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136 lines
3.7 KiB
JavaScript
136 lines
3.7 KiB
JavaScript
(function (exports) {
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'use strict';
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exports.longestIncreasingSubsequence = (function () {
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/**
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* Find the index of the first largest element in array.
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* Complexity: O(N).
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*
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* @private
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* @param {Array} array The array in which the largest
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* element should be found.
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* @return {Number} index of the first largest element
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*/
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function max(array) {
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if (!array || !array.length) {
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return -1;
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}
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var maxIdx = 0;
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for (var i = 1; i < array.length; i += 1) {
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if (array[maxIdx].distance < array[i].distance) {
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maxIdx = i;
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}
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}
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return maxIdx;
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}
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/**
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* Default comparison method.
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* @private
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*/
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function asc(a, b) {
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return a - b;
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}
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/**
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* Creates directed graph from given array.
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* Each element's neighbours are the elements which can be
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* after the element in the resulting sequence.<br><br>
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* Complexity: O(N^2).
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* @private
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* @param {Array} array The input array.
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* @param {Function} cmp Comparator.
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* @return {Object} Graph represented with list of neighbours.
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*/
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function buildDag(array, cmp) {
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var result = [];
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for (var i = 0; i < array.length; i += 1) {
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result[i] = [];
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for (var j = i + 1; j < array.length; j += 1) {
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if (cmp(array[i], array[j]) < 0) {
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result[i].push(j);
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}
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}
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}
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return result;
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}
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/**
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* Finds the longest increasing sub-sequence for given node.<br><br>
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* Complexity: O(N^N).
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* @private
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* @param {Object} dag Graph represented with list of neighbours.
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* @param {number} node The current node.
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* @return {object} The longest increasing sub-sequence for given node.
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*/
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function find(dag, node) {
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node = node || 0;
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if (find.memo[node]) {
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return find.memo[node];
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}
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var neighbours = dag[node];
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var neighboursDistance = [];
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var maxDist;
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var maxNode;
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var distance;
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var result;
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if (!neighbours.length) {
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return { distance: 1, neighbour: undefined, node: node };
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}
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for (var i = 0; i < neighbours.length; i += 1) {
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neighboursDistance[i] = find(dag, neighbours[i]);
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}
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maxDist = max(neighboursDistance);
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maxNode = neighbours[maxDist];
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distance = 1 + neighboursDistance[maxDist].distance;
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find.memo[node] = result = {
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distance: distance,
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neighbour: neighboursDistance[maxDist],
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node: node
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};
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return result;
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}
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/**
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* Algorithm from dynamic programming. It finds the longest
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* sub-sequence of increasing numbers. It is not required
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* the numbers to be neighboring. For example for 1, 5, 2
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* sequence the longest sub-sequence is 1, 2.
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*
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* @example
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* var subsequence = require('path-to-algorithms/src/searching/'+
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* 'longest-increasing-subsequence').longestIncreasingSubsequence;
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* console.log(subsequence([1, 0, 4, 3, 5])); // 1, 4, 5
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*
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* @public
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* @module searching/longest-increasing-subsequence
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* @param {Array} array Input sequence.
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* @param {Function} cmp Comparator.
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* @return {Array} Longest increasing subsequence.
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*/
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return function (array, cmp) {
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cmp = cmp || asc;
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var results = [];
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var dag = buildDag(array, cmp);
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var maxPath;
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find.memo = [];
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for (var i = 0; i < array.length; i += 1) {
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results.push(find(dag, i));
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}
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maxPath = results[max(results)];
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results = [];
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while (maxPath) {
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results.push(array[maxPath.node]);
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maxPath = maxPath.neighbour;
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}
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return results;
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};
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})();
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})(typeof window === 'undefined' ? module.exports : window);
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