[Luogu] 运输计划

https://www.luogu.org/problemnew/show/2680

inline 神奇的东西

最好戒掉吧（read()除外）

这道题将求解性问题转化为判定性问题，当然就是二分答案了

二分删掉边后最短路径的最大值 mid

将所有的比mid大的询问求交集：树上差分，cnt[s] ++, cnt[t] ++, cnt[lca(s, t)] -= 2

　　　　　　　　　　　　　　  最后统计每个节点以及该节点的子树的cnt的和，若

　　　　　　　　　　　　　 　 和==比mid大的询问数量，则说明该点与其父亲组成

　　　　　　　　　　　　　  　的这条边在所有边的交集上

判断 ：最大路径-最大的交集中的边

#include <bits/stdc++.h>

using namespace std;
const int N = 3e5 + 10;

#define gc getchar()

int Cnt[N], tree[N], fa[N], siz[N], son[N], topp[N], deep[N], head[N];
int n, m, now = 1, tim;
int L[N], R[N], D[N], dis[N];
int LCA[N];
struct Node {int u, v, w, nxt;} G[N << 1];
int js; 

inline int read(){
    int x = 0; char c = gc;
    while(c < '0' || c > '9') c = gc;
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = gc;
    return x;
}

void add(int u, int v, int w){
    G[now].u = u; G[now].v = v; G[now].w = w; G[now].nxt = head[u]; head[u] = now ++;
}

void dfs_find_son(int u, int f_, int dep){
    fa[u] = f_; deep[u] = dep; siz[u] = 1;
    for(int i = head[u]; ~ i; i = G[i].nxt){
        int v = G[i].v;
        if(v != f_){
            dis[v] = dis[u] + G[i].w;
            dfs_find_son(v, u, dep + 1);
            siz[u] += siz[v];
            if(siz[v] > siz[son[u]]) son[u] = v;
        }
    } 
}

void dfs_to_un(int u, int tp){
    topp[u] = tp;
    tree[u] = ++ tim;
    if(!son[u]) return ;
    dfs_to_un(son[u], tp);
    for(int i = head[u]; ~ i; i = G[i].nxt){
        int v = G[i].v;
        if(v != son[u] && v != fa[u]) dfs_to_un(v, v);
    }
}

int Lca(int x, int y){
    int tp1 = topp[x], tp2 = topp[y];
    while(tp1 != tp2){
        if(deep[tp1] < deep[tp2]) swap(x, y), swap(tp1, tp2);
        x = fa[tp1];
        tp1 = topp[x]; 
    }
    return deep[x] > deep[y] ? y : x;
}

void Calc(int u){
    if(!son[u]) return ;
    for(int i = head[u]; ~ i; i = G[i].nxt){
        int v = G[i].v;
        if(v != fa[u]){
            Calc(v);
            Cnt[u] += Cnt[v];    
        } 
    }
}

bool See(int x){
    for(int i = 1; i <= n; i ++) Cnt[i] = 0;
    int B(0); int Max_dis = -1, Max_w = -1;
    for(int i = 1; i <= m; i ++)
        if(D[i] > x) Max_dis = max(Max_dis, D[i]), B ++, Cnt[L[i]] ++, Cnt[R[i]] ++, Cnt[LCA[i]] -= 2;
    Calc(1);
    for(int i = 1; i <= n; i ++) if(Cnt[i] == B) Max_w = max(Max_w, dis[i] - dis[fa[i]]);
    return Max_dis - Max_w <= x ? 1 : 0;
}

int main()
{
    n = read(); m = read();
    int l = 0, r = 0, ans;
    for(int i = 1; i <= n; i ++) head[i] = -1;
    for(int i = 1; i < n; i ++){
        int u = read(), v = read(), w = read();
        add(u, v, w); add(v, u, w);
    }
    dfs_find_son(1, 0, 1);
    dfs_to_un(1, 1);
    for(int i = 1; i <= m; i ++){
        L[i] = read(); R[i] = read();
        LCA[i] = Lca(L[i], R[i]);
        D[i] = dis[L[i]] + dis[R[i]] - (dis[LCA[i]] * 2);
        r = max(r, D[i]);
    }
    
    while(l <= r){
        int mid = (l + r) >> 1;
        if(See(mid)) ans = mid, r = mid - 1;
        else l = mid + 1;
    }
    printf("%d", ans);
    return 0;
}
/*
6 3 
1 2 3 
1 6 4 
3 1 7 
4 3 6 
3 5 5 
3 6 
2 5 
4 5
*/