From d26b7c091ac76299b4492006ae645fc0d3b7f18a Mon Sep 17 00:00:00 2001
From: ayushig2610 <92207924+ayushig2610@users.noreply.github.com>
Date: Sun, 10 Oct 2021 21:28:51 +0530
Subject: [PATCH] Added Matrix_Chain_Multiplication_DP

---
 .../Matrix_Chain_Multiplication_DP.cpp        | 41 +++++++++++++++++++
 1 file changed, 41 insertions(+)
 create mode 100644 Data Structure Algorithms/Matrix_Chain_Multiplication_DP.cpp

diff --git a/Data Structure Algorithms/Matrix_Chain_Multiplication_DP.cpp b/Data Structure Algorithms/Matrix_Chain_Multiplication_DP.cpp
new file mode 100644
index 0000000..a96253b
--- /dev/null
+++ b/Data Structure Algorithms/Matrix_Chain_Multiplication_DP.cpp	
@@ -0,0 +1,41 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+/*Following is the implementation of the Matrix Chain Multiplication problem 
+  using Dynamic Programming */
+
+class Solution{
+public:
+    int dp[102][102];
+    int fun(int a[],int n,int i,int j)
+    {
+        if(i>=j)return 0;
+        if(dp[i][j]!=-1)return dp[i][j];
+        int mn=INT_MAX;
+        for(int k=i;k<j;k++)
+        {
+            int temp=fun(a,n,i,k)+fun(a,n,k+1,j)+a[i-1]*a[k]*a[j];
+            mn=min(mn,temp);
+        }
+        return dp[i][j]=mn;
+    }
+    int matrixMultiplication(int N, int arr[])
+    {
+        memset(dp,-1,sizeof(dp));
+        return fun(arr,N,1,N-1);
+    }
+};
+
+int main(){
+    
+        int N;
+        cin>>N;
+        int arr[N];
+        for(int i = 0;i < N;i++)
+            cin>>arr[i];
+        
+        Solution ob;
+        cout<<ob.matrixMultiplication(N, arr)<<endl;
+
+    return 0;
+}  
\ No newline at end of file