CCPC 2017 哈尔滨 L. Color a Tree && HDU 6241（二分+树形DP）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=6241

题意：给你一棵有 n 个结点的树，每个结点初始颜色都为白色，有 A 个条件：结点 x_i 的黑色结点数目不少于 y_i 个，同时有 B 个条件，除了结点 x_j 及其子树外至少有 y_j 个结点，求把最少要染成黑色结点的数目使得满足 A + B 个条件。

题解：参考自：https://blog.csdn.net/u013534123/article/details/78523559

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>
#include <cmath>
#include <stack>
#include <queue>
#include <vector>
#include <map>
#include <set>
#include <bitset>
using namespace std;
#define ll long long
#define ull unsigned long long
#define mst(a,b) memset((a),(b),sizeof(a))
#define pii pair<int,int>
#define pII pair<ll,ll>
#define pi acos(-1)
#define pb push_back
const double eps = 1e-6;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const int MAXN = 1e5 + 10;
const int MAXM = 1e6 + 10;

int n;
vector<int>vec[MAXN];
int siz[MAXN],b[MAXN],mn[MAXN],mx[MAXN];
int up[MAXN],down[MAXN];

void init() {
    for(int i = 0; i <= n; i++) {
        vec[i].clear();
        b[i] = mn[i] = 0;
    }
}

void getsize(int u,int fa) {
    siz[u] = 1;
    for(int i = 0; i < vec[u].size(); i++) {
        int v = vec[u][i];
        if(v == fa) continue;
        getsize(v,u);
        siz[u] += siz[v];
    }
}

bool dfs(int u,int fa) {
    int l = 0, r = 1;
    for(int i = 0; i < vec[u].size(); i++) {
        int v = vec[u][i];
        if(v == fa) continue;
        if(!dfs(v,u)) return false;
        l += down[v], r += up[v];
    }
    down[u] = max(l, mn[u]), up[u] = min(r, mx[u]);
    return down[u] <= up[u];
}

bool check(int x) {
    for(int i = 1; i <= n; i++) {
        mx[i] = min(x - b[i],siz[i]);
        if(mx[i] < 0) return false;
    }
    return dfs(1,0) && down[1] <= x && x <= up[1];
}


int main() {
#ifdef local
    freopen("data.txt", "r", stdin);
#endif
    int t;
    scanf("%d",&t);
    while(t--) {
        scanf("%d",&n);
        init();
        for(int i = 1; i < n; i++) {
            int u,v;
            scanf("%d%d",&u,&v);
            vec[u].pb(v);
            vec[v].pb(u);
        }
        getsize(1,0);
        int m;
        bool flag = true;
        scanf("%d",&m);
        while(m--) {
            int x,y;
            scanf("%d%d",&x,&y);
            mn[x] = max(mn[x],y);
            if(y > siz[x]) flag = false;
        }
        scanf("%d",&m);
        while(m--) {
            int x,y;
            scanf("%d%d",&x,&y);
            b[x] = max(b[x],y);
            if(y > n - siz[x]) flag = false;
        }
        if(!flag) {
            puts("-1");
            continue;
        }
        int l = 0, r = n, ans = -1;
        while(l <= r) {
            int mid = (l + r) >> 1;
            if(check(mid)) ans = mid, r = mid - 1;
            else l = mid + 1;
        }
        printf("%d
",ans);
    }
    return 0;
}