Task: Matrix chain multiplication




Go: package main

import "fmt"




func PrintMatrixChainOrder(dims []int) {
	n := len(dims) - 1
	m, s := newSquareMatrices(n)

	
	
	
	
	
	for lenMinusOne := 1; lenMinusOne < n; lenMinusOne++ {
		for i := 0; i < n-lenMinusOne; i++ {
			j := i + lenMinusOne
			m[i][j] = -1
			for k := i; k < j; k++ {
				cost := m[i][k] + m[k+1][j] + dims[i]*dims[k+1]*dims[j+1]
				if m[i][j] < 0 || cost < m[i][j] {
					m[i][j] = cost
					s[i][j] = k
				}
			}
		}
	}

	
	const MatrixNames = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
	var subprint func(int, int)
	subprint = func(i, j int) {
		if i == j {
			return
		}
		k := s[i][j]
		subprint(i, k)
		subprint(k+1, j)
		fmt.Printf("%*s -> %s × %s%*scost=%d\n",
			n, MatrixNames[i:j+1],
			MatrixNames[i:k+1],
			MatrixNames[k+1:j+1],
			n+i-j, "", m[i][j],
		)
	}
	subprint(0, n-1)
}

func newSquareMatrices(n int) (m, s [][]int) {
	
	
	m = make([][]int, 2*n)
	m, s = m[:n:n], m[n:]
	tmp := make([]int, 2*n*n)
	for i := range m {
		m[i], tmp = tmp[:n:n], tmp[n:]
	}
	for i := range s {
		s[i], tmp = tmp[:n:n], tmp[n:]
	}
	return m, s
}

func main() {
	cases := [...][]int{
		{1, 5, 25, 30, 100, 70, 2, 1, 100, 250, 1, 1000, 2},
		{1000, 1, 500, 12, 1, 700, 2500, 3, 2, 5, 14, 10},
	}
	for _, tc := range cases {
		fmt.Println("Dimensions:", tc)
		PrintMatrixChainOrder(tc)
		fmt.Println()
	}
}


Java: import java.util.Arrays;

public class MatrixChainMultiplication {

    public static void main(String[] args) {
        runMatrixChainMultiplication(new int[] {5, 6, 3, 1});
        runMatrixChainMultiplication(new int[] {1, 5, 25, 30, 100, 70, 2, 1, 100, 250, 1, 1000, 2});
        runMatrixChainMultiplication(new int[] {1000, 1, 500, 12, 1, 700, 2500, 3, 2, 5, 14, 10});
    }
    
    private static void runMatrixChainMultiplication(int[] dims) {
        System.out.printf("Array Dimension  = %s%n", Arrays.toString(dims));
        System.out.printf("Cost             = %d%n", matrixChainOrder(dims));
        System.out.printf("Optimal Multiply = %s%n%n", getOptimalParenthesizations());
    }

    private static int[][]cost;
    private static int[][]order;
    
    public static int matrixChainOrder(int[] dims) {
        int n = dims.length - 1;
        cost = new int[n][n];
        order = new int[n][n];

        for (int lenMinusOne = 1 ; lenMinusOne < n ; lenMinusOne++) {
            for (int i = 0; i < n - lenMinusOne; i++) {
                int j = i + lenMinusOne;
                cost[i][j] = Integer.MAX_VALUE;
                for (int k = i; k < j; k++) {
                    int currentCost = cost[i][k] + cost[k+1][j] + dims[i]*dims[k+1]*dims[j+1];
                    if (currentCost < cost[i][j]) {
                        cost[i][j] = currentCost;
                        order[i][j] = k;
                    }
                }
            }
        }
        return cost[0][n-1];
    }

    private static String getOptimalParenthesizations() {
        return getOptimalParenthesizations(order, 0, order.length - 1);
    }
    
    private static String getOptimalParenthesizations(int[][]s, int i, int j) {
        if (i == j) {
            return String.format("%c", i+65);
        }
        else {
            StringBuilder sb = new StringBuilder();
            sb.append("(");
            sb.append(getOptimalParenthesizations(s, i, s[i][j]));
            sb.append(" * ");
            sb.append(getOptimalParenthesizations(s, s[i][j] + 1, j));
            sb.append(")");
            return sb.toString();
        }
    }

}