动态规划策略编程实现矩阵链乘法问题

public class MatrixChainMultiplication {
   public static int matrixChainOrder(int[] p) {
       int n = p.length;
       int[][] m = new int[n][n];
       int[][] s = new int[n][n];
       for (int i = 1; i < n; i++) {
           m[i][i] = 0;
       }
       for (int L = 2; L < n; L++) {
           for (int i = 1; i < n - L + 1; i++) {
               int j = i + L - 1;
               m[i][j] = Integer.MAX_VALUE;
               for (int k = i; k <= j - 1; 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;
                   }
               }
           }
       }
       System.out.println("Minimum number of multiplications is " + m[1][n-1]);
       return m[1][n-1];
   }

   public static String printOptimalParenthesis(int[][] s, int i, int j) {
       if (i == j) {
           return "A" + i;
       } else {
           return "(" +
                   printOptimalParenthesis(s, i, s[i][j]) +
                   printOptimalParenthesis(s, s[i][j] + 1, j) +
                   ")";
       }
   }

   public static void main(String[] args) {
       int[] p = {10, 20, 30, 40, 30};
       int n = p.length;
       int[][] m = new int[n][n];
       int[][] s = new int[n][n];
       for (int i = 1; i < n; i++) {
           m[i][i] = 0;
       }
       for (int L = 2; L < n; L++) {
           for (int i = 1; i < n - L + 1; i++) {
               int j = i + L - 1;
               m[i][j] = Integer.MAX_VALUE;
               for (int k = i; k <= j - 1; 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;
                   }
               }
           }
       }
       System.out.println("最少标量乘法次数是： " + m[1][n-1]);
       System.out.println("最优方案是: " + printOptimalParenthesis(s, 1, n-1));
   }
}