From 3ce4138213cc6eec8c7c0c5d880521712e28ef9e Mon Sep 17 00:00:00 2001
From: Vanshika Nehra <72328934+VanshikaNehra23@users.noreply.github.com>
Date: Sat, 2 Oct 2021 23:31:24 +0530
Subject: [PATCH] Create matrix_chain_multiplication.cpp

---
 .../matrix_chain_multiplication.cpp           | 42 +++++++++++++++++++
 1 file changed, 42 insertions(+)
 create mode 100644 Dynamic Programing/matrix_chain_multiplication.cpp

diff --git a/Dynamic Programing/matrix_chain_multiplication.cpp b/Dynamic Programing/matrix_chain_multiplication.cpp
new file mode 100644
index 00000000..9ab88c2c
--- /dev/null
+++ b/Dynamic Programing/matrix_chain_multiplication.cpp	
@@ -0,0 +1,42 @@
+// C++ program using memoization
+#include <bits/stdc++.h>
+using namespace std;
+int dp[100][100];
+
+// Function for matrix chain multiplication
+int matrixChainMemoised(int* p, int i, int j)
+{
+	if (i == j)
+	{
+		return 0;
+	}
+	if (dp[i][j] != -1)
+	{
+		return dp[i][j];
+	}
+	dp[i][j] = INT_MAX;
+	for (int k = i; k < j; k++)
+	{
+		dp[i][j] = min(
+			dp[i][j], matrixChainMemoised(p, i, k)
+					+ matrixChainMemoised(p, k + 1, j)
+					+ p[i - 1] * p[k] * p[j]);
+	}
+	return dp[i][j];
+}
+int MatrixChainOrder(int* p, int n)
+{
+	int i = 1, j = n - 1;
+	return matrixChainMemoised(p, i, j);
+}
+
+// Driver Code
+int main()
+{
+	int arr[] = { 1, 2, 3, 4 };
+	int n = sizeof(arr) / sizeof(arr[0]);
+	memset(dp, -1, sizeof dp);
+
+	cout << "Minimum number of multiplications is "
+		<< MatrixChainOrder(arr, n);
+}