【动态规划】矩阵链乘法代码

CLRS 15.2

#include <stdio.h>
#include <limits.h>
#include <string.h>

int m[101][101];
int s[101][101];

void matrix_chain_order(int p[], int 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] = INT_MAX;
            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;
                }
            }
        }
    }
}

void print_optimal_parens(int i, int j)
{
    if(i == j)
        printf("A%d", i);
    else
    {
        printf("(");
        print_optimal_parens(i, s[i][j]);
        print_optimal_parens(s[i][j]+1, j);
        printf(")");
    }
}

int main()
{
    int p[7] = {30, 35, 15, 5, 10, 20, 25};
    memset(m, 0, sizeof(int)*101*101);
    memset(s, 0, sizeof(int)*101*101);
    matrix_chain_order(p, 6);
    printf("%d\n", m[1][6]);
    print_optimal_parens(1, 6);
    return 0;
}