動態規劃-矩陣鏈乘法

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Java實現：

package dp;public class MatrixChainOrder {    public static void matrixChainOrder(int[] p, int[][] m, int[][] s) {        int n = p.length - 1;        for (int i = 1; i <= n ; i++) {            m[i][i] = 0;        }        for (int len = 2; len <= n; len++) {            for (int i = 1; i <= n-len+1 ; i++) {                int j = len + i - 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;                    }                }            }        }    }    public static void printOptimalSolution(int[][] s, int i, int j) {        if (i == j) {            System.out.print("A_" + i);        } else {            System.out.print("(");            printOptimalSolution(s, i, s[i][j]);            printOptimalSolution(s, s[i][j] + 1, j);            System.out.print(")");        }    }    public static void main(String[] args) {        int[] p ={30, 35, 15, 5, 10, 20, 25};        int n = p.length - 1;        int[][] m = new int[n+1][n+1];        int[][] s = new int[n+1][n+1];        matrixChainOrder(p, m, s);        System.out.println("The optimal value:" + m[1][n]);        System.out.print("The optimal solution is:\n\t");        printOptimalSolution(s, 1, n);    }}

 

動態規劃-矩陣鏈乘法