HNOI2018 道路

Posted 2020-10-31 zcdhj

Luogu

真·普及 DP

令 \(f_{x,y,z}\) 为在 \(i\) 点，有 \(y\) 条公路没修，有 \(z\) 条铁路没修

\[f_{x,y,z}=\max{f_{s_i,y+1,z}+f_{t_i,y,z},f_{s_i,y,z}+f_{s_i,y,z+1}}\]

由于树的高是保证的，所以并不会被卡空间

可以先把 \(dfn\) 跑出来后倒着推，也可以直接 \(dfs\)

注意下细节

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

typedef long long ll;

const int MaxN = 4e4 + 5;

int N;
int Ch[MaxN][2], A[MaxN], B[MaxN], C[MaxN];
ll Dp[MaxN][41][41];

inline void dfs(int x, int s1, int s2)
{
    if(x >= N)
    {
        for(int i = 0; i <= s1; ++i)
            for(int j = 0; j <= s2; ++j)
                Dp[x][i][j] = 1ll * C[x] * (A[x] + i) * (B[x] + j);
        return;
    }
    dfs(Ch[x][0], s1 + 1, s2);
    dfs(Ch[x][1], s1, s2 + 1);
    for(int i = 0; i <= s1; ++i)
        for(int j = 0; j <= s2; ++j)
            Dp[x][i][j] = std::min(Dp[Ch[x][0]][i + 1][j] + Dp[Ch[x][1]][i][j], Dp[Ch[x][0]][i][j] + Dp[Ch[x][1]][i][j + 1]);
}

int main()
{
    int x, y;
    scanf("%d", &N);
    for(int i = 1; i < N; ++i)
    {
        scanf("%d %d", &x, &y);
        if(x < 0) x = -x + N - 1;
        if(y < 0) y = -y + N - 1;
        Ch[i][0] = x;
        Ch[i][1] = y;
    }
    for(int i = 1; i <= N; ++i)
    {
        x = i + N - 1;
        scanf("%d %d %d" ,&A[x], &B[x], &C[x]);
    }
    dfs(1, 0, 0);
    printf("%lld\n", Dp[1][0][0]);
    return 0;
}