From 2da7d89123520702c38fbbcb5fee53f88ee2152a Mon Sep 17 00:00:00 2001
From: SunggyuLee <sq0216@gmail.com>
Date: Wed, 19 Dec 2018 23:42:15 +0900
Subject: [PATCH]  add Matrix chain multiplication algorithm

---
 .../MatrixChainMultiplication.java            | 120 ++++++++++++++++++
 1 file changed, 120 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 000000000..b22312355
--- /dev/null
+++ b/Dynamic Programming/MatrixChainMultiplication.java	
@@ -0,0 +1,120 @@
+import java.util.ArrayList;
+import java.util.Scanner;
+
+public class MatrixChainMultiplicationTest {
+	private static Scanner scan = new Scanner(System.in);
+	private static ArrayList<Matrix> mArray = new ArrayList<>();
+	private static int size;
+	private static int[][] m;
+	private static int[][] s;
+	private static int[] p;
+	
+	public static void main(String[] args) {
+		int count = 1;
+		while(true) {
+			String [] mSize = input("input size of matrix A("+count+") ( ex. 10 20 ) : ");
+			int col = Integer.parseInt(mSize[0]);
+			if (col==0) break;
+			int row = Integer.parseInt(mSize[1]);
+			
+			Matrix matrix = new Matrix(count, col, row);
+			mArray.add(matrix);
+			count++;	
+		}
+		for(Matrix m : mArray) {
+			System.out.format("A(%d)  =  %2d  x  %2d\n", m.count(), m.col(), m.row());
+		}
+		
+		size = mArray.size();
+		m = new int[size + 1][size + 1];
+		s = new int[size + 1][size + 1];
+		p = new int[size + 1];
+
+		for (int i=0; i<size+1; i++) {
+			for (int j=0; j<size+1; j++) {
+				m[i][j] = -1;
+				s[i][j] = -1;
+			}
+		}
+
+		for (int i=0; i<p.length; i++) {
+			if (i == 0) {
+				p[i] = mArray.get(i).col();
+			} else {
+				p[i] = mArray.get(i-1).row();
+			}
+		}
+		
+		matrixChainOrder();
+		for(int i=0; i<size; i++) { System.out.print("-------"); }
+		System.out.println();
+		printArray(m);
+		for(int i=0; i<size; i++) { System.out.print("-------"); }
+		System.out.println();
+		printArray(s);
+		for(int i=0; i<size; i++) { System.out.print("-------"); }
+		System.out.println();
+		
+		System.out.println("Optimal solution : "+ m[1][size]);
+		System.out.print("Optimal parens : ");
+		printOptimalParens(1, size);
+	}
+	private static void printOptimalParens(int i, int j) {
+		if (i == j) {
+			System.out.print("A" + i);
+		} else {
+			System.out.print("(");
+			printOptimalParens(i, s[i][j]);
+			printOptimalParens(s[i][j] + 1, j);
+			System.out.print(")");
+		}
+	}
+	private static void printArray(int[][] array) {
+		for (int i = 1; i < size+1; i++) {
+			for (int j = 1; j < size+1; j++) {
+				System.out.print(String.format("%7d", array[i][j]));
+			}
+			System.out.println();
+		}
+	}
+	
+	private static void matrixChainOrder() {
+		for (int i = 1; i<size+1; i++) {
+			m[i][i] = 0;
+		}
+
+		for (int l = 2; l <size+1; l++) {
+			for (int i = 1; i<size-l+2; i++) {
+				int j = i+l-1;
+				m[i][j] = Integer.MAX_VALUE;
+
+				for (int k = i; k < j; k++) {
+					int q = m[i][k] + m[k+1][j] + p[i-1] * p[k] * p[j];
+					if (q < m[i][j]) {
+						m[i][j] = q;
+						s[i][j] = k;
+					}
+				}
+			}
+		}
+	}
+	
+	private static String[] input(String string) {
+		System.out.print(string);
+		return (scan.nextLine().split(" ") );
+	}
+
+}
+class Matrix {
+	private int count;
+	private int col;
+	private int row;
+	public Matrix(int count, int col, int row) {
+		this.count = count;
+		this.col = col;
+		this.row = row;
+	}
+	public int count() { return this.count; }
+	public int col() { return this.col; }
+	public int row() { return this.row; }
+}