merge sort expressed mathematically code example

Example: merge sort

// @see https://www.youtube.com/watch?v=es2T6KY45cA&vl=en
// @see https://www.cs.usfca.edu/~galles/visualization/ComparisonSort.html

function merge(list, start, midpoint, end) {
    const left = list.slice(start, midpoint);
    const right = list.slice(midpoint, end);
    for (let topLeft = 0, topRight = 0, i = start; i < end; i += 1) {
        if (topLeft >= left.length) {
            list[i] = right[topRight++];
        } else if (topRight >= right.length) {
            list[i] = left[topLeft++];
        } else if (left[topLeft] < right[topRight]) {
            list[i] = left[topLeft++];
        } else {
            list[i] = right[topRight++];
        }
    }
}

function mergesort(list, start = 0, end = undefined) {
    if (end === undefined) {
        end = list.length;
    }
    if (end - start > 1) {
        const midpoint = ((end + start) / 2) >> 0;
        mergesort(list, start, midpoint);
        mergesort(list, midpoint, end);
        merge(list, start, midpoint, end);
    }
    return list;
}

mergesort([4, 7, 2, 6, 4, 1, 8, 3]);