洛谷4438 [Hnoi2018]道路 树形dp

Posted 2020-11-02 Mychael

题目

题目太长懒得打

题解

HNOI2018惊现普及+/提高？
由最长路径很短，设\(f[i][x][y]\)表示\(i\)号点到根有\(x\)条未修公路，\(y\)条未修铁路，子树所有乡村不便利值的最小值
如果\(i\)为乡村，直接等于公式
如果\(i\)不为乡村，枚举修哪边儿子
\(f[i][x][y] = min\{f[ls][x + 1][y] + f[rs][x][y],f[ls][x][y] + f[rs][x][y + 1]\}\)

\(ans = f[1][0][0]\)
很多\(f\)用完就丢了，可以滚一下数组省空间

完了

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#define LL long long int
#define Redge(u) for (int k = h[u],to; k; k = ed[k].nxt)
#define REP(i,n) for (int i = 1; i <= (n); i++)
#define BUG(s,n) for (int i = 1; i <= (n); i++) cout<<s[i]<<‘ ‘; puts("");
using namespace std;
const int maxn = 40005,maxm = 100005,INF = 1000000000;
inline int read(){
    int out = 0,flag = 1; char c = getchar();
    while (c < 48 || c > 57){if (c == ‘-‘) flag = -1; c = getchar();}
    while (c >= 48 && c <= 57){out = (out << 3) + (out << 1) + c - 48; c = getchar();}
    return out * flag;
}
LL f[110][41][41];
int n,s[maxn],t[maxn],a[maxn],b[maxn],c[maxn],dep[maxn];
int st[maxn],top,id[maxn];
void dfs(int u){
    if (u >= n){
        int x = u - n + 1; id[u] = st[top--];
        for (int i = 0; i <= dep[u]; i++)
            for (int j = 0; j <= dep[u]; j++)
                f[id[u]][i][j] = 1ll * c[x] * (a[x] + i) * (b[x] + j);
        return;
    }
    dep[s[u]] = dep[t[u]] = dep[u] + 1;
    dfs(s[u]); dfs(t[u]);
    id[u] = st[top--];
    for (int i = 0; i <= dep[u]; i++)
        for (int j = 0; j <= dep[u]; j++)
            f[id[u]][i][j] = min(f[id[s[u]]][i][j] + f[id[t[u]]][i][j + 1],f[id[s[u]]][i + 1][j] + f[id[t[u]]][i][j]);
    st[++top] = id[s[u]]; st[++top] = id[t[u]];
}
int main(){
    n = read();
    for (int i = 1; i < n; i++){
        s[i] = read(); t[i] = read();
        if (s[i] < 0) s[i] = -s[i] + n - 1;
        if (t[i] < 0) t[i] = -t[i] + n - 1;
    }
    for (int i = 1; i <= n; i++) a[i] = read(),b[i] = read(),c[i] = read();
    top = 99;
    REP(i,top) st[i] = i;
    dfs(1);
    printf("%lld\n",f[id[1]][0][0]);
    return 0;
}