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/javascript/chapter_sorting/bubble_sort.js

@@ -6,9 +6,9 @@
 
 /* Bubble sort */
 function bubbleSort(nums) {
-    // Outer loop: unsorted range is [0, i]
+    // Outer loop: the unsorted range is [0, i]
     for (let i = nums.length - 1; i > 0; i--) {
-        // Inner loop: swap the largest element in the unsorted range [0, i] to the rightmost end of that range
+        // Inner loop: move the largest element in the unsorted range [0, i] to its right end through swaps
         for (let j = 0; j < i; j++) {
             if (nums[j] > nums[j + 1]) {
                 // Swap nums[j] and nums[j + 1]
@@ -20,30 +20,30 @@ function bubbleSort(nums) {
     }
 }
 
-/* Bubble sort (flag optimization) */
+/* Bubble sort (flag optimization)*/
 function bubbleSortWithFlag(nums) {
-    // Outer loop: unsorted range is [0, i]
+    // Outer loop: the unsorted range is [0, i]
     for (let i = nums.length - 1; i > 0; i--) {
-        let flag = false; // Initialize flag
-        // Inner loop: swap the largest element in the unsorted range [0, i] to the rightmost end of that range
+        let flag = false; // Initialize the flag
+        // Inner loop: move the largest element in the unsorted range [0, i] to its right end through swaps
         for (let j = 0; j < i; j++) {
             if (nums[j] > nums[j + 1]) {
                 // Swap nums[j] and nums[j + 1]
                 let tmp = nums[j];
                 nums[j] = nums[j + 1];
                 nums[j + 1] = tmp;
-                flag = true; // Record element swap
+                flag = true; // Record that a swap occurred
             }
         }
-        if (!flag) break; // No elements were swapped in this round of "bubbling", exit directly
+        if (!flag) break; // Exit immediately if this pass made no swaps
     }
 }
 
-/* Driver Code */
+/* Driver code */
 const nums = [4, 1, 3, 1, 5, 2];
 bubbleSort(nums);
-console.log('After bubble sort, nums =', nums);
+console.log('After bubble sort, array =', nums);
 
 const nums1 = [4, 1, 3, 1, 5, 2];
 bubbleSortWithFlag(nums1);
-console.log('After bubble sort, nums =', nums1);
+console.log('After bubble sort, array =', nums1);

en/codes/javascript/chapter_sorting/bucket_sort.js

@@ -6,25 +6,25 @@
 
 /* Bucket sort */
 function bucketSort(nums) {
-    // Initialize k = n/2 buckets, expected to allocate 2 elements per bucket
+    // Initialize ceil(n/2) buckets, aiming for about 2 elements per bucket
     const k = nums.length / 2;
     const buckets = [];
     for (let i = 0; i < k; i++) {
         buckets.push([]);
     }
-    // 1. Distribute array elements into various buckets
+    // 1. Distribute the array elements among the buckets
     for (const num of nums) {
-        // Input data range is [0, 1), use num * k to map to index range [0, k-1]
+        // The input range is [0, 1); floor(num * k) maps values to indices from 0 to ceil(k)-1
         const i = Math.floor(num * k);
         // Add num to bucket i
         buckets[i].push(num);
     }
     // 2. Sort each bucket
     for (const bucket of 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((a, b) => a - b);
     }
-    // 3. Traverse buckets to merge results
+    // 3. Traverse the buckets to combine the results
     let i = 0;
     for (const bucket of buckets) {
         for (const num of bucket) {
@@ -33,7 +33,7 @@ function bucketSort(nums) {
     }
 }
 
-/* Driver Code */
+/* Driver code */
 const nums = [0.49, 0.96, 0.82, 0.09, 0.57, 0.43, 0.91, 0.75, 0.15, 0.37];
 bucketSort(nums);
 console.log('After bucket sort, nums =', nums);

en/codes/javascript/chapter_sorting/counting_sort.js

@@ -5,17 +5,17 @@
  */
 
 /* Counting sort */
-// Simple implementation, cannot be used for sorting objects
+// Simple implementation; cannot be used to sort objects
 function countingSortNaive(nums) {
-    // 1. Count the maximum element m in the array
+    // 1. Find the maximum array element m
     let m = Math.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
     const counter = new Array(m + 1).fill(0);
     for (const num of nums) {
         counter[num]++;
     }
-    // 3. Traverse counter, filling each element back into the original array nums
+    // 3. Traverse counter and fill the original array nums with the elements
     let i = 0;
     for (let num = 0; num < m + 1; num++) {
         for (let j = 0; j < counter[num]; j++, i++) {
@@ -25,37 +25,37 @@ function countingSortNaive(nums) {
 }
 
 /* Counting sort */
-// Complete implementation, can sort objects and is a stable sort
+// Full implementation; stable and adaptable to sorting objects
 function countingSort(nums) {
-    // 1. Count the maximum element m in the array
+    // 1. Find the maximum array element m
     let m = Math.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
     const counter = new Array(m + 1).fill(0);
     for (const num of nums) {
         counter[num]++;
     }
-    // 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 (let i = 0; i < m; i++) {
         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
     const n = nums.length;
     const res = new Array(n);
     for (let i = n - 1; i >= 0; i--) {
         const num = nums[i];
         res[counter[num] - 1] = num; // Place num at the corresponding index
-        counter[num]--; // Decrement the prefix sum by 1, getting the next index to place num
+        counter[num]--; // Decrement the prefix sum by 1 to determine where to place the next occurrence of num
     }
-    // Use result array res to overwrite the original array nums
+    // Overwrite the original array nums with the result array res
     for (let i = 0; i < n; i++) {
         nums[i] = res[i];
     }
 }
 
-/* Driver Code */
+/* Driver code */
 const nums = [1, 0, 1, 2, 0, 4, 0, 2, 2, 4];
 countingSortNaive(nums);
 console.log('After counting sort (cannot sort objects), nums =', nums);

en/codes/javascript/chapter_sorting/heap_sort.js

@@ -4,10 +4,10 @@
  * Author: Justin (xiefahit@gmail.com)
  */
 
-/* Heap length is n, start heapifying node i, from top to bottom */
+/* Sift down from node i in a heap of size n */
 function siftDown(nums, n, i) {
     while (true) {
-        // If node i is largest or indices l, r are out of bounds, no need to continue heapify, break
+        // Find the node with the largest value among i, l, and r, and store its index in ma
         let l = 2 * i + 1;
         let r = 2 * i + 2;
         let ma = i;
@@ -17,33 +17,33 @@ function siftDown(nums, n, i) {
         if (r < n && nums[r] > nums[ma]) {
             ma = r;
         }
-        // Swap two nodes
+        // 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;
     }
 }
 
 /* Heap sort */
 function heapSort(nums) {
-    // Build heap operation: heapify all nodes except leaves
+    // Build the heap by sifting down from every non-leaf node
     for (let i = Math.floor(nums.length / 2) - 1; i >= 0; i--) {
         siftDown(nums, nums.length, 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 (let i = nums.length - 1; i > 0; i--) {
-        // Delete node
+        // 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
         siftDown(nums, i, 0);
     }
 }
 
-/* Driver Code */
+/* Driver code */
 const nums = [4, 1, 3, 1, 5, 2];
 heapSort(nums);
 console.log('After heap sort, nums =', nums);

en/codes/javascript/chapter_sorting/insertion_sort.js

@@ -6,20 +6,20 @@
 
 /* Insertion sort */
 function insertionSort(nums) {
-    // Outer loop: sorted interval is [0, i-1]
+    // Outer loop: the sorted range is [0, i-1]
     for (let i = 1; i < nums.length; i++) {
         let 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 && 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--;
         }
-        nums[j + 1] = base; // Assign base to the correct position
+        nums[j + 1] = base; // Place base at the correct position
     }
 }
 
-/* Driver Code */
+/* Driver code */
 const nums = [4, 1, 3, 1, 5, 2];
 insertionSort(nums);
 console.log('After insertion sort, nums =', nums);

en/codes/javascript/chapter_sorting/merge_sort.js

@@ -4,16 +4,16 @@
  * Author: IsChristina (christinaxia77@foxmail.com)
  */
 
-/* Merge left subarray and right subarray */
+/* Merge the left and right subarrays */
 function merge(nums, left, mid, right) {
-    // Left subarray interval is [left, mid], right subarray interval is [mid+1, right]
-    // Create a temporary array tmp to store the merged results
+    // The left subarray spans [left, mid], and the right subarray spans [mid+1, right]
+    // Create a temporary array tmp to store the merged result
     const tmp = new Array(right - left + 1);
-    // Initialize the start indices of the left and right subarrays
+    // Initialize the starting indices of the left and right subarrays
     let i = left,
         j = mid + 1,
         k = 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 && j <= right) {
         if (nums[i] <= nums[j]) {
             tmp[k++] = nums[i++];
@@ -28,7 +28,7 @@ function merge(nums, left, mid, right) {
     while (j <= right) {
         tmp[k++] = nums[j++];
     }
-    // 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 = 0; k < tmp.length; k++) {
         nums[left + k] = tmp[k];
     }
@@ -36,17 +36,17 @@ function merge(nums, left, mid, right) {
 
 /* Merge sort */
 function mergeSort(nums, left, right) {
-    // Termination condition
-    if (left >= right) return; // Terminate recursion when subarray length is 1
-    // Divide and conquer stage
-    let mid = Math.floor(left + (right - left) / 2); // Calculate midpoint
-    mergeSort(nums, left, mid); // Recursively process the left subarray
-    mergeSort(nums, mid + 1, right); // Recursively process the right subarray
-    // Merge stage
+    // Base case
+    if (left >= right) return; // Stop recursing when the subarray has at most one element
+    // Divide phase
+    let mid = Math.floor(left + (right - left) / 2); // Calculate the midpoint
+    mergeSort(nums, left, mid); // Recurse on the left subarray
+    mergeSort(nums, mid + 1, right); // Recurse on the right subarray
+    // Merge phase
     merge(nums, left, mid, right);
 }
 
-/* Driver Code */
+/* Driver code */
 const nums = [7, 3, 2, 6, 0, 1, 5, 4];
 mergeSort(nums, 0, nums.length - 1);
 console.log('After merge sort, nums =', nums);

en/codes/javascript/chapter_sorting/quick_sort.js

@@ -6,39 +6,39 @@
 
 /* Quick sort class */
 class QuickSort {
-    /* Swap elements */
+    /* Swap the elements */
     swap(nums, i, j) {
         let tmp = nums[i];
         nums[i] = nums[j];
         nums[j] = tmp;
     }
 
-    /* Sentinel partition */
+    /* Two-pointer partitioning */
     partition(nums, left, right) {
         // Use nums[left] as the pivot
         let i = left,
             j = right;
         while (i < j) {
             while (i < j && 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 && nums[i] <= nums[left]) {
-                i += 1; // Search from left to right for the first element greater than the pivot
+                i += 1; // Scan from left to right for the first element larger than the pivot
             }
-            // Swap elements
+            // Swap the elements
             this.swap(nums, i, j); // Swap these two elements
         }
-        this.swap(nums, i, left); // Swap the pivot to the boundary between the two subarrays
-        return i; // Return the index of the pivot
+        this.swap(nums, i, left); // Swap the pivot into the boundary position between the two subarrays
+        return i; // Return the pivot index
     }
 
     /* Quick sort */
     quickSort(nums, left, right) {
-        // 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
         const pivot = this.partition(nums, left, right);
-        // Recursively process the left subarray and right subarray
+        // Recurse on the left and right subarrays
         this.quickSort(nums, left, pivot - 1);
         this.quickSort(nums, pivot + 1, right);
     }
@@ -46,7 +46,7 @@ class QuickSort {
 
 /* Quick sort class (median pivot optimization) */
 class QuickSortMedian {
-    /* Swap elements */
+    /* Swap the elements */
     swap(nums, i, j) {
         let tmp = nums[i];
         nums[i] = nums[j];
@@ -58,14 +58,14 @@ class QuickSortMedian {
         let l = nums[left],
             m = nums[mid],
             r = nums[right];
-        // m is between l and r
+        // m lies between l and r
         if ((l <= m && m <= r) || (r <= m && m <= l)) return mid;
-        // l is between m and r
+        // l lies between m and r
         if ((m <= l && l <= r) || (r <= l && l <= m)) return left;
         return right;
     }
 
-    /* Sentinel partition (median of three) */
+    /* Two-pointer partitioning (median of three) */
     partition(nums, left, right) {
         // Select the median of three candidate elements
         let med = this.medianThree(
@@ -74,27 +74,27 @@ class QuickSortMedian {
             Math.floor((left + right) / 2),
             right
         );
-        // Swap the median to the array's leftmost position
+        // Swap the median into the leftmost position of the current subarray
         this.swap(nums, left, med);
         // Use nums[left] as the pivot
         let i = left,
             j = right;
         while (i < j) {
-            while (i < j && nums[j] >= nums[left]) j--; // Search from right to left for the first element smaller than the pivot
-            while (i < j && nums[i] <= nums[left]) i++; // Search from left to right for the first element greater than the pivot
+            while (i < j && nums[j] >= nums[left]) j--; // Scan from right to left for the first element smaller than the pivot
+            while (i < j && nums[i] <= nums[left]) i++; // Scan from left to right for the first element larger than the pivot
             this.swap(nums, i, j); // Swap these two elements
         }
-        this.swap(nums, i, left); // Swap the pivot to the boundary between the two subarrays
-        return i; // Return the index of the pivot
+        this.swap(nums, i, left); // Swap the pivot into the boundary position between the two subarrays
+        return i; // Return the pivot index
     }
 
     /* Quick sort */
     quickSort(nums, left, right) {
-        // 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
         const pivot = this.partition(nums, left, right);
-        // Recursively process the left subarray and right subarray
+        // Recurse on the left and right subarrays
         this.quickSort(nums, left, pivot - 1);
         this.quickSort(nums, pivot + 1, right);
     }
@@ -102,60 +102,60 @@ class QuickSortMedian {
 
 /* Quick sort class (recursion depth optimization) */
 class QuickSortTailCall {
-    /* Swap elements */
+    /* Swap the elements */
     swap(nums, i, j) {
         let tmp = nums[i];
         nums[i] = nums[j];
         nums[j] = tmp;
     }
 
-    /* Sentinel partition */
+    /* Two-pointer partitioning */
     partition(nums, left, right) {
         // Use nums[left] as the pivot
         let i = left,
             j = right;
         while (i < j) {
-            while (i < j && nums[j] >= nums[left]) j--; // Search from right to left for the first element smaller than the pivot
-            while (i < j && nums[i] <= nums[left]) i++; // Search from left to right for the first element greater than the pivot
+            while (i < j && nums[j] >= nums[left]) j--; // Scan from right to left for the first element smaller than the pivot
+            while (i < j && nums[i] <= nums[left]) i++; // Scan from left to right for the first element larger than the pivot
             this.swap(nums, i, j); // Swap these two elements
         }
-        this.swap(nums, i, left); // Swap the pivot to the boundary between the two subarrays
-        return i; // Return the index of the pivot
+        this.swap(nums, i, left); // Swap the pivot into the boundary position between the two subarrays
+        return i; // Return the pivot index
     }
 
     /* Quick sort (recursion depth optimization) */
     quickSort(nums, left, right) {
-        // 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
             let pivot = this.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) {
                 this.quickSort(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 {
                 this.quickSort(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 */
-/* Quick sort */
+/* Driver code */
+/* Quick sort  */
 const nums = [2, 4, 1, 0, 3, 5];
 const quickSort = new QuickSort();
 quickSort.quickSort(nums, 0, nums.length - 1);
 console.log('After quick sort, nums =', nums);
 
-/* Quick sort (recursion depth optimization) */
+/* Quick sort (median pivot optimization) */
 const nums1 = [2, 4, 1, 0, 3, 5];
 const quickSortMedian = new QuickSortMedian();
 quickSortMedian.quickSort(nums1, 0, nums1.length - 1);
-console.log('After quick sort (median pivot optimization), nums =', nums1);
+console.log('After quick sort (median pivot optimization), nums1 =', nums1);
 
 /* Quick sort (recursion depth optimization) */
 const nums2 = [2, 4, 1, 0, 3, 5];
 const quickSortTailCall = new QuickSortTailCall();
 quickSortTailCall.quickSort(nums2, 0, nums2.length - 1);
-console.log('After quick sort (recursion depth optimization), nums =', nums2);
+console.log('After quick sort (recursion depth optimization), nums2 =', nums2);

en/codes/javascript/chapter_sorting/radix_sort.js

@@ -4,35 +4,35 @@
  * Author: Justin (xiefahit@gmail.com)
  */
 
-/* Get the k-th digit of element num, where exp = 10^(k-1) */
+/* Get the k-th digit of num, where exp = 10^(k-1) */
 function digit(num, exp) {
-    // Passing exp instead of k can avoid repeated expensive exponentiation here
+    // Passing exp instead of k avoids repeatedly performing expensive exponentiation here
     return Math.floor(num / exp) % 10;
 }
 
-/* Counting sort (based on nums k-th digit) */
+/* Counting sort (sort nums by the k-th digit) */
 function countingSortDigit(nums, exp) {
-    // Decimal digit range is 0~9, therefore need a bucket array of length 10
+    // Decimal digits range from 0 to 9, so the bucket array needs length 10
     const counter = new Array(10).fill(0);
     const n = nums.length;
-    // Count the occurrence of digits 0~9
+    // Count the occurrences of each digit from 0 to 9
     for (let i = 0; i < n; i++) {
-        const d = digit(nums[i], exp); // Get the k-th digit of nums[i], noted as d
-        counter[d]++; // Count the occurrence of digit d
+        const d = digit(nums[i], exp); // Get the k-th digit of nums[i] and store it in d
+        counter[d]++; // Count the occurrences of digit d
     }
-    // Calculate prefix sum, converting "occurrence count" into "array index"
+    // Compute prefix sums to convert occurrence counts into array positions
     for (let i = 1; i < 10; i++) {
         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
     const res = new Array(n).fill(0);
     for (let i = n - 1; i >= 0; i--) {
         const d = digit(nums[i], exp);
-        const j = counter[d] - 1; // Get the index j for d in the array
+        const 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]--; // Decrease the count of d by 1
+        counter[d]--; // Decrease the count for d by 1
     }
-    // Use result to overwrite the original array nums
+    // Overwrite the original array nums with the result
     for (let i = 0; i < n; i++) {
         nums[i] = res[i];
     }
@@ -40,19 +40,19 @@ function countingSortDigit(nums, exp) {
 
 /* Radix sort */
 function radixSort(nums) {
-    // 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
     let m = Math.max(... nums);
-    // Traverse from the lowest to the highest digit
+    // Process digits from least significant to most significant
     for (let exp = 1; exp <= m; exp *= 10) {
-        // 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)
         countingSortDigit(nums, exp);
     }
 }
 
-/* Driver Code */
+/* Driver code */
 const nums = [
     10546151, 35663510, 42865989, 34862445, 81883077, 88906420, 72429244,
     30524779, 82060337, 63832996,

en/codes/javascript/chapter_sorting/selection_sort.js

@@ -7,21 +7,21 @@
 /* Selection sort */
 function selectionSort(nums) {
     let n = nums.length;
-    // Outer loop: unsorted interval is [i, n-1]
+    // Outer loop: the unsorted range is [i, n-1]
     for (let i = 0; i < n - 1; i++) {
-        // Inner loop: find the smallest element within the unsorted interval
+        // Inner loop: find the smallest element in the unsorted range
         let k = i;
         for (let j = i + 1; j < n; j++) {
             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 */
 const nums = [4, 1, 3, 1, 5, 2];
 selectionSort(nums);
 console.log('After selection sort, nums =', nums);