矩阵连乘问题

区间合并 dp[i][j] = min(dp[i][k] + dp[k+1][j] + p[i-1]*p[k]*p[j]) {  i<=k<j  }

 

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
const int N = 10;
const ll INF = 1e18;

ll dp[N][N], p[N];
int s[N][N];

void dfs(int i,int j) {
    if(i == j) return ;
    dfs(i,s[i][j]);
    dfs(s[i][j]+1,j);
    printf("[A(%d,%d) A(%d,%d)]\n",i,s[i][j],s[i][j]+1,j);
}

int main () {
    int n = 5;
    p[0] = 20; p[1] = 30;
    p[2] = 50; p[3] = 10;
    p[4] = 35; p[5] = 25;
    memset(dp, 0, sizeof(dp));
    for(int len=2; len<=n; len++) {
        for(int i=1; i+len-1<=n; i++) {
            int j = i+len-1;
            dp[i][j] = INF;
            for(int k=i; k<j; k++) {
                ll ans = dp[i][k] + dp[k+1][j] + 1LL*p[i-1]*p[k]*p[j];
                dp[i][j] = min(dp[i][j], ans);
                if(dp[i][j] == ans) {
                    s[i][j] = k;
                }
            }
        }
    }

    for(int i=1;i<=n;i++) {
        for(int j=i;j<=n;j++) {
            printf("%lld ", dp[i][j]);
        }
        puts("");
    }
    printf("%lld\n", dp[1][n]);
    dfs(1, n);
    return 0;
}