From 31a9aeaa4a64a63e38205650d08b3e295d67c9c6 Mon Sep 17 00:00:00 2001
From: Sanchit Gupta <sunnyg.98@gmail.com>
Date: Wed, 10 Oct 2018 14:45:46 +0530
Subject: [PATCH] Matrix Chain Multiplication Added

---
 .../Matrix_Chain_Multipliaction.cpp           | 75 +++++++++++++++++++
 1 file changed, 75 insertions(+)
 create mode 100644 Matrix Chain Multiplication (MCM)/Matrix_Chain_Multipliaction.cpp

diff --git a/Matrix Chain Multiplication (MCM)/Matrix_Chain_Multipliaction.cpp b/Matrix Chain Multiplication (MCM)/Matrix_Chain_Multipliaction.cpp
new file mode 100644
index 0000000..6d25a6e
--- /dev/null
+++ b/Matrix Chain Multiplication (MCM)/Matrix_Chain_Multipliaction.cpp	
@@ -0,0 +1,75 @@
+#include<iostream>
+#include<conio.h>
+using namespace std;
+long int m[50][50],p[50],s[50][50];
+void matrix_chain(int n){
+long 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]=20000;
+	for(k=i;k<j;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;
+			s[i][j]=k;
+		}
+	}	
+	}
+}
+}
+void display(long int s[50][50],int i,int j)
+{
+	if(i==j)
+	{
+		cout<<"A"<<i;
+	}
+	else
+	{
+		cout<<"(";
+		display(s,i,s[i][j]);
+		display(s,s[i][j]+1,j);
+		
+}
+}
+main()
+{
+	long int n,i,j;
+	cout<<"Enter number of matrices:";
+	cin>>n;
+	cout<<"Enter Order Array:"<<endl;
+for(i=0;i<=n;i++)
+{
+	cin>>p[i];
+}
+	matrix_chain(n);
+	cout<<"M Table : "<<endl;
+for(int l=1;l<=n;l++)
+{
+	for(int i=1;i<=n;i++)
+	{
+		cout<<m[l][i]<<"\t";
+	}
+	cout<<endl;
+}
+cout<<"S Table : "<<endl;
+for(int l=1;l<=n;l++)
+{
+	for(int i=1;i<=n;i++)
+	{
+		cout<<s[l][i]<<"\t";
+	}
+	cout<<endl;
+}
+cout<<"Most efficient way to multiply given sequence of
+matrices is:"<<endl;
+display(s,1,n);
+getch();
+}
\ No newline at end of file