Sorting

Merge Sort (Top-Down)

Split the array recursively, sort each half, then merge two sorted runs into one sorted result.

Algorithm

The checked-in replay follows the same small input and final output across all 21 DSA books, so this JavaScript DSA implementation can be compared directly with the other languages.

divide and conquer Each recursive call solves a smaller sorted subproblem.
merge step Two sorted halves are combined by repeatedly taking the smaller front item.

Visual walkthrough

The pinned input is [5, 1, 4, 2, 8]. The diagrams show the split into recursive halves, the sorted subarrays, and the final merge choices.

Step 1 - Split the input

The first midpoint splits [5, 1, 4, 2, 8] into left [5, 1] and right [4, 2, 8].

Top-down split used by merge_sort.[5,1,4,2,8]mid = 2[5,1]left[4,2,8]right

Step 2 - Sorted halves return

Recursive calls return [1, 5] and [2, 4, 8] before the final merge begins.

Returned subarrays before the final merge.sidebefore sortafter sortleft[5, 1][1, 5]right[4, 2, 8][2, 4, 8]

Step 3 - Merge by taking smaller fronts

Take 1 from left, then 2 and 4 from right, then the remaining 5 and 8.

Final merge produces [1, 2, 4, 5, 8].choiceleft frontright frontmergedtake 112[1]take 252[1, 2]take 454[1, 2, 4]extend58[1, 2, 4, 5, 8]

Basic Implementation

basic.js 
function mergeSort(values) {
    if (values.length <= 1) {
        return values;
    }
    const mid = Math.floor(values.length / 2);
    const left = mergeSort(values.slice(0, mid));
    const right = mergeSort(values.slice(mid));
    const merged = [];
    let i = 0;
    let j = 0;
    while (i < left.length && j < right.length) {
        if (left[i] <= right[j]) {
            merged.push(left[i++]);
        } else {
            merged.push(right[j++]);
        }
    }
    return merged.concat(left.slice(i)).concat(right.slice(j));
}

const arr = [5, 1, 4, 2, 8];
console.log(JSON.stringify(mergeSort(arr)));

Complexity

  • Time: O(n log n)
  • Space: O(n)
  • Stable: yes

Implementation notes

  • JavaScript stores the input as a const Array of Number values. mergeSort returns a sorted array instead of mutating the original arr; only length-0 or length-1 base cases return the existing array reference.
  • Each recursive split uses Math.floor(values.length / 2) plus values.slice(0, mid) and values.slice(mid), so the left and right halves are copied arrays before the recursive calls.
  • merge state is held in a fresh merged array and index variables i and j. The numeric comparison left[i] <= right[j] takes the left value on ties, preserving stability for equal Number values.
  • Values are appended with merged.push(...); remaining tails are appended via merged.concat(left.slice(i)).concat(right.slice(j)), which allocates the tail slices and concatenated result arrays.
  • The replay-visible states split [5, 1, 4, 2, 8] into [5, 1] and [4, 2, 8], sort them to [1, 5] and [2, 4, 8], then merge [1, 2, 4, 5, 8]. console.log(JSON.stringify(mergeSort(arr))) creates the compact output string [1,2,4,5,8]; temporary arrays and strings are handled by the JavaScript runtime GC.