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  • [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
    */
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  • 原文地址:https://www.cnblogs.com/shandongs1/p/8228492.html
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