Merge pull request #715 from ShivangiBhatnagar-246/StrassenAlgoinC

Strassen's Algo Matrix Multiplication in C

Author: smv1999

Arrays/Strassen's_Algo.c

@@ -0,0 +1,75 @@
+// Problem Description: Strassens Algorithm in C Language for Matrix Multiplication
+#include<stdio.h>
+int main(){
+  int mat1[2][2], mat2[2][2], mat3[2][2], i, j;
+  int a, b, c, d , e, f, g;
+ 
+  printf("Enter the elements of first matrix:\n"); //Input elements for matrix 1
+  for(i = 0;i < 2; i++)
+  {
+      for(j = 0;j < 2; j++)
+      {
+           scanf("%d", &mat1[i][j]);
+      }
+  }
+ 
+  printf("Enter the elements of second matrix:\n"); // Input elements for matrix 2
+  for(i = 0; i < 2; i++)
+  {
+      for(j = 0;j < 2; j++)
+      {
+           scanf("%d", &mat2[i][j]);
+      }
+  }
+  //Displaying
+  printf("The Matrix 1:\n"); //Displaying matrix 1 elements
+  for(i = 0; i < 2; i++)
+  {
+      for(j = 0; j < 2; j++)
+      {
+           printf("%d\t", mat1[i][j]);
+      }
+      printf("\n");
+  }
+ 
+  printf("The Matrix 2:\n"); //Displayimg matrix 2 elements
+  for(i = 0;i < 2; i++)
+  {
+      for(j = 0;j < 2; j++)
+      {
+           printf("%d \t", mat2[i][j]);
+      }
+      printf("\n");
+  }
+
+ //reduced eight times Time Complexity  to Seven Times i.e T(N) = 7T(N/2) +  O(N^2)
+ 
+ // Compexity: before O(n^3) when used Standard Matrix Multiplication , now :O(n^2.808) when used Strassen's Algorithm
+ 
+ //Now we can calculate the product of mat1[i][j] and mat2[i][j] with the following formulas:
+  a= (mat1[0][0] + mat1[1][1]) * (mat2[0][0] + mat2[1][1]);  
+  b= (mat1[1][0] + mat1[1][1]) * mat2[0][0];
+  c= mat1[0][0] * (mat2[0][1] - mat2[1][1]);
+  d= mat1[1][1] * (mat2[1][0] - mat2[0][0]);
+  e= (mat1[0][0] + mat1[0][1]) * mat2[1][1];
+  f= (mat1[1][0] - mat1[0][0]) * (mat2[0][0]+mat2[0][1]);
+  g= (mat1[0][1] - mat1[1][1]) * (mat2[1][0]+mat2[1][1]);
+ //Now with a,b,c,d,e,f,g which are the submatrices of size N/2*N/2
+ 
+ //Calculate the elements of matrix 3, The resultant matrix mat3[i][j]
+  mat3[0][0] = a + d- e + g;
+  mat3[0][1] = c + e;
+  mat3[1][0] = b + d;
+  mat3[1][1] = a - b + c + f;
+ 
+   printf("Strassen's algorithm : Matrix Multiplication\n"); //Resultant matrix after applying Strassen's Algo
+   for(i = 0; i < 2 ; i++)
+   {
+      for(j = 0;j < 2; j++)
+      {
+           printf("%d\t", mat3[i][j]); //displaying resultant matrix
+      }
+      printf("\n");
+   }
+   return 0;
+}