algorithm Longest Common Subsequence


Example

If we are given with the two strings we have to find the longest common sub-sequence present in both of them.

Example

LCS for input Sequences “ABCDGH” and “AEDFHR” is “ADH” of length 3.

LCS for input Sequences “AGGTAB” and “GXTXAYB” is “GTAB” of length 4.

Implementation in Java

public class LCS {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        String str1 = "AGGTAB";
        String str2 = "GXTXAYB";
        LCS obj = new LCS();
        System.out.println(obj.lcs(str1, str2, str1.length(), str2.length()));
        System.out.println(obj.lcs2(str1, str2));
    }
    
    //Recursive function
    public int lcs(String str1, String str2, int m, int n){
        if(m==0 || n==0)
            return 0;
        if(str1.charAt(m-1) == str2.charAt(n-1))
            return 1 + lcs(str1, str2, m-1, n-1);
        else
            return Math.max(lcs(str1, str2, m-1, n), lcs(str1, str2, m, n-1));
    }
    
    //Iterative function
    public int lcs2(String str1, String str2){
        int lcs[][] = new int[str1.length()+1][str2.length()+1];
        
        for(int i=0;i<=str1.length();i++){
            for(int j=0;j<=str2.length();j++){
                if(i==0 || j== 0){
                    lcs[i][j] = 0;
                }
                else if(str1.charAt(i-1) == str2.charAt(j-1)){
                    lcs[i][j] = 1 + lcs[i-1][j-1]; 
                }else{
                    lcs[i][j] = Math.max(lcs[i-1][j], lcs[i][j-1]);
                }
            }
        }
        
        return lcs[str1.length()][str2.length()];
    }

}

Output

4