longest-increasing-subsequence.js

/**
 * Longest Increasing Subsequence
 * 
 * The Longest Increasing Subsequence (LIS) problem is to find the length
 * of the longest subsequence of a given sequence such that all elements
 * of the subsequence are sorted in increasing order. For example, the
 * length of LIS for {10, 22, 9, 33, 21, 50, 41, 60, 80} is 6 and LIS is
 * {10, 22, 33, 50, 60, 80}.
 * 
 * @author Yong Su <jean.timex@gmail.com>
 */

export default class Solution {
  /**
   * lis() returns the length of the longest increasing subsequence
   * in arr[] of size n
   * @param {number[]} arr
   * @returns {number}
   */
  lis(arr) {
    const n = arr.length;
    const res = [];
    let max = 0;

    // Compute optimized LIS values in bottom up manner
    for (let i = 0; i < n; i++) {
      res[i] = 1;

      for (let j = 0; j < i; j++) {
        if (arr[i] > arr[j] && res[i] < res[j] + 1) {
          res[i] = res[j] + 1;
        }
      }

      max = Math.max(max, res[i]);
    }

    return max;
  }
}