Merge pull request dubesar#520 from abhinavtiwary04/Updated-Strassen-Algorithm

Strassen Algorithm

Author: dubesar

Algorithms/Strassen Algorithm.java

@@ -0,0 +1,153 @@
+import java.util.Scanner;
+ 
+
+public class Strassen
+{
+    // Function to multiply matrices
+    public int[][] multiply(int[][] A, int[][] B)
+    {        
+        int n = A.length;
+        int[][] R = new int[n][n];
+
+        /** base case **/
+        if (n == 1)
+            R[0][0] = A[0][0] * B[0][0];
+        else
+        {
+            int[][] A11 = new int[n/2][n/2];
+            int[][] A12 = new int[n/2][n/2];
+            int[][] A21 = new int[n/2][n/2];
+            int[][] A22 = new int[n/2][n/2];
+            int[][] B11 = new int[n/2][n/2];
+            int[][] B12 = new int[n/2][n/2];
+            int[][] B21 = new int[n/2][n/2];
+            int[][] B22 = new int[n/2][n/2];
+ 
+            /** Dividing matrix A into 4 halves **/
+            split(A, A11, 0 , 0);
+            split(A, A12, 0 , n/2);
+            split(A, A21, n/2, 0);
+            split(A, A22, n/2, n/2);
+
+
+            /** Dividing matrix B into 4 halves **/
+            split(B, B11, 0 , 0);
+            split(B, B12, 0 , n/2);
+            split(B, B21, n/2, 0);
+            split(B, B22, n/2, n/2);
+ 
+            /** 
+              M1 = (A11 + A22)(B11 + B22)
+              M2 = (A21 + A22) B11
+              M3 = A11 (B12 - B22)
+              M4 = A22 (B21 - B11)
+              M5 = (A11 + A12) B22
+              M6 = (A21 - A11) (B11 + B12)
+              M7 = (A12 - A22) (B21 + B22)
+            **/
+ 
+            int [][] M1 = multiply(add(A11, A22), add(B11, B22));
+            int [][] M2 = multiply(add(A21, A22), B11);
+            int [][] M3 = multiply(A11, sub(B12, B22));
+            int [][] M4 = multiply(A22, sub(B21, B11));
+            int [][] M5 = multiply(add(A11, A12), B22);
+            int [][] M6 = multiply(sub(A21, A11), add(B11, B12));
+            int [][] M7 = multiply(sub(A12, A22), add(B21, B22));
+ 
+            /**
+              C11 = M1 + M4 - M5 + M7
+              C12 = M3 + M5
+              C21 = M2 + M4
+              C22 = M1 - M2 + M3 + M6
+            **/
+
+            int [][] C11 = add(sub(add(M1, M4), M5), M7);
+            int [][] C12 = add(M3, M5);
+            int [][] C21 = add(M2, M4);
+            int [][] C22 = add(sub(add(M1, M3), M2), M6);
+ 
+            /** Joining 4 halves into one result matrix **/
+            join(C11, R, 0 , 0);
+            join(C12, R, 0 , n/2);
+            join(C21, R, n/2, 0);
+            join(C22, R, n/2, n/2);
+        }
+
+        /** Returning the resultant matrix **/    
+        return R;
+    }
+
+    /** Funtion to add two matrices **/
+    public int[][] add(int[][] A, int[][] B)
+    {
+        int n = A.length;
+        int[][] C = new int[n][n];
+        for (int i = 0; i < n; i++)
+            for (int j = 0; j < n; j++)
+                C[i][j] = A[i][j] + B[i][j];
+        return C;
+    }
+
+    /** Funtion to subtract two matrices **/
+    public int[][] sub(int[][] A, int[][] B)
+    {
+        int n = A.length;
+        int[][] C = new int[n][n];
+        for (int i = 0; i < n; i++)
+            for (int j = 0; j < n; j++)
+                C[i][j] = A[i][j] - B[i][j];
+        return C;
+    }
+
+    /** Funtion to split parent matrix into child matrices **/
+    public void split(int[][] P, int[][] C, int iB, int jB) 
+    {
+        for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++)
+            for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++)
+                C[i1][j1] = P[i2][j2];
+    }
+
+    /** Funtion to join child matrices intp parent matrix **/
+    public void join(int[][] C, int[][] P, int iB, int jB) 
+    {
+        for(int i1 = 0, i2 = iB; i1 < C.length; i1++, i2++)
+            for(int j1 = 0, j2 = jB; j1 < C.length; j1++, j2++)
+                P[i2][j2] = C[i1][j1];
+    }
+
+    /** Main function **/
+    public static void main (String[] args) 
+    {
+        Scanner sc = new Scanner(System.in);
+
+        /** Making an object of Strassen class **/
+        Strassen s = new Strassen();
+ 
+        System.out.println("Enter the order of matrices (n) :");
+        int N = sc.nextInt();
+
+        /** Accepting two 2d matrices **/
+        System.out.println("Enter N*N order matrix 1\n");
+        int[][] A = new int[N][N];
+        for (int i = 0; i < N; i++)
+            for (int j = 0; j < N; j++)
+                A[i][j] = sc.nextInt();
+ 
+        System.out.println("Enter N*N order matrix 2\n");
+        int[][] B = new int[N][N];
+        for (int i = 0; i < N; i++)
+            for (int j = 0; j < N; j++)
+                B[i][j] = sc.nextInt();
+ 
+        int[][] C = s.multiply(A, B);
+ 
+        System.out.println("\nProduct of matrices 1 and 2 is : ");
+        for (int i = 0; i < N; i++)
+        {
+            for (int j = 0; j < N; j++)
+                System.out.print(C[i][j] +" ");
+            System.out.println();
+        }
+ 
+    }
+}