Heap sort in javascript

heapsort.js

var a = [ 9, 10, 2, 1, 5, 4, 3, 6, 8, 7, 13 ];

function swap(a, i, j) {
    var tmp = a[i];
    a[i] = a[j];
    a[j] = tmp;
}

function max_heapify(a, i, length) {
    while (true) {
        var left = i*2 + 1;
        var right = i*2 + 2;
        var largest = i;

        if (left < length && a[left] > a[largest]) {
            largest = left;
        }

        if (right < length && a[right] > a[largest]) {
            largest = right;
        }

        if (i == largest) {
            break;
        }

        swap(a, i, largest);
        i = largest;
    }
}

function heapify(a, length) {
    for (var i = Math.floor(length/2); i >= 0; i--) {
        max_heapify(a, i, length);
    }
}

function heapsort(a) {
    heapify(a, a.length);

    for (var i = a.length - 1; i > 0; i--) {
        swap(a, i, 0);

        max_heapify(a, 0, i-1);
    }
}

heapsort(a);

https://gist.github.com/gyoshev/4038839#file-heapsort-js-L44

-        max_heapify(a, 0, i-1);
+        max_heapify(a, 0, i);

I believe line # 33 should be for (var i = Math.floor(length/2 - 1); i >= 0; i--) { to avoid one excessive child check.

This doesn't work.

To be specific my array ends up being

[ 1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 13 ]

and when debugging it i'm realizing the largest isn't always correct

left: 5, right: 6, largest: 5

I too see the outcome that @Dellybro sees. @SuperPaintman's fix solves the test case included, I'm not sure it's enough to fix the algo though.

a = [5, 4, 3, 2, 1];
heapsort(a);
console.log(a);// 1, 3, 2, 4, 5