Add Shortest Common Supersequence Length (#2516)

DynamicProgramming/ShortestCommonSupersequenceLength.java

@@ -0,0 +1,59 @@
+// 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));
+    }
+}