题目链接：uva 11354 - Bond

题目大意：给定一张图，每次询问两个节点路径上进过边的危险值的最大值的最小值。

解题思路：首先建立最小生成数，然后根据这棵树做树链剖分。

#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>

using namespace std;
const int maxn = 50005;
const int INF = 0x3f3f3f3f;

struct Edge {
    int u, v, w;
    Edge (int u = 0, int v = 0, int w = 0) { set(u, v, w); }
    void set(int u, int v, int w) {
        this->u = u;
        this->v = v;
        this->w = w;
    }
    friend bool operator < (const Edge& a, const Edge& b) {
        return a.w < b.w;
    }
}ed[maxn * 2];

int N, M, Q, ne, f[maxn], first[maxn], jump[maxn * 2], val[maxn];
int id, idx[maxn], top[maxn], far[maxn], son[maxn], dep[maxn], cnt[maxn];
vector<Edge> vec;

inline int getfar(int x) {
    return x == f[x] ? x : f[x] = getfar(f[x]);
}

inline void add_Edge (int u, int v, int w) {
    ed[ne].set(u, v, w);
    jump[ne] = first[u];
    first[u] = ne++;
}

void dfs (int u, int pre, int d) {
    far[u] = pre;
    dep[u] = d;
    son[u] = 0;
    cnt[u] = 1;

    for (int i = first[u]; i + 1; i = jump[i]) {
        int v = ed[i].v;
        if (v == pre)
            continue;
        dfs(v, u, d + 1);
        cnt[u] += cnt[v];
        if (cnt[son[u]] < cnt[v])
            son[u] = v;
    }
}

void dfs (int u, int rot) {
    top[u] = rot;
    idx[u] = ++id;
    if (son[u])
        dfs(son[u], rot);
    for (int i = first[u]; i + 1; i = jump[i]) {
        int v = ed[i].v;
        if (v == far[u] || v == son[u])
            continue;
        dfs(v, v);
    }
}

#define lson(x) ((x)<<1)
#define rson(x) (((x)<<1)|1)
int lc[maxn << 2], rc[maxn << 2], s[maxn << 2];

inline void pushup(int u) {
    s[u] = max(s[lson(u)], s[rson(u)]);
}

void build (int u, int l, int r) {
    lc[u] = l;
    rc[u] = r;

    if (l == r) {
        s[u] = val[l];
        return;
    }

    int mid = (l + r) / 2;
    build(lson(u), l, mid);
    build(rson(u), mid + 1, r);
    pushup(u);
}

int query(int u, int l, int r) {
    if (l <= lc[u] && rc[u] <= r)
        return s[u];
    int mid = (lc[u] + rc[u]) / 2, ret = 0;
    if (l <= mid)
        ret = max(ret, query(lson(u), l, r));
    if (r > mid)
        ret = max(ret, query(rson(u), l, r));
    return ret;
}

void init () {
    int u, v, w;
    ne = id = 0;
    vec.clear();
    memset(first, -1, sizeof(first));
    for (int i = 1; i <= N; i++)
        f[i] = i;

    for (int i = 0; i < M; i++) {
        scanf("%d%d%d", &u, &v, &w);
        vec.push_back(Edge(u, v, w));
    }
    sort(vec.begin(), vec.end());
    for (int i = 0; i < vec.size(); i++) {
        int p = getfar(vec[i].u);
        int q = getfar(vec[i].v);
        if (p == q)
            continue;
        add_Edge(vec[i].u, vec[i].v, vec[i].w);
        add_Edge(vec[i].v, vec[i].u, vec[i].w);
        f[p] = q;
    }

    dfs(1, 0, 0);
    dfs(1, 1);
    for (int i = 0; i < N - 1; i++) {
        int t = i * 2;
        u = (dep[ed[t].u] < dep[ed[t].v] ? ed[t].v : ed[t].u);
        val[idx[u]] = ed[t].w;
    }
    build(1, 1, N);
}

int solve (int u, int v) {
    int p = top[u], q = top[v], ret = 0;
    while (p != q) {
        if (dep[p] < dep[q]) {
            swap(p, q);
            swap(u, v);
        }
        ret = max(ret, query(1, idx[p], idx[u]));
        u = far[p];
        p = top[u];
    }
    if (u == v)
        return ret;
    if (dep[u] > dep[v])
        swap(u, v);
    ret = max(ret, query(1, idx[son[u]], idx[v]));
    return ret;
}

int main () {
    int cas = 0;
    while (scanf("%d%d", &N, &M) == 2) {
        if (cas++)
            printf("\n");

        init();

        int u, v;
        scanf("%d", &Q);
        while (Q--) {
            scanf("%d%d", &u, &v);
            printf("%d\n", solve(u, v));
        }
    }
    return 0;
}

uva 11354 - Bond(树链剖分)