From 2adf07240eba400ec5cbbef46d5b5efad9c3d0a4 Mon Sep 17 00:00:00 2001
From: Shrey Gupta <75122294+Shreygupta2002@users.noreply.github.com>
Date: Sat, 7 Oct 2023 13:39:36 +0530
Subject: [PATCH] Added Strassens Algorithm

Please add the hacktoberfest tag
---
 c++/strassen_algo.cpp | 179 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 179 insertions(+)
 create mode 100644 c++/strassen_algo.cpp

diff --git a/c++/strassen_algo.cpp b/c++/strassen_algo.cpp
new file mode 100644
index 0000000..15e96e9
--- /dev/null
+++ b/c++/strassen_algo.cpp
@@ -0,0 +1,179 @@
+#include<bits/stdc++.h>
+using namespace std;
+typedef long long int ll;
+int nextpowerof2(int x)
+{
+	int temp=1;
+	while(temp<x)
+	{
+		temp=temp*2;
+	}
+	return temp;
+}
+vector<vector<int>> padding(vector<vector<int>> A, int n)
+{
+	vector<vector<int>> ans(n,vector<int>(n));
+	for(int i=0;i<A.size();i++)
+	{
+		for(int j=0;j<A[i].size();j++)
+		{
+			ans[i][j]=A[i][j];
+		}
+	}
+	return ans;
+}
+vector<vector<int>> addMatrix(vector<vector<int>> A, vector<vector<int>>B, int n)
+{
+	vector<vector<int>> sum(n,vector<int>(n));
+	for(int i=0;i<n;i++)
+	{
+		for(int j=0;j<n;j++)
+		{
+			sum[i][j]=A[i][j]+B[i][j];
+		}
+	}
+	return sum;
+}
+vector<vector<int>> subtractMatrix(vector<vector<int>> A, vector<vector<int>>B, int n)
+{
+	vector<vector<int>> diff(n,vector<int>(n));
+	for(int i=0;i<n;i++)
+	{
+		for(int j=0;j<n;j++)
+		{
+			diff[i][j]=A[i][j]-B[i][j];
+		}
+	}
+	return diff;
+}
+
+vector<vector<int>> Strassen(vector<vector<int>> A, vector<vector<int>> B, int n)
+{
+	vector<vector<int>> prod(n,vector<int>(n));
+	if(n==1)
+	{
+		prod[0][0]=A[0][0]*B[0][0];
+		return prod;
+	}
+
+	vector<vector<int>> a(n/2,vector<int>(n/2));
+	vector<vector<int>> b(n/2,vector<int>(n/2));
+	vector<vector<int>> c(n/2,vector<int>(n/2));
+	vector<vector<int>> d(n/2,vector<int>(n/2));
+
+	vector<vector<int>> e(n/2,vector<int>(n/2));
+	vector<vector<int>> f(n/2,vector<int>(n/2));
+	vector<vector<int>> g(n/2,vector<int>(n/2));
+	vector<vector<int>> h(n/2,vector<int>(n/2));
+
+	for(int i=0;i<n/2;i++)
+	{
+		for(int j=0;j<n/2;j++)
+		{
+			a[i][j]=A[i][j];
+			b[i][j]=A[i][j+n/2];
+			c[i][j]=A[i+n/2][j];
+			d[i][j]=A[i+n/2][j+n/2];
+
+			e[i][j]=B[i][j];
+			f[i][j]=B[i][j+n/2];
+			g[i][j]=B[i+n/2][j];
+			h[i][j]=B[i+n/2][j+n/2];
+		}
+	}
+	vector<vector<int>> p1(n/2,vector<int>(n/2));
+	vector<vector<int>> p2(n/2,vector<int>(n/2));
+	vector<vector<int>> p3(n/2,vector<int>(n/2));
+	vector<vector<int>> p4(n/2,vector<int>(n/2));
+	vector<vector<int>> p5(n/2,vector<int>(n/2));
+	vector<vector<int>> p6(n/2,vector<int>(n/2));
+	vector<vector<int>> p7(n/2,vector<int>(n/2));
+
+	p1=Strassen(a,subtractMatrix(f,h,n/2),n/2);
+	p2=Strassen(addMatrix(a,b,n/2),h,n/2);
+	p3=Strassen(addMatrix(c,d,n/2),e,n/2);
+	p4=Strassen(d,subtractMatrix(g,e,n/2),n/2);
+	p5=Strassen(addMatrix(a,d,n/2),addMatrix(e,h,n/2),n/2);
+	p6=Strassen(subtractMatrix(b,d,n/2),addMatrix(g,h,n/2),n/2);
+	p7=Strassen(subtractMatrix(a,c,n/2),addMatrix(e,f,n/2),n/2);
+
+	for(int i=0;i<n/2;i++)
+	{
+		for(int j=0;j<n/2;j++)
+		{
+			prod[i][j]=p5[i][j]+p4[i][j]-p2[i][j]+p6[i][j];
+		}
+		for(int j=n/2;j<n;j++)
+		{
+			prod[i][j]=p1[i][j-n/2]+p2[i][j-n/2];
+		}
+	}
+	for(int i=n/2;i<n;i++)
+	{
+		for(int j=0;j<n/2;j++)
+		{
+			prod[i][j]=p3[i-n/2][j]+p4[i-n/2][j];
+		}
+		for(int j=n/2;j<n;j++)
+		{
+			prod[i][j]=p1[i-n/2][j-n/2]+p5[i-n/2][j-n/2]-p3[i-n/2][j-n/2]-p7[i-n/2][j-n/2];
+		}
+	}
+	return prod;
+}
+int main()
+{
+    ios::sync_with_stdio(0);cin.tie(0);
+    mt19937 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());
+    auto start=chrono::high_resolution_clock::now();
+    
+    //code here
+    
+    int n1, m1;
+    cin>>n1>>m1;
+    vector<vector<int>> A(n1,vector<int>(m1));
+    for(int i=0;i<n1;i++)
+    {
+    	for(int j=0;j<m1;j++)
+    	{
+    		cin>>A[i][j];
+    	}
+    }
+    int n2, m2;
+    cin>>n2>>m2;
+    vector<vector<int>> B(n2,vector<int>(m2));
+    for(int i=0;i<n2;i++)
+    {
+    	for(int j=0;j<m2;j++)
+    	{
+    		cin>>B[i][j];
+    	}
+    }
+    if(m1!=n2)
+    {
+    	cout<<"Matrix Multiplication Not Possible!!"<<endl;
+    	exit(0);
+    }
+
+    int temp=max(n1,max(n2,max(m1,m2)));
+    int n=nextpowerof2(temp);
+    A=padding(A,n);
+    B=padding(B,n);
+    vector<vector<int>> C(n,vector<int>(n));
+    C=Strassen(A,B,n);
+
+    for(int i=0;i<n1;i++)
+    {
+    	for(int j=0;j<m2;j++)
+    	{
+    		cout<<C[i][j]<<"\t ";
+    	}
+    	cout<<endl;
+    }
+
+
+
+    auto stop=chrono::high_resolution_clock::now();
+    auto duration=chrono::duration_cast<chrono::microseconds>(stop-start);
+    cerr<<duration.count()/1000.0<<" ms\n";
+}
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