SPOJ 375 QTREE Query on a tree 树链剖分水题

题目大意：

给定一棵树后两种操作

修改边权, 询问两点间路径上的边权的最大值

大致思路：

树链剖分水题

剖分之后线段树维护最大值即可, 单点更新区间查询

代码如下：

Result  :  Accepted     Memory  :  4403 KB     Time  :  490 ms

/*
 * Author: Gatevin
 * Created Time:  2015/9/8 19:36:25
 * File Name: Sakura_Chiyo.cpp
 */
#include<iostream>
#include<sstream>
#include<fstream>
#include<vector>
#include<list>
#include<deque>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<bitset>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cctype>
#include<cmath>
#include<ctime>
#include<iomanip>
using namespace std;
const double eps(1e-8);
typedef long long lint;

#define maxn 10010
int top[maxn];
int grandson[maxn];
int dep[maxn];
int siz[maxn];
int belong[maxn];
int father[maxn];
int Q[maxn];
int cnt;
int hson[maxn];
int n;
bool vis[maxn];
int id[maxn];
int antiID[maxn];

struct Edge
{
    int u, v, w, nex;
    Edge(int _u, int _v, int _w, int _nex)
    {
        u = _u, v = _v, w = _w, nex = _nex;
    }
    Edge(){}
};

int head[maxn];
int tot;
Edge edge[maxn << 1];
int w[maxn];

void add_Edge(int x, int y, int w)
{
    edge[++tot] = Edge(x, y, w, head[x]);
    head[x] = tot;
}

void split()
{
    cnt = 0;
    int l = 0, r = 1;
    dep[Q[r] = 1] = 1;
    father[r] = -1;
    w[r] = 0;
    while(l < r)
    {
        int x = Q[++l];
        if(head[x] == -1) continue;
        for(int j = head[x]; j + 1; j = edge[j].nex)
        {
            int y = edge[j].v;
            if(y == father[x]) continue;
            w[y] = edge[j].w;
            dep[Q[++r] = y] = dep[x] + 1;
            father[y] = x;
        }
    }
    for(int i = n; i; i--)
    {
        int x = Q[i], p = -1;
        siz[x] = 1;
        if(head[x] == -1) continue;
        for(int j = head[x]; j + 1; j = edge[j].nex)
        {
            int y = edge[j].v;
            if(y == father[x]) continue;
            siz[x] += siz[y];
            if(p == -1 || (p > 0 && siz[y] > siz[p]))
                p = y;
        }
        if(p == -1)
        {
            hson[x] = -1;
            grandson[++cnt] = x;
            belong[top[cnt] = x] = cnt;
        }
        else
        {
            hson[x] = p;
            belong[x] = belong[p];
            top[belong[x]] = x;
        }
    }
    int idx = 0;
    memset(vis, 0, sizeof(vis));
    for(int i = n; i; i--)
    {
        int x = Q[i];
        if(vis[x]) continue;
        vis[x] = 1;
        id[x] = ++idx;
        antiID[idx] = x;
        while(father[x] != -1 && belong[father[x]] == belong[x] && !vis[father[x]])
        {
            x = father[x];
            id[x] = ++idx;
            antiID[idx] = x;
            vis[x] = 1;
        }
    }
    return;
}

struct Segment_Tree
{
#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
    int ma[maxn << 2];
    void pushUp(int rt)
    {
        ma[rt] = max(ma[rt << 1], ma[rt << 1 | 1]);
        return;
    }
    void build(int l, int r, int rt)
    {
        if(l == r)
        {
            ma[rt] = w[antiID[l]];
            return;
        }
        int mid = (l + r) >> 1;
        build(lson);
        build(rson);
        pushUp(rt);
    }
    void update(int l, int r, int rt, int pos, int value)
    {
        if(l == r)
        {
            ma[rt] = value;
            return;
        }
        int mid = (l + r) >> 1;
        if(mid >= pos) update(lson, pos, value);
        else update(rson, pos, value);
        pushUp(rt);
    }
    int query(int l, int r, int rt, int L, int R)
    {
        if(l >= L && r <= R)
            return ma[rt];
        int mid = (l + r) >> 1;
        int ret = -1e9;
        if(mid >= L) ret = max(ret, query(lson, L, R));
        if(mid + 1 <= R) ret = max(ret, query(rson, L, R));
        return ret;
    }
};

Segment_Tree st;

int answer(int x, int y)
{
    int ans = -1e9;
    while(top[belong[x]] != top[belong[y]])
    {
        if(dep[top[belong[x]]] < dep[top[belong[y]]])
            swap(x, y);
        ans = max(ans, st.query(1, n, 1, id[x], id[top[belong[x]]]));
        x = father[top[belong[x]]];
    }
    if(x == y) return ans;
    if(dep[x] < dep[y]) swap(x, y);
    ans = max(ans, st.query(1, n, 1, id[x], id[hson[y]]));
    return ans;
}

int main()
{
    int T;
    scanf("%d", &T);
    while(T--)
    {
        scanf("%d", &n);
        tot = 0;
        memset(head, -1, sizeof(head));
        int u, v, w, x;
        for(int i = 1; i < n; i++)
        {
            scanf("%d %d %d", &u, &v, &w);
            add_Edge(u, v, w);
            add_Edge(v, u, w);
        }
        split();
        st.build(1, n, 1);
        char op[10];
        while(scanf("%s", op))
        {
            if(op[0] == 'D') break;
            if(op[0] == 'Q')
            {
                scanf("%d %d", &u, &v);
                printf("%d\n", answer(u, v));
            }
            else
            {
                scanf("%d %d", &x, &w);
                u = edge[x << 1].u;
                v = edge[x << 1].v;
                if(father[u] == v) st.update(1, n, 1, id[u], w);
                else st.update(1, n, 1, id[v], w);
            }
        }
    }
    return 0;
}