JavaAlgorithms/DynamicProgramming/ShortestCommonSupersequenceLength.java

package DynamicProgramming;

// Java program to find length of the shortest supersequence
class ShortestSuperSequence {
 
    // Function to find length of the
    // shortest supersequence of X and Y.
    static int shortestSuperSequence(String X, String Y)
    {
        int m = X.length();
        int n = Y.length();
 
        // find lcs
        int l = lcs(X, Y, m, n);
 
        // Result is sum of input string
        // lengths - length of lcs
        return (m + n - l);
    }
 
    // Returns length of LCS
    // for X[0..m - 1], Y[0..n - 1]
    static int lcs(String X, String Y, int m, int n)
    {
        int[][] L = new int[m + 1][n + 1];
        int i, j;
 
        // Following steps build L[m + 1][n + 1]
        // in bottom up fashion. Note that
        // L[i][j] contains length of LCS
        // of X[0..i - 1]and Y[0..j - 1]
        for (i = 0; i <= m; i++) {
            for (j = 0; j <= n; j++) {
                if (i == 0 || j == 0)
                    L[i][j] = 0;
 
                else if (X.charAt(i - 1) == Y.charAt(j - 1))
                    L[i][j] = L[i - 1][j - 1] + 1;
 
                else
                    L[i][j] = Math.max(L[i - 1][j],
                                       L[i][j - 1]);
            }
        }
 
        // L[m][n] contains length of LCS
        // for X[0..n - 1] and Y[0..m - 1]
        return L[m][n];
    }
 
    // Driver code
    public static void main(String args[])
    {
        String X = "AGGTAB";
        String Y = "GXTXAYB";
 
        System.out.println("Length of the shortest "
                           + "supersequence is "
                           + shortestSuperSequence(X, Y));
    }
}