Matrix Chain Multiplication DP solution

DP/MatrixChainMultiplication.java

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+package DP;
+
+public class MCM {
+
+	public static void main(String[] args) {
+		int[] arr = { 4, 2, 3, 5, 1 };
+		System.out.println(MCMRecursion(arr, 0, arr.length - 1));
+		System.out.println(MCMTD(arr, 0, arr.length - 1, new int[arr.length][arr.length]));
+		System.out.println(MCMBU(arr));
+	}
+
+	//Recursive Solution
+	public static int MCMRecursion(int[] arr, int si, int ei) {
+		if (si + 1 == ei) {
+			return 0;
+		}
+		int min = Integer.MAX_VALUE;
+		for (int k = si + 1; k <= ei - 1; k++) {
+
+			int fp = MCMRecursion(arr, si, k);
+			int sp = MCMRecursion(arr, k, ei);
+
+			int sw = arr[si] * arr[k] * arr[ei];
+			int total = fp + sp + sw;
+
+			if (total < min) {
+				min = total;
+			}
+		}
+		return min;
+	}
+
+
+	//Top-Down Approach
+	public static int MCMTD(int[] arr, int si, int ei, int[][] strg) {
+		if (si + 1 == ei) {
+			return 0;
+		}
+		if (strg[si][ei] != 0) {
+			return strg[si][ei];
+		}
+		int min = Integer.MAX_VALUE;
+		for (int k = si + 1; k <= ei - 1; k++) {
+
+			int fp = MCMTD(arr, si, k, strg);
+			int sp = MCMTD(arr, k, ei, strg);
+
+			int sw = arr[si] * arr[k] * arr[ei];
+			int total = fp + sp + sw;
+
+			if (total < min) {
+				min = total;
+			}
+		}
+		strg[si][ei] = min;
+		return min;
+	}
+
+
+	//Bottom Up Approach
+	public static int MCMBU(int[] arr) {
+		int n = arr.length;
+		int[][] strg = new int[n][n];
+		for (int slide = 1; slide <= n - 1; slide++) {
+			for (int si = 0; si <= n - slide - 1; si++) {
+
+				int ei = si + slide;
+				if (si + 1 == ei) {
+					strg[si][ei] = 0;
+				} else {
+					int min = Integer.MAX_VALUE;
+					for (int k = si + 1; k <= ei - 1; k++) {
+
+						int fp = strg[si][k];
+						int sp = strg[k][ei];
+
+						int sw = arr[si] * arr[k] * arr[ei];
+						int total = fp + sp + sw;
+
+						if (total < min) {
+							min = total;
+						}
+					}
+					strg[si][ei] = min;
+				}
+
+			}
+		}
+		return strg[0][n-1];
+
+	}
+}