HDU4008 Parent and son(树形DP LCA)

先记录以1为根时每个节点子树儿子节点的最大与次小值,询问x, y时,先判断x在不在y的子树范围内,若不在,结果为y的儿子结点,后继的最小值。

若x在y的子树范围内,若y儿子最小值是x的前驱,从次小值与父亲节点转移,否则从最小值与父亲节点转移。

 

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#include<cstdio>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<string>
#include<algorithm>
#include<map>
#include<queue>
#include<vector>
#include<cmath>
#include<utility>
using namespace std;
typedef long long LL;
const int N = 100008, INF = 0x3F3F3F3F;
#define MS(a, num) memset(a, num, sizeof(a))
#define PB(A) push_back(A)
#define FOR(i, n) for(int i = 0; i < n; i++)
 
int dfn[N][2];
int fa[N];
int son[N][2], des[N];
struct Node{
    int to,next;
}edge[N * 2];
 
 
int head[N],tot, deg[N];
int tim;
void init(){
    memset(head, -1, sizeof(head));
    memset(deg, 0, sizeof(deg));
    tot = 0;
}
void add(int u, int to){
    edge[tot].to=to;
    edge[tot].next=head[u];
    deg[u]++;
    head[u]=tot++;
}
 
void dfs(int u, int f){
    fa[u] = f;
    dfn[u][0] = tim++;
 
    son[u][0] = INF;
    son[u][1] = INF;
    des[u] = INF;
    for(int i = head[u]; ~i ; i = edge[i].next){
        int v = edge[i].to;
        if(v != f){
            dfs(v, u);
            son[u][1] = min(son[u][1], v);
            if(son[u][0] > son[u][1]){
                swap(son[u][0], son[u][1]);
            }
            des[u] = min(des[u], v);
            des[u] = min(des[u], des[v]);
        }
    }
    dfn[u][1] = tim++;
}
 
bool isFa(int x, int y){
    if(dfn[x][0] <= dfn[y][0]  && dfn[x][1] >= dfn[y][0]){
        return true;
    }
    return false;
}
 
int main(){
    int t;
    cin>>t;
    while(t--){
        int n, q;
        scanf("%d %d",  &n, &q);
        init();
        for(int i = 0; i < n - 1; i++){
            int u, v;
            scanf("%d %d", &u, &v);
            add(u, v);
            add(v, u);
        }
        tim = 0;
        dfs(1, INF);//1号节点父亲注意要为NF,便于处理
 
        int des2 = INF;//1号节点子树后继次小值
        int minv  = INF;//判断1号节点子树后继最小值从哪个儿子节点发出
        for(int i = head[1]; ~i; i = edge[i].next){
            int v = edge[i].to;
            int tp = min(v, des[v]);
            if(tp != des[1] && tp < des2){
                des2 = tp;
            }
            if(tp == des[1]){
                minv = v;
            }
        }
 
        while(q--){
            int x, y;
            scanf("%d %d", &x, &y);
            if(deg[y] == 1){
                printf("no answers!\n");
                continue;
            }
            if(isFa(y, x)){//x在y子树范围内(以1为根时)
                int mson, mdes;
                if(isFa(son[y][0], x)){
                    mson = min(son[y][1], fa[y]);
                }else{
                    mson = min(son[y][0], fa[y]);
                }
 
                if(y != 1){
                    mdes = 1;
                }else{
                    //y不是节点1,要判断
                    if(isFa(minv, x)){
                        mdes = des2;
                    }else{
                        mdes = des[y];
                    }
                }
                printf("%d %d\n", mson, mdes);
 
            }else{
                //x不在y子树范围内(以1为根时),直接输出
                printf("%d %d\n", son[y][0], des[y]);
            }
        }
        printf("\n");
    }
 
    return 0;
}

  

posted @   vwirtveurit  阅读(315)  评论(0编辑  收藏  举报
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