81 lines
2.5 KiB
JavaScript
81 lines
2.5 KiB
JavaScript
|
(function (exports) {
|
||
|
|
'use strict';
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Accepts an array and range. Finds the maximum sum of elements
|
||
|
|
* around the middle of the range.
|
||
|
|
* @private
|
||
|
|
* @param {Array} array Input array.
|
||
|
|
* @param {Number} left Left interval of the range.
|
||
|
|
* @param {Number} middle Middle of the range.
|
||
|
|
* @param {Number} right Right side of the range.
|
||
|
|
* @return {Number} The maximum sum including the middle element.
|
||
|
|
*/
|
||
|
|
function crossSubarray(array, left, middle, right) {
|
||
|
|
var leftSum = -Infinity;
|
||
|
|
var rightSum = -Infinity;
|
||
|
|
var sum = 0;
|
||
|
|
var i;
|
||
|
|
|
||
|
|
for (i = middle; i >= left; i -= 1) {
|
||
|
|
if (sum + array[i] >= leftSum) {
|
||
|
|
leftSum = sum + array[i];
|
||
|
|
}
|
||
|
|
sum += array[i];
|
||
|
|
}
|
||
|
|
sum = 0;
|
||
|
|
for (i = middle + 1; i < right; i += 1) {
|
||
|
|
if (sum + array[i] >= rightSum) {
|
||
|
|
rightSum = sum + array[i];
|
||
|
|
}
|
||
|
|
sum += array[i];
|
||
|
|
}
|
||
|
|
return leftSum + rightSum;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* @private
|
||
|
|
* @param {Array} array Input array.
|
||
|
|
* @param {Number} left Left side of the range.
|
||
|
|
* @param {Number} right Right side of the range.
|
||
|
|
* @return {Number} Maximum sum of the elements of
|
||
|
|
* subarray whithin the given range.
|
||
|
|
*/
|
||
|
|
function maxSubarrayPartitioner(array, left, right) {
|
||
|
|
if (right - left <= 1) {
|
||
|
|
return array[left];
|
||
|
|
}
|
||
|
|
var middle = Math.floor((left + right) / 2);
|
||
|
|
var leftSum = maxSubarrayPartitioner(array, left, middle);
|
||
|
|
var rightSum = maxSubarrayPartitioner(array, middle, right);
|
||
|
|
var crossSum = crossSubarray(array, left, middle, right);
|
||
|
|
|
||
|
|
return Math.max(crossSum, leftSum, rightSum);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Finds the maximum sum of the elements of a subarray in a given array
|
||
|
|
* using the divide and conquer algorithm by Bentley, Jon (1984).
|
||
|
|
* For example, for the sequence of values -2, 1, -3, 4, -1, 2, 1, -5, 4
|
||
|
|
* the contiguous subarray with the largest sum is 4, -1, 2, 1, with sum 6.
|
||
|
|
* <br><br>
|
||
|
|
* Time complexity: O(N log N).
|
||
|
|
*
|
||
|
|
* @example
|
||
|
|
* var max = require('path-to-algorithms/src/searching/'+
|
||
|
|
* 'maximum-subarray-divide-and-conquer').maxSubarray;
|
||
|
|
* console.log(max([-2, 1, -3, 4, -1, 2, 1, -5, 4])); // 6
|
||
|
|
*
|
||
|
|
* @public
|
||
|
|
* @module searching/maximum-subarray-divide-and-conquer
|
||
|
|
* @param {Array} array Input array.
|
||
|
|
* @return {Number} Maximum sum of the elements of a subarray.
|
||
|
|
*/
|
||
|
|
function maxSubarray(array) {
|
||
|
|
return maxSubarrayPartitioner(array, 0, array.length);
|
||
|
|
}
|
||
|
|
|
||
|
|
exports.maxSubarray = maxSubarray;
|
||
|
|
|
||
|
|
})(typeof window === 'undefined' ? module.exports : window);
|