an implementation of the Longest Common Subsequence Algorithm (LCS) - Java Algorithm

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Description

an implementation of the Longest Common Subsequence Algorithm (LCS)

Demo Code

import java.util.ArrayList;
//This is an implementation of the Longest Common Subsequence Algorithm (LCS)
//Runtime: O(n*m) where n is the length of string 1 and m is length of string 2.

public class LongestCommonSubsequence {
    /**/*  w w  w . ja v  a 2s. c o  m*/
     * 
     * @param a 
     * @param b
     * @return the longest common subequence between a and b. Example: a= "abcdaf", b="acbcf" --> result = "abcf"
     */
    public static ArrayList<Character> lcs(String a, String b) {
        int[][] lcs = new int[a.length() + 1][b.length() + 1];//The first column and row represent the longest common sequence when we have 0 characters    
        for (int i = 1; i < lcs.length; i++) {
            for (int j = 1; j < lcs[0].length; j++) {
                if (a.charAt(i - 1) == b.charAt(j - 1)) {
                    lcs[i][j] = lcs[i - 1][j - 1] + 1;//if we have a common char then the longest subsequence is the longuest subsequence of the two strings without this character + 1 
                } else {
                    lcs[i][j] = Math.max(lcs[i - 1][j], lcs[i][j - 1]); //the longest subsequence is the maximum between the longest subsequence of each of the two strings without the last character
                }
            }
        }
        return collect(b, lcs, a.length(), b.length());
    }

    private static ArrayList<Character> collect(String b, int[][] lcs,
            int i, int j) {
        if (lcs[i][j] == 0) {//we reached the end
            return new ArrayList<Character>();
        } else if (lcs[i][j] == lcs[i - 1][j]) {
            return collect(b, lcs, i - 1, j);
        } else if (lcs[i][j] == lcs[i][j - 1]) {
            return collect(b, lcs, i, j - 1);
        } else {//if the number came from the upper corner, it means that this character was selected in the optimal solution
            ArrayList<Character> temp = collect(b, lcs, i - 1, j - 1);
            temp.add(b.charAt(j - 1));
            return temp;
        }
    }

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        System.out.println(LongestCommonSubsequence.lcs("abcdaf", "acbcf"));

    }

}

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