Create PrintShortestCommonSupersequence.java

Author: 17tanya

DynamicProgramming/ShortestCommonSupersequence/PrintShortestCommonSupersequence.java

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+/*
+https://www.techiedelight.com/shortest-common-supersequence-finding-scs/
+*/
+
+//Find one Shortest Common Supersequence
+// length(X) = m and length(Y) = n
+
+public String findSCS(String X, String Y, int m, int n,int T[][]){
+
+    if(m == 0) return Y.substring(0,n);
+    
+    else if(n == 0) return X.substring(0,m);
+    
+    else if( X.charAt(n-1) == Y.charAt(m-1) ){
+        return findSCS(X, Y, m-1, n-1, T) + X.charAt(n-1);
+    }
+    else if( T[m-1][n] < T[m][n-1] ){
+        return findSCS(X, Y, m-1, n, T) + X.charAt(m-1);
+    }
+    else{
+        return findSCS(X, Y, m, n-1, T) + Y.charAt(n-1);
+    }
+}
+
+//Print all Shortest Common Supersequence
+// length(X) = m and length(Y) = n
+
+public List<String> findSCS(String X, String Y, int m, int n, int T[][]){
+    if( m == 0){
+        List<String> l = new ArrayList<>();
+        l.add(Y.substring(0,n));
+        return l;
+    }
+    else if( n == 0){
+        List<String> l = new ArrayList<>();
+        l.add(X.substring(0,m));
+        return l;
+    }
+    else if( X.charAt(m-1) == Y.charAt(n-1) ){
+        List<String> scs = findSCS(X, Y, m-1, n-1, T);
+        List<String> res = new ArrayList<>();
+        for(String s : scs){
+            res.add(s+X.charAt(m-1));
+        }
+        return res;
+    }
+    else if( T[m-1][n] < T[m][n-1] ){
+        List<String> scs = findSCS(X, Y, m-1, n, T);
+        List<String> res = new ArrayList<>();
+        for(String s : scs){
+            res.add(s+X.charAt(m-1));
+        }
+        return res;
+    }
+    else if( T[m-1][n] > T[m][n-1] ){
+        List<String> scs = findSCS(X, Y, m, n-1, T);
+        List<String> res = new ArrayList<>();
+        for(String s : scs){
+            res.add(s+Y.charAt(n-1));
+        }
+        return res;
+    }
+    else{ //T[m-1][n] == T[m][n-1]
+        List<String> top = findSCS(X, Y, m-1, n, T);
+        List<String> left = findSCS(X, Y, m, n-1, T);
+        List<String> res = new ArrayList<>();
+        for(String s : top){
+            res.add(s + X.charAt(m-1));
+        }
+        for(String s : left){
+            res.add(s + Y.charAt(n-1));
+        }
+        return res;
+    }
+    
+}
+
+
+// Function to fill lookup table by finding length of SCS of
+// sequences X[0..m-1] and Y[0..n-1]
+public static void SCSLength(String X, String Y, int m, int n, int[][] T)
+{
+	// initialize first column of the lookup table
+	for (int i = 0; i <= m; i++) {
+		T[i][0] = i;
+	}
+
+	// initialize first row of the lookup table
+	for (int j = 0; j <= n; j++) {
+		T[0][j] = j;
+	}
+
+	// fill the lookup table in bottom-up manner
+	for (int i = 1; i <= m; i++)
+	{
+		for (int j = 1; j <= n; j++)
+		{
+			// if current character of X and Y matches
+			if (X.charAt(i - 1) == Y.charAt(j - 1)) {
+				T[i][j] = T[i - 1][j - 1] + 1;
+			}
+			// else if current character of X and Y don't match
+			else {
+				T[i][j] = Integer.min(T[i - 1][j] + 1, T[i][j - 1] + 1);
+			}
+		}
+	}
+}