binary-search.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
 */
if (typeof define !== 'function') {
    var define = require('amdefine')(module, require);
}
define(function (require, exports, module) {

  exports.GREATEST_LOWER_BOUND = 1;
  exports.LEAST_UPPER_BOUND = 2;

  /**
   * Recursive implementation of binary search.
   *
   * @param aLow Indices here and lower do not contain the needle.
   * @param aHigh Indices here and higher do not contain the needle.
   * @param aNeedle The element being searched for.
   * @param aHaystack The non-empty array being searched.
   * @param aCompare Function which takes two elements and returns -1, 0, or 1.
   * @param aBias Either 'binarySearch.GREATEST_LOWER_BOUND' or
   *     'binarySearch.LEAST_UPPER_BOUND'. Specifies whether to return the
   *     closest element that is smaller than or greater than the one we are
   *     searching for, respectively, if the exact element cannot be found.
   */
  function recursiveSearch(aLow, aHigh, aNeedle, aHaystack, aCompare, aBias) {
    // This function terminates when one of the following is true:
    //
    //   1. We find the exact element we are looking for.
    //
    //   2. We did not find the exact element, but we can return the index of
    //      the next-closest element.
    //
    //   3. We did not find the exact element, and there is no next-closest
    //      element than the one we are searching for, so we return -1.
    var mid = Math.floor((aHigh - aLow) / 2) + aLow;
    var cmp = aCompare(aNeedle, aHaystack[mid], true);
    if (cmp === 0) {
      // Found the element we are looking for.
      return mid;
    }
    else if (cmp > 0) {
      // Our needle is greater than aHaystack[mid].
      if (aHigh - mid > 1) {
        // The element is in the upper half.
        return recursiveSearch(mid, aHigh, aNeedle, aHaystack, aCompare, aBias);
      }

      // The exact needle element was not found in this haystack. Determine if
      // we are in termination case (3) or (2) and return the appropriate thing.
      if (aBias == exports.LEAST_UPPER_BOUND) {
        return aHigh < aHaystack.length ? aHigh : -1;
      } else {
        return mid;
      }
    }
    else {
      // Our needle is less than aHaystack[mid].
      if (mid - aLow > 1) {
        // The element is in the lower half.
        return recursiveSearch(aLow, mid, aNeedle, aHaystack, aCompare, aBias);
      }

      // we are in termination case (3) or (2) and return the appropriate thing.
      if (aBias == exports.LEAST_UPPER_BOUND) {
        return mid;
      } else {
        return aLow < 0 ? -1 : aLow;
      }
    }
  }

  /**
   * This is an implementation of binary search which will always try and return
   * the index of the closest element if there is no exact hit. This is because
   * mappings between original and generated line/col pairs are single points,
   * and there is an implicit region between each of them, so a miss just means
   * that you aren't on the very start of a region.
   *
   * @param aNeedle The element you are looking for.
   * @param aHaystack The array that is being searched.
   * @param aCompare A function which takes the needle and an element in the
   *     array and returns -1, 0, or 1 depending on whether the needle is less
   *     than, equal to, or greater than the element, respectively.
   * @param aBias Either 'binarySearch.GREATEST_LOWER_BOUND' or
   *     'binarySearch.LEAST_UPPER_BOUND'. Specifies whether to return the
   *     closest element that is smaller than or greater than the one we are
   *     searching for, respectively, if the exact element cannot be found.
   *     Defaults to 'binarySearch.GREATEST_LOWER_BOUND'.
   */
  exports.search = function search(aNeedle, aHaystack, aCompare, aBias) {
    if (aHaystack.length === 0) {
      return -1;
    }

    var index = recursiveSearch(-1, aHaystack.length, aNeedle, aHaystack,
                                aCompare, aBias || exports.GREATEST_LOWER_BOUND);
    if (index < 0) {
      return -1;
    }

    // We have found either the exact element, or the next-closest element than
    // the one we are searching for. However, there may be more than one such
    // element. Make sure we always return the smallest of these.
    while (index - 1 >= 0) {
      if (aCompare(aHaystack[index], aHaystack[index - 1], true) !== 0) {
        break;
      }
      --index;
    }

    return index;
  };

});