Problem 2

$des$

一个无限长的 01 序列，初始全为 0，每次选择一个区间 [l,r] 进行操作，有三种操作：
1. l r 将 [l,r] 中所有元素变成 1。
2. l r 将 [l,r] 中所有元素变成 0。
3. l r 将 [l,r] 中所有元素异或上 1。
每次操作后询问最左边的 0 在哪个位置.

$sol$

线段树

将所有可能成为答案的点加入线段树的根节点维护

$code$

#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <cmath>
#include <cstring>

using namespace std;

#define LL long long
#define Rep(i, a, b) for(int i = a; i <= b; i ++)
#define gc getchar()

inline LL read() {
    LL 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;
}

const int N = 1e5 + 10, M = N * 6 * 2;

struct Node {
    LL opt, l, r;
} Ask[N];
LL A[M], js;
int n;

struct Node_ {
    int Cnt[2][M << 2], Size[M << 2], F[M << 2];
    
    #define lson jd << 1
    #define rson jd << 1 | 1
    
    void Build_tree(int l, int r, int jd) {
        F[jd] = -1;
        Size[jd] = r - l + 1;
        Cnt[0][jd] = Size[jd];
        if(l == r) return ;
        int mid = (l + r) >> 1;
        Build_tree(l, mid, lson), Build_tree(mid + 1, r, rson);
    }
    
    void Push_down(int jd) {
        int f = F[jd];
        if(f == 1) {
            F[lson] = F[rson] = 1;
            Cnt[1][lson] = Size[lson], Cnt[1][rson] = Size[rson];
            Cnt[0][lson] = 0, Cnt[0][rson] = 0;
            F[jd] = -1;
        } else if(f == 0) {
            F[lson] = F[rson] = 0;
            Cnt[0][lson] = Size[lson], Cnt[0][rson] = Size[rson];
            Cnt[1][lson] = 0, Cnt[1][rson] = 0;
            F[jd] = -1;
        } else {
            if(F[lson] == 2) {
                swap(Cnt[1][lson], Cnt[0][lson]);
                F[lson] = -1;
            } else {
                if(F[lson] == -1) {
                    F[lson] = 2;
                    swap(Cnt[1][lson], Cnt[0][lson]);
                } else if(F[lson] == 0) {
                    F[lson] = 1;
                    Cnt[1][lson] = Size[lson], Cnt[0][lson] = 0;
                } else {
                    F[lson] = 0;
                    Cnt[0][lson] = Size[lson], Cnt[1][lson] = 0;
                }
            }
            if(F[rson] == 2) {
                swap(Cnt[1][rson], Cnt[0][rson]);
                F[rson] = -1;
            } else {
                if(F[rson] == -1) {
                    F[rson] = 2;
                    swap(Cnt[1][rson], Cnt[0][rson]);
                } else if(F[rson] == 0) {
                    F[rson] = 1;
                    Cnt[1][rson] = Size[rson], Cnt[0][rson] = 0;
                } else {
                    F[rson] = 0;
                    Cnt[0][rson] = Size[rson], Cnt[1][rson] = 0;
                }
            }
            F[jd] = -1;
        }
    }
    
    void Sec_G(int l, int r, int jd, int x, int y, int num){
        if(x <= l && r <= y) {
            Cnt[num][jd] = Size[jd];
            Cnt[num ^ 1][jd] = 0;
            F[jd] = num;
//            cout << Cnt[1][jd] << " " << Cnt[0][jd] << "\n";
            return ;
        }
        if(F[jd] != -1) Push_down(jd);
        int mid = (l + r) >> 1;
//        cout << Cnt[0][lson] << "\n";
        if(x <= mid) Sec_G(l, mid, lson, x, y, num);
        if(y > mid)  Sec_G(mid + 1, r, rson, x, y, num);
        Cnt[1][jd] = Cnt[1][lson] + Cnt[1][rson];
        Cnt[0][jd] = Cnt[0][lson] + Cnt[0][rson];
    }
    
    int Ask(int l, int r, int jd) {
        if(l == r) {
            return l;
        }        
        if(F[jd] != -1) Push_down(jd);
        int mid = (l + r) >> 1;
//        cout << Cnt[0][lson] << "\n";
        if(Cnt[0][lson]) return Ask(l, mid, lson);
        else return Ask(mid + 1, r, rson);
    }
    
    void Seg_fz(int l, int r, int jd, int x, int y) {
        if(x <= l && r <= y) {
            if(F[jd] == -1) {
                swap(Cnt[1][jd], Cnt[0][jd]);
                F[jd] = 2;
                return ;                    
            } else if(F[jd] == 0) {
                F[jd] = 1;
                Cnt[1][jd] = Size[jd];
                Cnt[0][jd] = 0;
            } else if(F[jd] == 1) {
                F[jd] = 0;
                Cnt[1][jd] = 0;
                Cnt[0][jd] = Size[jd];
            } else {
                F[jd] = -1;
                swap(Cnt[1][jd], Cnt[0][jd]);
            }
            return ;
        }
        if(F[jd] != -1) Push_down(jd);
        int mid = (l + r) >> 1;
//        cout << Cnt[0][lson] << "\n";
        if(x <= mid) Seg_fz(l, mid, lson, x, y);
        if(y > mid)  Seg_fz(mid + 1, r, rson, x, y);
        Cnt[1][jd] = Cnt[1][lson] + Cnt[1][rson];
        Cnt[0][jd] = Cnt[0][lson] + Cnt[0][rson];
    }    
} Segtree;

inline LL Getans() {
    int w = Segtree.Ask(1, js, 1);
//    if(A[w - 1] + 1 != A[w]) return A[w - 1] + 1;
//    else return A[w];
    return A[w];
}

int main() {
    freopen("a.in", "r", stdin);
    freopen("a.out", "w", stdout);
    n = read();
    Rep(i, 1, n) {
        LL opt = read(), l = read(), r = read();
        A[++ js] = l, A[++ js] = r; A[++ js] = max(1ll, l - 1), A[++ js] = r + 1;
        Ask[i] = (Node) {
            opt, l, r
        };
    }
    A[++ js] = 1;
    sort(A + 1, A + js + 1);
    js = unique(A + 1, A + js + 1) - A - 1;
    Segtree.Build_tree(1, js, 1);
//    Rep(i, 1, 10) cout << Segtree.F[i] << " ";
//    return 0;
    Rep(i, 1, n) {
        LL opt = Ask[i].opt, l = Ask[i].l, r = Ask[i].r;
        int wl = lower_bound(A + 1, A + js + 1, l) - A;
        int wr = lower_bound(A + 1, A + js + 1, r) - A;
        if(opt == 1) {
            Segtree.Sec_G(1, js, 1, wl, wr, 1);    
            cout << Getans() << "\n";
        } else if(opt == 2) {
            Segtree.Sec_G(1, js, 1, wl, wr, 0);
            cout << Getans() << "\n";
        } else {
            Segtree.Seg_fz(1, js, 1, wl, wr);
            cout << Getans() << "\n";
        }
    }
    
    
    return 0;
}