hdu 6241

Color a Tree

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 385 Accepted Submission(s): 86

Problem Description
Bob intends to color the nodes of a tree with a pen. The tree consists of N nodes. These nodes are numbered 1,2,…,N. The root of the tree is node 1. The initial color of each node is white. Bob can use one unit energy to color one node into black. To prevent Bob being lazy with painting, Alice proposed A+B rules. Each rule is represent by two numbers xi and yi.
For the first A rules, it means that there should be no less than yi nodes painted black for the subtree of node xi.
For the other B rules, it means that there should be no less than yi nodes painted black for all nodes except the subtree of node xi.
You need to help Bob to calculate the minimum energy he needs for the painting with all rules proposed by Alice satisfied.

Input
The first line is the number of test cases. For each test case, the first line contains one positive number N(1≤N≤100000), indicating the number of trees nodes.

The following N−1 lines describe the edges. Each line contains two integers u,v(1≤u,v≤N), denoting there is a edge between node u and node v.

The following one line contains one number A(A≤100000), indicating the first A rules.

The following A lines describe the first A rules. Each line contains two numbers xi and yi as described above.

The following one line contains one number B(B≤100000), indicating the other B rules.

The following B lines describe the other B rules. Each line contains two numbers xi and yi as described above.

Output
For each test case, output a integer donating the minimum energy Bob needs to use with all rules propose by Alice satisfied. If there is no solution, output −1 instead.

Sample Input
2
5
1 2
2 3
3 4
1 5
2
2 1
5 1
1
2 1
5
1 2
2 3
3 4
1 5
3
1 2
2 2
5 1
1
3 5

Sample Output
2
-1
题意：给出一个树，有两种规则，A：以xi为根的子树至少有yi个黑点，B：除了xi为根的子树上的点之外的点至少有yi个黑点。
做法：二分需要的黑点数，对于每一个节点l[u]代表以u为根的子树至少要涂多少个黑点，r[u]代表以u为根的子树至多涂多少个黑点。如多mid在l[1]和r[1]之间就代表这个mid是可行的，原理就是对于一个mid如果在l[1]和r[1]之间，那么我每次先把每个儿子分配这个节点至少需要的黑点数，然后把剩余的随便分（只要不超过这个点的r[u]），这样必定可以分出来答案。

#include<bits/stdc++.h>#define LL long longusing namespace std;const int N = 1e5+100;int son[N];int head[N],nex[N*2],num[N*2],A[N],B[N];LL l[N],r[N];int tot;int n,m,m2;void dfs(int u,int f){    son[u] = 1;    int cns = 0;    for(int i = head[u];i != -1;i = nex[i]){        int v = num[i];        if(v == f) continue;        dfs(v,u);        son[u] += son[v];        cns += A[v];    }    A[u] = max(A[u],cns);}void check(int x,int u,int f){    l[u] = A[u],r[u] = min(son[u],x-B[u]);    LL cl = 0,cr = 0;    bool tmp= false;    for(int i = head[u];i != -1;i = nex[i]){        int v = num[i];        if(v == f) continue;        tmp = true;        check(x,v,u);        //l[u]+=l[v];r[u]+=r[v];        cl += l[v],cr += r[v];    }    l[u] = max(l[u],cl);    if(tmp) r[u] = min(cr+1,r[u]);}bool judge(int x){    check(x,1,-1);    bool tmp = true;    if(x < l[1] || x > r[1]) tmp = false;    for(int i = 1;i < n;i ++){        if(l[i] > r[i]) tmp = false;    }    return tmp;}int main(){    int T;    cin >> T;    while(T--){        memset(head,-1,sizeof(head));        memset(A,0,sizeof(A));        memset(B,0,sizeof(B));        tot = 0;        scanf("%d",&n);        for(int i = 1;i < n;i ++){            int u,v;            scanf("%d %d",&u,&v);            num[tot] = v;            nex[tot] = head[u];            head[u] = tot++;            num[tot] = u;            nex[tot] = head[v];            head[v] = tot++;        }        scanf("%d",&m);        for(int i= 1;i <= m;i ++){            int x,y;            scanf("%d %d",&x,&y);            A[x] = max(A[x],y);        }        scanf("%d",&m2);        for(int i = 1;i <= m2;i ++){            int x,y;            scanf("%d %d",&x,&y);            B[x] = max(B[x],y);        }        dfs(1,-1);        bool tmp= false;        for(int i = 1;i <= n;i ++){            if(A[i] > son[i]||B[i]+son[i] > n) {                tmp = true;            }        }        if(tmp){            puts("-1");            continue;        }        int l = -1,r = n;        for(int i = 1;i <= n;i ++) l = max(l,A[i]+B[i]);        l--;        while(r-l>1){            int mid = l+r>>1;            //cout << mid << ' '<< judge(mid) << endl;            if(judge(mid)) r = mid;            else l = mid;        }        //cout<<"!!" << endl;        cout << r << endl;    }    return 0;}