Luogu 4899 [IOI2018] werewolf 狼人

UOJ 407

kruskal重构树

所有边的边权记为两个点的$max$建立一棵重构树，这样子可以做出一个点走不超过$R$能到达的点的集合，再把所有边的边权记为两个点的$min$建立重构树，这样子可以做出一个点走不少于$L$所能到达的点的集合

注意到这两个集合其实是重构树叶子的一段区间，问题有解等价于区间有交，这样子就变成了一个二维数点问题

暴力线段树合并过不去，别问我是怎么知道的

一开始交的时候边数开错了

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include "werewolf.h"
using namespace std;

const int N = 8e5 + 5;
const int M = 2e5 + 5;
const int Lg = 22;
const int inf = 1 << 30;

int n, m, qn, tot = 0, head[N], ufs[N];
int rt1, rt2, ncnt, w[N], fa[N][Lg];
int ln[N], rn[N], dfsc = 0, id1[M], id2[M], px1[M], px2[M], ans[M];

struct Edge {
    int to, nxt;
} e[N];

inline void add(int from, int to) {
    e[++tot].to = to;
    e[tot].nxt = head[from];
    head[from] = tot;
}

struct Path {
    int u, v, val;

    friend bool operator < (const Path x, const Path y) {
        return x.val < y.val;
    }

} pat[M << 1];

struct Query {
    int s, t, lv, rv;
} q[M];

struct Seg {
    int l, r, id, type;
};
vector <Seg> vec[M];

namespace Fread {
    const int L = 1 << 15;
    
    char buffer[L], *S, *T;
    
    inline char Getchar() {
        if(S == T) {
            T = (S = buffer) + fread(buffer, 1, L, stdin);
            if(S == T) return EOF;
        }
        return *S++;
    }
    
    template <class T> 
    inline void read(T &X) {
        char ch; T op = 1;
        for(ch = Getchar(); ch > '9' || ch < '0'; ch = Getchar())
            if(ch == '-') op = -1;
        for(X = 0; ch >= '0' && ch <= '9'; ch = Getchar()) 
            X = (X << 1) + (X << 3) + ch - '0'; 
        X *= op;
    }
    
} using Fread :: read;   

namespace Fwrite {
    const int L = 1 << 15;
    
    char buf[L], *pp = buf;
    
    void Putchar(const char c) {
        if(pp - buf == L) fwrite(buf, 1, L, stdout), pp = buf;
        *pp++ = c;
    }
    
    template<typename T>
    void print(T x) {
        if(x < 0) {
            Putchar('-');
            x = -x;
        }
        if(x > 9) print(x / 10);
        Putchar(x % 10 + '0');
    }
    
    void fsh() {
        fwrite(buf, 1, pp - buf, stdout);
        pp = buf;
    }
    
    template <typename T>
    inline void write(T x, char ch = 0) {
        print(x);
        if (ch != 0) Putchar(ch);
    }

} using Fwrite :: write;

/*
namespace SegT {
    struct Node {
        int lc, rc, sum;
    } s[N * 20];
    
    int root[N], pcnt = 0, top = 0, pool[N * 20];

    #define lc(p) s[p].lc
    #define rc(p) s[p].rc
    #define sum(p) s[p].sum
    #define mid ((l + r) >> 1)

    inline void up(int p) {
        if (!p) return;
        sum(p) = sum(lc(p)) + sum(rc(p));
    }

    inline int newNode() {
        if (top) return pool[top--];
        else return ++pcnt;
    }

    inline void del(int p) {
        pool[++top] = p;
    }

    int merge(int u, int v, int l, int r) {
        if (!u || !v) return u + v;
        int p = newNode();
        if (l == r) {
            sum(p) = sum(u) + sum(v);
        } else {
            lc(p) = merge(lc(u), lc(v), l, mid);
            rc(p) = merge(rc(u), rc(v), mid + 1, r);
            up(p);    
        }
        del(u), del(v);
        return p;
    }

    void build(int &p, int l, int r, int x) {
        if (!p) p = newNode();
        if (l == r) {
            ++sum(p);
            return;
        }
        if (x <= mid) build(lc(p), l, mid, x);
        else build(rc(p), mid + 1, r, x);
        up(p);
    }

    int query(int p, int l, int r, int x, int y) {
        if (!p) return 0;
        if (x <= l && y >= r) return sum(p);
        int res = 0;
        if (x <= mid) res += query(lc(p), l, mid, x, y);
        if (y > mid) res += query(rc(p), mid + 1, r, x, y);
        up(p);
        return res;
    }

    void print(int k) {
        printf("%d : ", k);
        for (int i = 1; i <= n; i++)
            printf("%d ", query(root[k], 1, n, i, i));
        puts("");
    }

    #undef mid

} using namespace SegT;    */

int find(int x) {
    return ufs[x] == x ? x : ufs[x] = find(ufs[x]);
}

void dfs1(int x, int fat) {
    bool isLeaf = 1; 
    ln[x] = inf, rn[x] = -inf;
    fa[x][0] = fat;
    for (int i = 1; i <= 20; i++) fa[x][i] = fa[fa[x][i - 1]][i - 1];
    for (int i = head[x]; i; i = e[i].nxt) {
        int y = e[i].to;
        isLeaf = 0;
        dfs1(y, x);
        ln[x] = min(ln[x], ln[y]);
        rn[x] = max(rn[x], rn[y]);
    }
    if (isLeaf) {
        id1[++dfsc] = x; 
        px1[x] = dfsc;
        ln[x] = rn[x] = dfsc;
    }
}

void dfs2(int x, int fat) {
    bool isLeaf = 1; 
    ln[x] = inf, rn[x] = -inf;
    fa[x][0] = fat;
    for (int i = 1; i <= 20; i++) fa[x][i] = fa[fa[x][i - 1]][i - 1];
    for (int i = head[x]; i; i = e[i].nxt) {
        int y = e[i].to;
        isLeaf = 0;
        dfs2(y, x);
        ln[x] = min(ln[x], ln[y]);
        rn[x] = max(rn[x], rn[y]);
    }
    if (isLeaf) {
        id2[++dfsc] = x - 2 * n;
        px2[x - 2 * n] = dfsc;
        ln[x] = rn[x] = dfsc;
    }
}

inline int getPos1(int x, int val) {
    w[0] = inf;
    for (int i = 20; i >= 0; i--)
        if (w[fa[x][i]] <= val) x = fa[x][i];
    return x;
}

inline int getPos2(int x, int val) {
    w[0] = 0;
    for (int i = 20; i >= 0; i--)
        if (w[fa[x][i]] >= val) x = fa[x][i];
    return x;
}   

/* void solve(int x, int fat) {
    stk[++tp] = x;
    for (int i = head[x]; i; i = e[i].nxt) {
        int y = e[i].to;
        solve(y, x);
        root[x] = merge(root[x], root[y], 1, n);
    }

    int siz = vec[x].size();
    for (int i = 0; i < siz; i++) {
        int qid = vec[x][i];
        int pos = getPos2(q[qid].s + 2 * n, q[qid].lv);
//        printf("%d %d\n", qid, pos);
        ans[qid] = query(root[x], 1, n, ln[pos - 2 * n], rn[pos - 2 * n]);
    }

//    print(x);
    --tp;
}    */

void debug(int x, int fat, bool is2 = 0) {
    printf("%d:%d\n", x, w[x]);
    if (is2) printf("%d::%d %d\n", x, ln[x - 2 * n], rn[x - 2 * n]);
    for (int i = head[x]; i; i = e[i].nxt) {
        int y = e[i].to;
        printf("%d %d\n", x, y);
        debug(y, x);
    }
}

namespace Bit {
    int s[M];

    #define lowbit(p) (p & (-p))

    inline void modify(int p) {
        for (; p <= n; p += lowbit(p)) ++s[p];
    }

    inline int query(int p) {
        int res = 0;
        for (; p > 0; p -= lowbit(p)) res += s[p];
        return res;
    }

} using namespace Bit;

/*int main() {
    #ifndef ONLINE_JUDGE
        freopen("sample.in", "r", stdin);
        freopen("my.out", "w", stdout);
    #endif

    read(n), read(m), read(qn);
    for (int i = 1; i <= m; i++) {
        read(pat[i].u), read(pat[i].v);
        ++pat[i].u, ++pat[i].v;
        pat[i].val = max(pat[i].u, pat[i].v);
    }

    for (int i = 1; i <= 4 * n; i++) ufs[i] = i;
    ncnt = n;
    sort(pat + 1, pat + 1 + m);
    for (int cnt = 0, i = 1; i <= m; i++) {
        int u = pat[i].u, v = pat[i].v;
        int fu = find(u), fv = find(v);
        if (fu == fv) continue;
        ++cnt, ++ncnt;
        w[ncnt] = pat[i].val;
        ufs[fu] = ufs[fv] = ncnt;
        add(ncnt, fu), add(ncnt, fv);
        if (cnt == n - 1) break;
    }
    rt1 = find(1), dfsc = 0;
    dfs1(rt1, 0);

    // debug(rt1, 0);

    for (int i = 1; i <= m; i++) pat[i].val = min(pat[i].u, pat[i].v);
    ncnt = 3 * n;
    sort(pat + 1, pat + 1 + m); 
    for (int cnt = 0, i = m; i >= 1; i--) {
        int u = pat[i].u + 2 * n, v = pat[i].v + 2 * n;
        int fu = find(u), fv = find(v);
        if (fu == fv) continue;
        ++cnt, ++ncnt;
        w[ncnt] = pat[i].val;
        ufs[fu] = ufs[fv] = ncnt;
        add(ncnt, fu), add(ncnt, fv);
        if (cnt == n - 1) break;
    }
    rt2 = find(2 * n + 1), dfsc = 0;
    dfs2(rt2, 0);
    
    // puts("");
    // debug(rt2, 0, 1);
    // for (int i = 1; i <= n; i++)
    //     printf("%d%c", id[i], " \n"[i == n]);   

    // for (int i = 1; i <= n; i++)
    //     printf("%d ", id1[i]);
    // printf("\n");
    // for (int i = 1; i <= n; i++)
    //     printf("%d ", id2[i]);
    // printf("\n");
    // for (int i = 1; i <= n; i++)
    //     printf("%d ", px2[id1[i]]);
    // printf("\n");

    for (int i = 1; i <= qn; i++) {
        read(q[i].s), read(q[i].t), read(q[i].lv), read(q[i].rv);
        ++q[i].s, ++q[i].t, ++q[i].lv, ++q[i].rv;
        int pos1 = getPos1(q[i].t, q[i].rv), pos2 = getPos2(q[i].s + 2 * n, q[i].lv);
//        printf("%d %d %d %d\n", ln[pos1], rn[pos1], ln[pos2], rn[pos2]);
        vec[ln[pos1] - 1].push_back((Seg) {ln[pos2], rn[pos2], i, -1});
        vec[rn[pos1]].push_back((Seg) {ln[pos2], rn[pos2], i, 1});
    }
    for (int i = 1; i <= n; i++) {
        int siz = vec[i].size();
        modify(px2[id1[i]]);
        for (int j = 0; j < siz; j++) {
            int l = vec[i][j].l, r = vec[i][j].r, t = vec[i][j].type, qid = vec[i][j].id;
            ans[qid] += t * (query(r) - query(l - 1));
        }
    }

    // for (int i = 1; i <= qn; i++)
    //     write(ans[i] > 0 ? 1 : 0, '\n');

    for (int i = 1; i <= qn; i++)
        write(ans[i] > 0 ? 1 : 0, '\n');
    Fwrite :: fsh();
    return 0;
}   */

vector<int> check_validity(int N, vector<int> X, vector<int> Y, vector<int> S, vector<int> E, vector<int> L, vector<int> R) {
    // read(n), read(m), read(qn);
    n = N, m = X.size(), qn = S.size();
    for (int i = 1; i <= m; i++) {
        // read(pat[i].u), read(pat[i].v);
        pat[i].u = X[i - 1], pat[i].v = Y[i - 1];
        ++pat[i].u, ++pat[i].v;
        pat[i].val = max(pat[i].u, pat[i].v);
    }

    for (int i = 1; i <= 4 * n; i++) ufs[i] = i;
    ncnt = n;
    sort(pat + 1, pat + 1 + m);
    for (int cnt = 0, i = 1; i <= m; i++) {
        int u = pat[i].u, v = pat[i].v;
        int fu = find(u), fv = find(v);
        if (fu == fv) continue;
        ++cnt, ++ncnt;
        w[ncnt] = pat[i].val;
        ufs[fu] = ufs[fv] = ncnt;
        add(ncnt, fu), add(ncnt, fv);
        if (cnt == n - 1) break;
    }
    rt1 = find(1), dfsc = 0;
    dfs1(rt1, 0);

    // debug(rt1, 0);

    for (int i = 1; i <= m; i++) pat[i].val = min(pat[i].u, pat[i].v);
    ncnt = 3 * n;
    sort(pat + 1, pat + 1 + m); 
    for (int cnt = 0, i = m; i >= 1; i--) {
        int u = pat[i].u + 2 * n, v = pat[i].v + 2 * n;
        int fu = find(u), fv = find(v);
        if (fu == fv) continue;
        ++cnt, ++ncnt;
        w[ncnt] = pat[i].val;
        ufs[fu] = ufs[fv] = ncnt;
        add(ncnt, fu), add(ncnt, fv);
        if (cnt == n - 1) break;
    }
    rt2 = find(2 * n + 1), dfsc = 0;
    dfs2(rt2, 0);
    
    // puts("");
    // debug(rt2, 0, 1);
    // for (int i = 1; i <= n; i++)
    //     printf("%d%c", id[i], " \n"[i == n]);   

    // for (int i = 1; i <= n; i++)
    //     printf("%d ", id1[i]);
    // printf("\n");
    // for (int i = 1; i <= n; i++)
    //     printf("%d ", id2[i]);
    // printf("\n");
    // for (int i = 1; i <= n; i++)
    //     printf("%d ", px2[id1[i]]);
    // printf("\n");

    for (int i = 1; i <= qn; i++) {
        // read(q[i].s), read(q[i].t), read(q[i].lv), read(q[i].rv);
        q[i].s = S[i - 1], q[i].t = E[i - 1], q[i].lv = L[i - 1], q[i].rv = R[i - 1];
        ++q[i].s, ++q[i].t, ++q[i].lv, ++q[i].rv;
        int pos1 = getPos1(q[i].t, q[i].rv), pos2 = getPos2(q[i].s + 2 * n, q[i].lv);
//        printf("%d %d %d %d\n", ln[pos1], rn[pos1], ln[pos2], rn[pos2]);
        vec[ln[pos1] - 1].push_back((Seg) {ln[pos2], rn[pos2], i, -1});
        vec[rn[pos1]].push_back((Seg) {ln[pos2], rn[pos2], i, 1});
    }
    for (int i = 1; i <= n; i++) {
        int siz = vec[i].size();
        modify(px2[id1[i]]);
        for (int j = 0; j < siz; j++) {
            int l = vec[i][j].l, r = vec[i][j].r, t = vec[i][j].type, qid = vec[i][j].id;
            ans[qid] += t * (query(r) - query(l - 1));
        }
    }

    // for (int i = 1; i <= qn; i++)
    //     write(ans[i] > 0 ? 1 : 0, '\n');

    // for (int i = 1; i <= qn; i++)
    //     write(ans[i] > 0 ? 1 : 0, '\n');
    // Fwrite :: fsh();
    vector <int>  retAns;
    for (int i = 1; i <= qn; i++) retAns.push_back(ans[i] > 0 ? 1 : 0);
    return retAns;
}