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