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 TypeScript 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.ts 
function mergeSort(values: number[]): number[] {
    if (values.length <= 1) {
        return values;
    }
    const mid: number = Math.floor(values.length / 2);
    const left: number[] = mergeSort(values.slice(0, mid));
    const right: number[] = mergeSort(values.slice(mid));
    const merged: number[] = [];
    let i: number = 0;
    let j: number = 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: number[] = [5, 1, 4, 2, 8];
console.log(JSON.stringify(mergeSort(arr)));

Complexity

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

Implementation notes

  • TypeScript declares mergeSort(values: number[]): number[], so each call accepts and returns arrays of number values.
  • Base cases return the existing short array reference. Larger calls compute const mid: number = Math.floor(values.length / 2) and allocate copied halves with values.slice(0, mid) and values.slice(mid).
  • Merge state is held in const merged: number[] = [] plus typed cursor bindings let i: number and let j: number.
  • The comparison left[i] <= right[j] uses numeric Number values through TypeScript's number type; taking from left on ties preserves equal-value order.
  • Remaining tails are copied with left.slice(i) and right.slice(j), then joined into the result with concat, so this implementation returns a new sorted array instead of mutating arr.
  • The replay splits [5, 1, 4, 2, 8] into [5, 1] and [4, 2, 8], sorts them to [1, 5] and [2, 4, 8], then prints [1,2,4,5,8] via JSON.stringify(mergeSort(arr)); visible allocation is the input array, copied slice arrays, merge arrays, concat result arrays, and JSON output string.