Merge pull request #49 from vermashresth/master

Stressens Multiplication and Matrix Chain Multiplication

Author: srbcheema1

divide_and_conquer/strassen.cpp

@@ -0,0 +1,236 @@
+#include<iostream>
+#include<cstdlib>
+#include<ctime>
+using namespace std;
+
+
+void createMatrix(int **A4,int size);
+void output(int **A, int size);
+void standardMult(int **A, int **B, int **C, int size);
+void strassens(int **A, int **B, int **C, int size);
+void Add(int **A, int **B, int **T, int n);
+void Sub(int **A, int **B, int **T, int n);
+
+
+
+
+int main() {
+	int size = 8;
+	
+	
+	int **A, **B, **C;
+
+	for(int size=16;size<2048;size*=2){
+
+	A = new int *[size];
+	B = new int *[size];
+	C = new int *[size];
+
+	
+	for(int i=0; i<size; i++) {
+		A[i] = new int[size];
+		B[i] = new int[size];
+		C[i] = new int[size];
+	}
+
+	//Matrices for i,j as i*j%1000
+	createMatrix(A,size);
+	createMatrix(B,size);
+
+
+	
+	cout<<"Size of the matrix : "<<size<<"*"<<size<<endl<<endl;
+	//Multiplying Matrices using Standard Method
+	
+	int time = clock();
+	standardMult(A,B,C,size);
+	int now=clock();
+	//output(C,size);
+	cout<<"Standard Multiplication: "<<(now-time)/1000000.0<<" Seconds"<<endl; 
+
+	//Multiplying Matrices using Strassen's Algorithm
+	//cout<<endl<<endl<<"Strassen's way" <<endl;
+	time = clock();
+	strassens(A,B,C,size);
+	now=clock();
+	//output(C,size);
+	cout<<"Stressen's multiplication : "<<(now-time)/1000000.0<<" Seconds"<<endl<<endl; 
+
+}}
+
+
+
+//Add matrices
+void Add(int **A, int **B, int **T, int n) {
+	for(int i=0; i<n; i++) {
+		for(int j=0; j<n; j++) {
+			T[i][j] = A[i][j] + B[i][j];
+		}
+	}
+}
+
+//Subtract matricess
+void Sub(int **A, int **B, int **T, int n) {
+	for(int i=0; i<n; i++) {
+		for(int j=0; j<n; j++) {
+			T[i][j] = A[i][j] - B[i][j];
+		}
+	}
+}
+
+
+//method for matrix generation
+void createMatrix(int **A,int size) {
+	for(int i=0; i<size; i++) {
+		for(int j=0; j<size; j++) {
+			A[i][j] = (i+1)*(j+1) % 1000;
+		}
+	}
+}
+
+//method to print a matrix
+void output(int **A, int size) {
+	cout<<endl;
+	for(int i=0; i<size; i++) {
+		for(int j=0; j<size; j++) {
+			cout<<A[i][j]<<" ";
+		}
+		cout<<endl;
+	}
+}
+
+//traditional method of multiplying two square matrices
+void standardMult(int **A, int **B, int **C, int size) {
+	for(int i=0; i<size; i++) {
+		for(int j=0; j<size; j++) {
+			C[i][j] = 0;
+			for(int k=0; k<size; k++) {
+				C[i][j] += A[i][k] * B [k][j];
+			}
+		}
+	}
+}
+
+//strassen's product
+void strassens(int **A, int **B, int **C, int size) {
+	if ( size <= 100)
+	{
+		standardMult(A,B,C,size);
+	}
+	else 
+	{
+		//Divide and conquer step
+		int n = size/2;
+		int N = size/2;
+		int newsize = size/2;
+
+		//Smaller matrices
+		int **A11, **A12, **A21, **A22, **B11, **B12, **B21, **B22, **C11, **C12, **C21, **C22;
+
+		//Matrices for Strassens
+		int **M1, **M2, **M3, **M4, **M5, **M6, **M7;
+
+	
+		int **P, **Q;
+
+		//memory allocation for columns
+		A11 = new int *[n];A12 = new int *[n];A21 = new int *[n];A22 = new int *[n];
+		B11 = new int *[n];B12 = new int *[n];B21 = new int *[n];B22 = new int *[n];
+		C11 = new int *[n];C12 = new int *[n];C21 = new int *[n];C22 = new int *[n];
+		
+		//stressens matrices
+		M1 = new int *[n];
+		M2 = new int *[n];
+		M3 = new int *[n];
+		M4 = new int *[n];
+		M5 = new int *[n];
+		M6 = new int *[n];
+		M7 = new int *[n];
+
+		P = new int *[n];
+		Q = new int *[n];
+
+		//memory allocation for columns
+		for(int i=0; i<N; i++) {
+			A11[i] = new int[N];A12[i] = new int[N];A21[i] = new int[N];A22[i] = new int[N];
+			B11[i] = new int[N];B12[i] = new int[N];B21[i] = new int[N];B22[i] = new int[N];
+			C11[i] = new int[N];C12[i] = new int[N];C21[i] = new int[N];C22[i] = new int[N];
+
+			M1[i] = new int[N];
+			M2[i] = new int[N];
+			M3[i] = new int[N];
+			M4[i] = new int[N];
+			M5[i] = new int[N];
+			M6[i] = new int[N];
+			M7[i] = new int[N];
+
+			P[i] = new int[N];
+			Q[i] = new int[N];
+
+		}
+
+		//Dividing input matrices A and B into 4 submatrices each.
+		for (int i = 0; i < newsize; i++) {
+			for (int j = 0; j < newsize; j++) {
+				A11[i][j] = A[i][j];
+				A12[i][j] = A[i][j + newsize];
+				A21[i][j] = A[i + newsize][j];
+				A22[i][j] = A[i + newsize][j + newsize];
+
+				B11[i][j] = B[i][j];
+				B12[i][j] = B[i][j + newsize];
+				B21[i][j] = B[i + newsize][j];
+				B22[i][j] = B[i + newsize][j + newsize];
+			}
+		}
+
+		//M1
+		Sub(B12,B22,P,n);strassens(A11,P,M1,n);
+
+		//M2
+		Add(A11,A12,P,n);strassens(P,B22,M2,n);
+
+		//M3
+		Add(A21,A22,P,n);strassens(P,B11,M3,n);
+
+		//M4
+		Sub(B21,B11,P,n);strassens(A22,P,M4,n);
+
+		//M5
+		Add(A11,A22,P,n);Add(B11,B22,Q,n);strassens(P,Q,M5,n);
+
+		//M6
+		Sub(A12,A22,P,n);Add(B21,B22,Q,n);strassens(P,Q,M6,n);
+
+		//M7
+		Sub(A11,A21,P,n);Add(B11,B12,Q,n);strassens(P,Q,M7,n);
+
+		//C11
+		Add(M4,M5,P,n);Sub(M6,M2,Q,n);Add(P,Q,C11,n);
+
+		//C12
+		Add(M1,M2,C12,n);
+
+		//C21
+		Add(M3,M4,C21,n);
+
+		//C22
+		Add(M1,M5,P,n);	Add(M3,M7,Q,n);	Sub(P,Q,C22,n);
+
+		//algorithm part
+		for (int i = 0; i < n ; i++) {
+			for (int j = 0 ; j < n ; j++) {
+				C[i][j] = C11[i][j];
+				C[i][j + n] = C12[i][j];
+				C[i + n][j] = C21[i][j];
+				C[i + n][j + n] = C22[i][j];
+			}
+		}
+	}
+}
+
+
+
+
+
+

dp/mcm.cpp

@@ -0,0 +1,69 @@
+#include<stdio.h>
+#include<iostream>
+#include<ctime>
+#include <fstream>
+
+using namespace std;
+//random matrix sizes
+int mat[]={10,5,2,8,16,10,5,3,8,9,18,15,3,6,11,5,3,2,8,3,9,7,4,9,3};
+//5 15 and 25 as number of matrices
+int nn[]={5,10,25};
+
+//funtion for matrix chain multiplication using div and cnquer
+int mcmdnc(int a,int b)
+{
+  int cost;
+    //base Case
+       if(a==b)
+        cost=0;
+       else
+      {
+     for(int i=a;i<b;i++)
+      {
+            if(i==a)
+                cost=mcmdnc(a,i)+mcmdnc(i+1,b)+mat[a-1]*mat[i]*mat[b];
+            else
+                cost=min(cost,(mcmdnc(a,i)+mcmdnc(i+1,b)+mat[a-1]*mat[i]*mat[b]));
+      }
+    }
+    return  cost;
+}
+   
+
+//function for matrix chain multiplication using dp
+int mcmdp(int p[], int n){
+    int m[n][n];
+    int i, j, k, L, q;
+    for (i = 1; i < n; i++)
+        m[i][i] = 0;
+    for (L=2; L<n; L++)   {
+        for (i=1; i<=n-L+1; i++){
+            j = i+L-1;
+            m[i][j] = 100000;
+            for (k=i; k<=j-1; k++){
+                q = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];
+                if (q < m[i][j])
+                    m[i][j] = q;
+            }
+        }
+    }
+    return m[1][n-1];
+}
+int main(){
+    int val;
+    
+    for (int i=0;i<3; i++){
+
+int t=clock();
+	val= mcmdp(mat,nn[i]);
+    cout<<"Optimised cost for "<<nn[i]<<" matrices is "<<val<<"(DP)"<<endl<<" time taken :"<< ((float)(clock()-t))/CLOCKS_PER_SEC<<endl;
+
+         t=clock();
+  
+
+	val=mcmdnc(1,nn[i]-1);
+    cout<<"Optimised cost for "<<nn[i]<<" matrices is "<<val<<"(DivAndConq)"<<endl<<" time taken :"<< ((float)(clock()-t))/CLOCKS_PER_SEC<<endl;
+
+	}
+    return 0;
+}