Matrix Chain Multiplication using DP

Love Babbar DSA Sheet Solutions/Dynamic Programming/Matrix-Chain-Multiplication-using-DP.cpp

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+#include <bits/stdc++.h>
+using namespace std;
+
+// Matrix Ai has dimension p[i-1] x p[i]
+// for i = 1..n
+int MatrixChainOrder(int p[], int i, int j)
+{
+ if (i == j)
+ return 0;
+ int k;
+ int min = INT_MAX;
+ int count;
+
+ // place parenthesis at different places
+ // between first and last matrix, recursively
+ // calculate count of multiplications for
+ // each parenthesis placement and return the
+ // minimum count
+ for (k = i; k < j; k++)
+ {
+ count = MatrixChainOrder(p, i, k)
+ + MatrixChainOrder(p, k + 1, j)
+ + p[i - 1] * p[k] * p[j];
+
+ if (count < min)
+ min = count;
+ }
+
+ // Return minimum count
+ return min;
+}
+
+// Driver Code
+int main()
+{
+ int arr[] = { 1, 2, 3, 4, 3 };
+ int n = sizeof(arr) / sizeof(arr[0]);
+
+ cout << "Minimum number of multiplications is "
+ << MatrixChainOrder(arr, 1, n - 1);
+}