From 5649edc57b14e9b99e3e84ff191ca832fec68896 Mon Sep 17 00:00:00 2001
From: Clayton <63671653+Claytonx210@users.noreply.github.com>
Date: Sat, 1 Oct 2022 00:19:13 +0530
Subject: [PATCH] MatrixChainMultiplication.java

Dynamic program
---
 .../MatrixChainMultiplication.java            | 45 +++++++++++++++++++
 1 file changed, 45 insertions(+)
 create mode 100644 dynamic-programming/MatrixChainMultiplication.java

diff --git a/dynamic-programming/MatrixChainMultiplication.java b/dynamic-programming/MatrixChainMultiplication.java
new file mode 100644
index 00000000..8cf56510
--- /dev/null
+++ b/dynamic-programming/MatrixChainMultiplication.java
@@ -0,0 +1,45 @@
+// Dynamic Programming Python implementation of Matrix
+// Chain Multiplication.
+public class MatrixChainMultiplication {
+// Matrix Ai has dimension p[i-1] x p[i] for i = 1..n
+		static int MatrixChainOrder(int p[], int n) {
+			/* For simplicity of the program, one extra row and one
+			extra column are allocated in m[][].  0th row and 0th
+			column of m[][] are not used */
+			int m[][] = new int[n][n];
+
+			int i, j, k, L, q;
+
+			/* m[i,j] = Minimum number of scalar multiplications needed
+			to compute the matrix A[i]A[i+1]...A[j] = A[i..j] where
+			dimension of A[i] is p[i-1] x p[i] */
+
+			// cost is zero when multiplying one matrix.
+			for (i = 1; i < n; i++)
+				m[i][i] = 0;
+
+			// L is chain length.
+			for (L=2; L<n; L++) {
+				for (i=1; i<n-L+1; i++) {
+					j = i+L-1;
+					if(j == n) continue;
+					m[i][j] = Integer.MAX_VALUE;
+					for (k=i; k<=j-1; k++) {
+					// q = cost/scalar multiplications
+						q = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];
+						if (q < m[i][j])
+							m[i][j] = q;
+					}
+				}
+			}
+		return m[1][n-1];
+		}
+
+		// Driver program to test above function
+		public static void main(String args[]) {
+			int arr[] = new int[] {1, 2, 3, 4};
+			int size = arr.length;
+			System.out.println("Minimum number of multiplications is "+
+			MatrixChainOrder(arr, size));
+		}
+}
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