洛谷 P1388 算式

题目传送门

先跑dfs,枚举出所有符合题意的符号放置方式,再跑区间dp.

#include<iostream>
#include<cstdio>
#include<cstring>

using namespace std;

int n,k,a[20],p[30];
long long ans,f[25][25];

inline int max(int s,int d) {
    if(s < d) return d;
    return s;
}

inline void dp() {
    for(int i = 1;i <= n; i++)
        f[i][i] = a[i];
    for(int len = 1;len < n; len++)
        for(int i = 1,j = i + len;j <= n; i++,j++)
            for(int k = i;k < j; k++)
                if(p[k] == 1)
                    f[i][j] = max(f[i][j],f[i][k] + f[k+1][j]);
                else if(p[k] == 2)
                        f[i][j] = max(f[i][j],f[i][k] * f[k+1][j]);
    ans = max(ans,f[1][n]);
}

inline void dfs(int d,int l,int r) {
    if(d == n) {
        memset(f,0,sizeof(f));
        dp();
        return ; 
    }
    if(l < k) {
        p[d] = 2;
        dfs(d + 1,l + 1,r);
    }
    if(r < n - k - 1) {
        p[d] = 1;
        dfs(d + 1,l,r + 1);
    }
}

int main() {
    scanf("%d%d",&n,&k);
    for(int i = 1;i <= n; i++)
        scanf("%d",&a[i]);
    dfs(1,0,0);
    printf("%lld",ans);
    return 0;
}