2019牛客暑期多校训练营（第八场）- Explorer

LCT

和魔法森林类似，先排序一个关键字，用LCT动态维护另一个关键字。

这里把r从大到小排序，然后动态加边。

因为r的顺序是确定的，每次加入新边以后，r肯定是看加入的这条边的，所以我们考虑l就好了。

对于l，我们要求能够通过的数量，肯定是要保留合法的大范围，因为小范围包含在了大范围里。

之后就和魔法森林一样维护1～n的链。

#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
#define full(a, b) memset(a, b, sizeof a)
#define __fastIn ios::sync_with_stdio(false), cin.tie(0)
#define pb push_back
using namespace std;
typedef long long LL;
inline int lowbit(int x){ return x & (-x); }
inline int read(){
    int ret = 0, w = 0; char ch = 0;
    while(!isdigit(ch)){
        w |= ch == '-', ch = getchar();
    }
    while(isdigit(ch)){
        ret = (ret << 3) + (ret << 1) + (ch ^ 48);
        ch = getchar();
    }
    return w ? -ret : ret;
}
template <typename A>
inline A __lcm(A a, A b){ return a / __gcd(a, b) * b; }
template <typename A, typename B, typename C>
inline A fpow(A x, B p, C lyd){
    A ans = 1;
    for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;
    return ans;
}
const int N = 200005;
int n, m, tot, ch[N][2], fa[N], rev[N], mx[N], id[N], st[N], w[N];
struct Edge{
    int u, v, l, r;
    bool operator < (const Edge &rhs) const {
        return r > rhs.r;
    }
}e[N];

int build(int val){
    ++ tot;
    w[tot] = mx[tot] = val, id[tot] = tot;
    ch[tot][0] = ch[tot][1] = rev[tot] = fa[tot] = 0;
    return tot;
}

bool isRoot(int x){
    return ch[fa[x]][0] != x && ch[fa[x]][1] != x;
}

void push_up(int rt){
    int l = ch[rt][0], r = ch[rt][1];
    id[rt] = rt, mx[rt] = w[rt];
    if(mx[l] > mx[rt]) mx[rt] = mx[l], id[rt] = id[l];
    if(mx[r] > mx[rt]) mx[rt] = mx[r], id[rt] = id[r];
}

void reverse(int x){
    rev[x] ^= 1;
    swap(ch[x][0], ch[x][1]);
}

void push_down(int x){
    if(rev[x]){
        int l = ch[x][0], r = ch[x][1];
        if(l) reverse(l);
        if(r) reverse(r);
        rev[x] ^= 1;
    }
}

void rotate(int x){
    int y = fa[x], z = fa[y], p = (ch[y][1] == x) ^ 1;
    ch[y][p ^ 1] = ch[x][p], fa[ch[x][p]] = y;
    if(!isRoot(y)) ch[z][ch[z][1] == y] = x;
    fa[x] = z, fa[y] = x, ch[x][p] = y;
    push_up(y), push_up(x);
}

void splay(int x){
    int pos = 0; st[++ pos] = x;
    for(int i = x; !isRoot(i); i = fa[i]) st[++ pos] = fa[i];
    while(pos) push_down(st[pos --]);
    while(!isRoot(x)){
        int y = fa[x], z = fa[y];
        if(!isRoot(y)){
            (ch[y][0] == x) ^ (ch[z][0] == y) ? rotate(x) : rotate(y);
        }
        rotate(x);
    }
    push_up(x);
}

void access(int x){
    for(int p = 0; x; p = x, x = fa[x])
        splay(x), ch[x][1] = p, push_up(x);
}

void makeRoot(int x){
    access(x), splay(x), reverse(x);
}

void link(int x, int y){
    makeRoot(x), fa[x] = y;
}

int findRoot(int x){
    access(x), splay(x);
    while(ch[x][0]) push_down(x), x = ch[x][0];
    splay(x);
    return x;
}

void split(int x, int y){
    makeRoot(x), access(y), splay(y);
}

bool isConnect(int x, int y){
    makeRoot(x);
    return findRoot(y) == x;
}

vector<pair<int, int>> ans;

int main(){

    n = read(), m = read();
    for(int i = 1; i <= m; i ++){
        e[i].u = read(), e[i].v = read(), e[i].l = read(), e[i].r = read();
    }
    for(int i = 1; i <= n; i ++) build(0);
    sort(e + 1, e + m + 1);
    for(int i = 1; i <= m; i ++){
        int u = e[i].u, v = e[i].v, t = build(e[i].l);
        if(!isConnect(u, v)){
            link(u, t), link(t, v);
        }
        else{
            split(u, v);
            if(mx[v] >= e[i].l){
                int p = id[v];
                splay(p);
                fa[ch[p][0]] = 0, fa[ch[p][1]] = 0;
                ch[p][0] = ch[p][1] = 0;
                link(u, t), link(t, v);
            }
        }
        if(isConnect(1, n)){
            split(1, n);
            if(mx[n] <= e[i].r) ans.pb(make_pair(mx[n], e[i].r));
        }
    }
    sort(ans.begin(), ans.end());
    int res = 0;
    for(int i = 0; i < ans.size(); i ++){
        int j = i, cur = ans[i].second;
        while(j + 1 < ans.size() && ans[j + 1].first <= cur) cur = max(cur, ans[++ j].second);
        res += cur - ans[i].first + 1;
        i = j;
    }
    printf("%d
", res);

    return 0;
}