After my last DP problem, I thought I would try another one. In this problem we are asked to find the longest common subsequence of chars between two words. I tried to follow up on my previous example and build an adjacency matrix from the words length and storing the common subsequence at that point in both words. (i.e. DP[i][j] will point to the longest common subsequence between firstWord truncated at i char and secondWord truncated at j char.)

Hence I tried to code this idea in Java and to my surprise everything fell in place pretty quickly.

## Find the Longest Common Subsequence

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/* * @Author: Ajk Palikuqi * * Given two words find the longest common sequence of characters between them */ package iqLib.arrayLib; public class LongestCommonSubSequence { public static int findLongestCommonSubSequence(String firstWord, String secondWord) { int cols = firstWord.length(); int rows = secondWord.length(); int[][] DP = new int[cols][rows]; int longestSubSequence = 0; for (int i = 0; i < cols; ++i) { for (int j = 0; j < rows; ++j) { if (firstWord.charAt(i) == secondWord.charAt(j)) { if (i == 0 || j == 0) { DP[i][j] = 1; } else { DP[i][j] = DP[i-1][j-1] + 1; } if (DP[i][j] > longestSubSequence ) { longestSubSequence = DP[i][j]; } } else { DP[i][j] = 0; } } } return longestSubSequence; } } |

For more info you can check Longest Common Subsequence on wikipedia!

Hope you guys enjoyed it… and I’ll see you guys next time ;D

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