added matrix chain multiplication question

Author: sunilkumarmaurya786693

leetcode/dynamic programming/maxtrix chain multiplication.cpp

@@ -0,0 +1,41 @@
+// Matrix Chain Multiplication
+// Given a sequence of matrices, find the most efficient way to multiply these matrices together. The efficient way is the one that involves the least number of multiplications.
+// The dimensions of the matrices are given in an array arr[] of size N (such that N = number of matrices + 1) where the ith matrix has the dimensions (arr[i-1] x arr[i]).
+// Example 1:
+// Input: N = 5
+// arr = {40, 20, 30, 10, 30}
+// Output: 26000
+// Explaination: There are 4 matrices of dimension 
+// 40x20, 20x30, 30x10, 10x30. Say the matrices are 
+// named as A, B, C, D. Out of all possible combinations,
+// the most efficient way is (A*(B*C))*D. 
+// The number of operations are -
+// 20*30*10 + 40*20*10 + 40*10*30 = 26000.
+ 
+// Example 2:
+// Input: N = 4
+// arr = {10, 30, 5, 60}
+// Output: 4500
+// Explaination: The matrices have dimensions 
+// 10*30, 30*5, 5*60. Say the matrices are A, B 
+// and C. Out of all possible combinations,the
+// most efficient way is (A*B)*C. The 
+// number of multiplications are -
+// 10*30*5 + 10*5*60 = 4500.
+int dp[101][101];
+int solve(int n, int arr[], int i,int j){
+   if(i>=j)return 0;
+   if(dp[i][j]!=-1)return dp[i][j];
+   int temp=INT_MAX;
+   for(int k=i;k<j;k++){
+       temp=min(temp,solve(n,arr,i,k)+solve(n,arr,k+1,j)+arr[i-1]*arr[k]*arr[j]);
+   }
+   dp[i][j]=temp;
+   return temp;
+  
+}
+   int matrixMultiplication(int N, int arr[])
+   {
+       memset(dp,-1, sizeof(dp));
+       return solve(N,arr,1,N-1);
+   }