quick-sort.js

/* -*- Mode: js; js-indent-level: 2; -*- */
/*
 * Copyright 2011 Mozilla Foundation and contributors
 * Licensed under the New BSD license. See LICENSE or:
 * http://opensource.org/licenses/BSD-3-Clause
 */

// It turns out that some (most?) JavaScript engines don't self-host
// `Array.prototype.sort`. This makes sense because C++ will likely remain
// faster than JS when doing raw CPU-intensive sorting. However, when using a
// custom comparator function, calling back and forth between the VM's C++ and
// JIT'd JS is rather slow *and* loses JIT type information, resulting in
// worse generated code for the comparator function than would be optimal. In
// fact, when sorting with a comparator, these costs outweigh the benefits of
// sorting in C++. By using our own JS-implemented Quick Sort (below), we get
// a ~3500ms mean speed-up in `bench/bench.html`.

/**
 * Swap the elements indexed by `x` and `y` in the array `ary`.
 *
 * @param {Array} ary
 *        The array.
 * @param {Number} x
 *        The index of the first item.
 * @param {Number} y
 *        The index of the second item.
 */
function swap(ary, x, y) {
  var temp = ary[x];
  ary[x] = ary[y];
  ary[y] = temp;
}

/**
 * Returns a random integer within the range `low .. high` inclusive.
 *
 * @param {Number} low
 *        The lower bound on the range.
 * @param {Number} high
 *        The upper bound on the range.
 */
function randomIntInRange(low, high) {
  return Math.round(low + (Math.random() * (high - low)));
}

/**
 * The Quick Sort algorithm.
 *
 * @param {Array} ary
 *        An array to sort.
 * @param {function} comparator
 *        Function to use to compare two items.
 * @param {Number} p
 *        Start index of the array
 * @param {Number} r
 *        End index of the array
 */
function doQuickSort(ary, comparator, p, r) {
  // If our lower bound is less than our upper bound, we (1) partition the
  // array into two pieces and (2) recurse on each half. If it is not, this is
  // the empty array and our base case.

  if (p < r) {
    // (1) Partitioning.
    //
    // The partitioning chooses a pivot between `p` and `r` and moves all
    // elements that are less than or equal to the pivot to the before it, and
    // all the elements that are greater than it after it. The effect is that
    // once partition is done, the pivot is in the exact place it will be when
    // the array is put in sorted order, and it will not need to be moved
    // again. This runs in O(n) time.

    // Always choose a random pivot so that an input array which is reverse
    // sorted does not cause O(n^2) running time.
    var pivotIndex = randomIntInRange(p, r);
    var i = p - 1;

    swap(ary, pivotIndex, r);
    var pivot = ary[r];

    // Immediately after `j` is incremented in this loop, the following hold
    // true:
    //
    //   * Every element in `ary[p .. i]` is less than or equal to the pivot.
    //
    //   * Every element in `ary[i+1 .. j-1]` is greater than the pivot.
    for (var j = p; j < r; j++) {
      if (comparator(ary[j], pivot) <= 0) {
        i += 1;
        swap(ary, i, j);
      }
    }

    swap(ary, i + 1, j);
    var q = i + 1;

    // (2) Recurse on each half.

    doQuickSort(ary, comparator, p, q - 1);
    doQuickSort(ary, comparator, q + 1, r);
  }
}

/**
 * Sort the given array in-place with the given comparator function.
 *
 * @param {Array} ary
 *        An array to sort.
 * @param {function} comparator
 *        Function to use to compare two items.
 */
exports.quickSort = function (ary, comparator) {
  doQuickSort(ary, comparator, 0, ary.length - 1);
};