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Merged
yanglbme merged 2 commits into from
Dec 21, 2018
Merged

add Matrix chain multiplication algorithm #664

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2da7d89
add Matrix chain multiplication algorithm
SunggyuLee Dec 19, 2018
3183957
Update MatrixChainMultiplication.java
yanglbme Dec 21, 2018
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134 changes: 134 additions & 0 deletions Dynamic Programming/MatrixChainMultiplication.java
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import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class MatrixChainMultiplication {
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++) {
Arrays.fill(m[i], -1);
Arrays.fill(s[i], -1);
}

for (int i = 0; i < p.length; i++) {
p[i] = i == 0 ? mArray.get(i).col() : 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;

Matrix(int count, int col, int row) {
this.count = count;
this.col = col;
this.row = row;
}

int count() {
return count;
}

int col() {
return col;
}

int row() {
return row;
}
}