nums1)
-    print("After bubble sort, nums =", nums1)
+    print("After bubble sort, array =", nums1)

en/codes/python/chapter_sorting/bucket_sort.py

@@ -7,20 +7,20 @@ Author: krahets (krahets@163.com)
 
 def bucket_sort(nums: list[float]):
     """Bucket sort"""
-    # Initialize k = n/2 buckets, expected to allocate 2 elements per bucket
+    # Initialize k = n/2 buckets, expecting 2 elements per bucket
     k = len(nums) // 2
     buckets = [[] for _ in range(k)]
-    # 1. Distribute array elements into various buckets
+    # 1. Distribute the array elements among the buckets
     for num in nums:
-        # Input data range is [0, 1), use num * k to map to index range [0, k-1]
+        # The input range is [0, 1); use num * k to map each value to an index in [0, k-1]
         i = int(num * k)
         # Add num to bucket i
         buckets[i].append(num)
     # 2. Sort each bucket
     for bucket in buckets:
-        # Use built-in sorting function, can also replace with other sorting algorithms
+        # Use the built-in sorting function, or replace it with another sorting algorithm
         bucket.sort()
-    # 3. Traverse buckets to merge results
+    # 3. Traverse the buckets to combine the results
     i = 0
     for bucket in buckets:
         for num in bucket:
@@ -29,7 +29,7 @@ def bucket_sort(nums: list[float]):
 
 
 if __name__ == "__main__":
-    # Assume input data is floating point, interval [0, 1)
+    # Assume the input consists of floating-point numbers in [0, 1)
     nums = [0.49, 0.96, 0.82, 0.09, 0.57, 0.43, 0.91, 0.75, 0.15, 0.37]
     bucket_sort(nums)
     print("After bucket sort, nums =", nums)

en/codes/python/chapter_sorting/counting_sort.py

@@ -7,17 +7,15 @@ Author: krahets (krahets@163.com)
 
 def counting_sort_naive(nums: list[int]):
     """Counting sort"""
-    # Simple implementation, cannot be used for sorting objects
-    # 1. Count the maximum element m in the array
-    m = 0
-    for num in nums:
-        m = max(m, num)
-    # 2. Count the occurrence of each number
-    # counter[num] represents the occurrence of num
+    # Simple implementation; cannot be used to sort objects
+    # 1. Find the maximum array element m
+    m = max(nums)
+    # 2. Count the occurrences of each number
+    # counter[num] is the number of occurrences of num
     counter = [0] * (m + 1)
     for num in nums:
         counter[num] += 1
-    # 3. Traverse counter, filling each element back into the original array nums
+    # 3. Traverse counter and fill the original array nums with the elements
     i = 0
     for num in range(m + 1):
         for _ in range(counter[num]):
@@ -27,37 +25,37 @@ def counting_sort_naive(nums: list[int]):
 
 def counting_sort(nums: list[int]):
     """Counting sort"""
-    # Complete implementation, can sort objects and is a stable sort
-    # 1. Count the maximum element m in the array
+    # Full implementation; stable and adaptable to sorting objects
+    # 1. Find the maximum array element m
     m = max(nums)
-    # 2. Count the occurrence of each number
-    # counter[num] represents the occurrence of num
+    # 2. Count the occurrences of each number
+    # counter[num] is the number of occurrences of num
     counter = [0] * (m + 1)
     for num in nums:
         counter[num] += 1
-    # 3. Calculate the prefix sum of counter, converting "occurrence count" to "tail index"
-    # counter[num]-1 is the last index where num appears in res
+    # 3. Compute prefix sums of counter to convert occurrence counts into end positions
+    # That is, counter[num]-1 is the index of the last occurrence of num in res
     for i in range(m):
         counter[i + 1] += counter[i]
-    # 4. Traverse nums in reverse order, placing each element into the result array res
-    # Initialize the array res to record results
+    # 4. Traverse nums in reverse and place each element in the result array res
+    # Initialize array res to store the result
     n = len(nums)
     res = [0] * n
     for i in range(n - 1, -1, -1):
         num = nums[i]
         res[counter[num] - 1] = num  # Place num at the corresponding index
-        counter[num] -= 1  # Decrement the prefix sum by 1, getting the next index to place num
-    # Use result array res to overwrite the original array nums
+        counter[num] -= 1  # Decrement the prefix sum by 1 to determine where to place the next occurrence of num
+    # Overwrite the original array nums with the result array res
     for i in range(n):
         nums[i] = res[i]
 
 
-"""Driver Code"""
+"""Driver code"""
 if __name__ == "__main__":
     nums = [1, 0, 1, 2, 0, 4, 0, 2, 2, 4]
 
     counting_sort_naive(nums)
-    print(f"After counting sort (unable to sort objects), nums = {nums}")
+    print(f"After counting sort (without support for objects), nums = {nums}")
 
     nums1 = [1, 0, 1, 2, 0, 4, 0, 2, 2, 4]
     counting_sort(nums1)

en/codes/python/chapter_sorting/heap_sort.py

@@ -6,9 +6,9 @@ Author: krahets (krahets@163.com)
 
 
 def sift_down(nums: list[int], n: int, i: int):
-    """Heap length is n, start heapifying node i, from top to bottom"""
+    """Sift down from node i in a heap of size n"""
     while True:
-        # Determine the largest node among i, l, r, noted as ma
+        # Find the node with the largest value among i, l, and r, and store its index in ma
         l = 2 * i + 1
         r = 2 * i + 2
         ma = i
@@ -16,29 +16,29 @@ def sift_down(nums: list[int], n: int, i: int):
             ma = l
         if r < n and nums[r] > nums[ma]:
             ma = r
-        # If node i is the largest or indices l, r are out of bounds, no further heapification needed, break
+        # Stop if node i is largest or both child indices l and r are out of bounds
         if ma == i:
             break
-        # Swap two nodes
+        # Swap the two nodes
         nums[i], nums[ma] = nums[ma], nums[i]
-        # Loop downwards heapification
+        # Continue sifting down
         i = ma
 
 
 def heap_sort(nums: list[int]):
     """Heap sort"""
-    # Build heap operation: heapify all nodes except leaves
+    # Build the heap by sifting down from every non-leaf node
     for i in range(len(nums) // 2 - 1, -1, -1):
         sift_down(nums, len(nums), i)
-    # Extract the largest element from the heap and repeat for n-1 rounds
+    # Extract the largest element from the heap, repeating for n-1 rounds
     for i in range(len(nums) - 1, 0, -1):
-        # Swap the root node with the rightmost leaf node (swap the first element with the last element)
+        # Swap the root with the rightmost leaf on the last level (the first and last elements of the current heap)
         nums[0], nums[i] = nums[i], nums[0]
-        # Start heapifying the root node, from top to bottom
+        # Sift down starting at the root
         sift_down(nums, i, 0)
 
 
-"""Driver Code"""
+"""Driver code"""
 if __name__ == "__main__":
     nums = [4, 1, 3, 1, 5, 2]
     heap_sort(nums)

en/codes/python/chapter_sorting/insertion_sort.py

@@ -7,18 +7,18 @@ Author: timi (xisunyy@163.com)
 
 def insertion_sort(nums: list[int]):
     """Insertion sort"""
-    # Outer loop: sorted interval is [0, i-1]
+    # Outer loop: the sorted range is [0, i-1]
     for i in range(1, len(nums)):
         base = nums[i]
         j = i - 1
-        # Inner loop: insert base into the correct position within the sorted interval [0, i-1]
+        # Inner loop: insert base at the correct position in the sorted range [0, i-1]
         while j >= 0 and nums[j] > base:
-            nums[j + 1] = nums[j]  # Move nums[j] to the right by one position
+            nums[j + 1] = nums[j]  # Shift nums[j] one position to the right
             j -= 1
-        nums[j + 1] = base  # Assign base to the correct position
+        nums[j + 1] = base  # Place base at the correct position
 
 
-"""Driver Code"""
+"""Driver code"""
 if __name__ == "__main__":
     nums = [4, 1, 3, 1, 5, 2]
     insertion_sort(nums)

en/codes/python/chapter_sorting/merge_sort.py

@@ -6,13 +6,13 @@ Author: timi (xisunyy@163.com), krahets (krahets@163.com)
 
 
 def merge(nums: list[int], left: int, mid: int, right: int):
-    """Merge left subarray and right subarray"""
-    # Left subarray interval is [left, mid], right subarray interval is [mid+1, right]
-    # Create a temporary array tmp to store the merged results
+    """Merge the left and right subarrays"""
+    # The left subarray spans [left, mid], and the right subarray spans [mid+1, right]
+    # Create a temporary array tmp to store the merged result
     tmp = [0] * (right - left + 1)
-    # Initialize the start indices of the left and right subarrays
+    # Initialize the starting indices of the left and right subarrays
     i, j, k = left, mid + 1, 0
-    # While both subarrays still have elements, compare and copy the smaller element into the temporary array
+    # While both subarrays have elements remaining, compare them and copy the smaller element into the temporary array
     while i <= mid and j <= right:
         if nums[i] <= nums[j]:
             tmp[k] = nums[i]
@@ -30,25 +30,25 @@ def merge(nums: list[int], left: int, mid: int, right: int):
         tmp[k] = nums[j]
         j += 1
         k += 1
-    # Copy the elements from the temporary array tmp back to the original array nums at the corresponding interval
+    # Copy the elements of temporary array tmp back into the corresponding range of the original array nums
     for k in range(0, len(tmp)):
         nums[left + k] = tmp[k]
 
 
 def merge_sort(nums: list[int], left: int, right: int):
     """Merge sort"""
-    # Termination condition
+    # Base case
     if left >= right:
-        return  # Terminate recursion when subarray length is 1
-    # Divide and conquer stage
-    mid = (left + right) // 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
+        return  # Stop recursing when the subarray has at most one element
+    # Divide phase
+    mid = (left + right) // 2 # Calculate the midpoint
+    merge_sort(nums, left, mid)  # Recurse on the left subarray
+    merge_sort(nums, mid + 1, right)  # Recurse on the right subarray
+    # Merge phase
     merge(nums, left, mid, right)
 
 
-"""Driver Code"""
+"""Driver code"""
 if __name__ == "__main__":
     nums = [7, 3, 2, 6, 0, 1, 5, 4]
     merge_sort(nums, 0, len(nums) - 1)

en/codes/python/chapter_sorting/quick_sort.py

@@ -9,28 +9,28 @@ class QuickSort:
     """Quick sort class"""
 
     def partition(self, nums: list[int], left: int, right: int) -> int:
-        """Sentinel partition"""
+        """Two-pointer partitioning"""
         # Use nums[left] as the pivot
         i, j = left, right
         while i < j:
             while i < j and nums[j] >= nums[left]:
-                j -= 1  # Search from right to left for the first element smaller than the pivot
+                j -= 1  # Scan from right to left for the first element smaller than the pivot
             while i < j and nums[i] <= nums[left]:
-                i += 1  # Search from left to right for the first element greater than the pivot
-            # Swap elements
+                i += 1  # Scan from left to right for the first element larger than the pivot
+            # Swap the elements
             nums[i], nums[j] = nums[j], nums[i]
-        # Swap the pivot to the boundary between the two subarrays
+        # Swap the pivot into the boundary position between the two subarrays
         nums[i], nums[left] = nums[left], nums[i]
-        return i  # Return the index of the pivot
+        return i  # Return the pivot index
 
     def quick_sort(self, nums: list[int], left: int, right: int):
         """Quick sort"""
-        # Terminate recursion when subarray length is 1
+        # Stop recursing when the subarray has at most one element
         if left >= right:
             return
-        # Sentinel partition
+        # Two-pointer partitioning
         pivot = self.partition(nums, left, right)
-        # Recursively process the left subarray and right subarray
+        # Recurse on the left and right subarrays
         self.quick_sort(nums, left, pivot - 1)
         self.quick_sort(nums, pivot + 1, right)
 
@@ -42,38 +42,38 @@ class QuickSortMedian:
         """Select the median of three candidate elements"""
         l, m, r = nums[left], nums[mid], nums[right]
         if (l <= m <= r) or (r <= m <= l):
-            return mid  # m is between l and r
+            return mid  # m lies between l and r
         if (m <= l <= r) or (r <= l <= m):
-            return left  # l is between m and r
+            return left  # l lies between m and r
         return right
 
     def partition(self, nums: list[int], left: int, right: int) -> int:
-        """Sentinel partition (median of three)"""
-        # Use nums[left] as the pivot
+        """Two-pointer partitioning (median of three)"""
+        # Select the median of the leftmost, middle, and rightmost elements as the pivot
         med = self.median_three(nums, left, (left + right) // 2, right)
-        # Swap the median to the array's leftmost position
+        # Swap the median into the leftmost position of the current subarray
         nums[left], nums[med] = nums[med], nums[left]
         # Use nums[left] as the pivot
         i, j = left, right
         while i < j:
             while i < j and nums[j] >= nums[left]:
-                j -= 1  # Search from right to left for the first element smaller than the pivot
+                j -= 1  # Scan from right to left for the first element smaller than the pivot
             while i < j and nums[i] <= nums[left]:
-                i += 1  # Search from left to right for the first element greater than the pivot
-            # Swap elements
+                i += 1  # Scan from left to right for the first element larger than the pivot
+            # Swap the elements
             nums[i], nums[j] = nums[j], nums[i]
-        # Swap the pivot to the boundary between the two subarrays
+        # Swap the pivot into the boundary position between the two subarrays
         nums[i], nums[left] = nums[left], nums[i]
-        return i  # Return the index of the pivot
+        return i  # Return the pivot index
 
     def quick_sort(self, nums: list[int], left: int, right: int):
         """Quick sort"""
-        # Terminate recursion when subarray length is 1
+        # Stop recursing when the subarray has at most one element
         if left >= right:
             return
-        # Sentinel partition
+        # Two-pointer partitioning
         pivot = self.partition(nums, left, right)
-        # Recursively process the left subarray and right subarray
+        # Recurse on the left and right subarrays
         self.quick_sort(nums, left, pivot - 1)
         self.quick_sort(nums, pivot + 1, right)
 
@@ -82,36 +82,36 @@ class QuickSortTailCall:
     """Quick sort class (recursion depth optimization)"""
 
     def partition(self, nums: list[int], left: int, right: int) -> int:
-        """Sentinel partition"""
+        """Two-pointer partitioning"""
         # Use nums[left] as the pivot
         i, j = left, right
         while i < j:
             while i < j and nums[j] >= nums[left]:
-                j -= 1  # Search from right to left for the first element smaller than the pivot
+                j -= 1  # Scan from right to left for the first element smaller than the pivot
             while i < j and nums[i] <= nums[left]:
-                i += 1  # Search from left to right for the first element greater than the pivot
-            # Swap elements
+                i += 1  # Scan from left to right for the first element larger than the pivot
+            # Swap the elements
             nums[i], nums[j] = nums[j], nums[i]
-        # Swap the pivot to the boundary between the two subarrays
+        # Swap the pivot into the boundary position between the two subarrays
         nums[i], nums[left] = nums[left], nums[i]
-        return i  # Return the index of the pivot
+        return i  # Return the pivot index
 
     def quick_sort(self, nums: list[int], left: int, right: int):
         """Quick sort (recursion depth optimization)"""
-        # Terminate when subarray length is 1
+        # Stop when the subarray has at most one element
         while left < right:
-            # Sentinel partition operation
+            # Perform two-pointer partitioning
             pivot = self.partition(nums, left, right)
-            # Perform quick sort on the shorter of the two subarrays
+            # Apply quick sort to the shorter of the two subarrays
             if pivot - left < right - pivot:
                 self.quick_sort(nums, left, pivot - 1)  # Recursively sort the left subarray
-                left = pivot + 1  # Remaining unsorted interval is [pivot + 1, right]
+                left = pivot + 1  # The remaining unsorted range is [pivot + 1, right]
             else:
                 self.quick_sort(nums, pivot + 1, right)  # Recursively sort the right subarray
-                right = pivot - 1  # Remaining unsorted interval is [left, pivot - 1]
+                right = pivot - 1  # The remaining unsorted range is [left, pivot - 1]
 
 
-"""Driver Code"""
+"""Driver code"""
 if __name__ == "__main__":
     # Quick sort
     nums = [2, 4, 1, 0, 3, 5]
@@ -121,9 +121,9 @@ if __name__ == "__main__":
     # Quick sort (median pivot optimization)
     nums1 = [2, 4, 1, 0, 3, 5]
     QuickSortMedian().quick_sort(nums1, 0, len(nums1) - 1)
-    print("After quick sort (median pivot optimization), nums =", nums1)
+    print("After quick sort (median pivot optimization), nums1 =", nums1)
 
     # Quick sort (recursion depth optimization)
     nums2 = [2, 4, 1, 0, 3, 5]
     QuickSortTailCall().quick_sort(nums2, 0, len(nums2) - 1)
-    print("After quick sort (recursion depth optimization), nums =", nums2)
+    print("After quick sort (recursion depth optimization), nums2 =", nums2)

en/codes/python/chapter_sorting/radix_sort.py

@@ -6,51 +6,51 @@ Author: krahets (krahets@163.com)
 
 
 def digit(num: int, exp: int) -> int:
-    """Get the k-th digit of element num, where exp = 10^(k-1)"""
-    # Passing exp instead of k can avoid repeated expensive exponentiation here
+    """Get the k-th digit of num, where exp = 10^(k-1)"""
+    # Passing exp instead of k avoids repeatedly performing expensive exponentiation here
     return (num // exp) % 10
 
 
 def counting_sort_digit(nums: list[int], exp: int):
-    """Counting sort (based on nums k-th digit)"""
-    # Decimal digit range is 0~9, therefore need a bucket array of length 10
+    """Counting sort (sort nums by the k-th digit)"""
+    # Decimal digits range from 0 to 9, so the bucket array needs length 10
     counter = [0] * 10
     n = len(nums)
-    # Count the occurrence of digits 0~9
+    # Count the occurrences of each digit from 0 to 9
     for i in range(n):
-        d = digit(nums[i], exp)  # Get the k-th digit of nums[i], noted as d
-        counter[d] += 1  # Count the occurrence of digit d
-    # Calculate prefix sum, converting "occurrence count" into "array index"
+        d = digit(nums[i], exp)  # Get the k-th digit of nums[i] and store it in d
+        counter[d] += 1  # Count the occurrences of digit d
+    # Compute prefix sums to convert occurrence counts into array positions
     for i in range(1, 10):
         counter[i] += counter[i - 1]
-    # Traverse in reverse, based on bucket statistics, place each element into res
+    # Traverse in reverse and place each element into res according to the bucket counts
     res = [0] * n
     for i in range(n - 1, -1, -1):
         d = digit(nums[i], exp)
-        j = counter[d] - 1  # Get the index j for d in the array
+        j = counter[d] - 1  # Get the destination index j for digit d in the array
         res[j] = nums[i]  # Place the current element at index j
-        counter[d] -= 1  # Decrease the count of d by 1
-    # Use result to overwrite the original array nums
+        counter[d] -= 1  # Decrease the count for d by 1
+    # Overwrite the original array nums with the result
     for i in range(n):
         nums[i] = res[i]
 
 
 def radix_sort(nums: list[int]):
     """Radix sort"""
-    # Get the maximum element of the array, used to determine the maximum number of digits
+    # Get the largest array element to determine the maximum number of digits
     m = max(nums)
-    # Traverse from the lowest to the highest digit
+    # Process digits from least significant to most significant
     exp = 1
     while exp <= m:
-        # Perform counting sort on the k-th digit of array elements
+        # Apply counting sort to the k-th digit of the array elements
         # k = 1 -> exp = 1
         # k = 2 -> exp = 10
-        # i.e., exp = 10^(k-1)
+        # That is, exp = 10^(k-1)
         counting_sort_digit(nums, exp)
         exp *= 10
 
 
-"""Driver Code"""
+"""Driver code"""
 if __name__ == "__main__":
     # Radix sort
     nums = [

en/codes/python/chapter_sorting/selection_sort.py

@@ -8,18 +8,18 @@ Author: krahets (krahets@163.com)
 def selection_sort(nums: list[int]):
     """Selection sort"""
     n = len(nums)
-    # Outer loop: unsorted interval is [i, n-1]
+    # Outer loop: the unsorted range is [i, n-1]
     for i in range(n - 1):
-        # Inner loop: find the smallest element within the unsorted interval
+        # Inner loop: find the smallest element in the unsorted range
         k = i
         for j in range(i + 1, n):
             if nums[j] < nums[k]:
                 k = j  # Record the index of the smallest element
-        # Swap the smallest element with the first element of the unsorted interval
+        # Swap the smallest element with the first element of the unsorted range
         nums[i], nums[k] = nums[k], nums[i]
 
 
-"""Driver Code"""
+"""Driver code"""
 if __name__ == "__main__":
     nums = [4, 1, 3, 1, 5, 2]
     selection_sort(nums)