Codeforces Beta Round #19 D線段樹

D. Points

time limit per test2 seconds
memory limit per test256 megabytes

Pete and Bob invented a new interesting game. Bob takes a sheet of paper and locates a Cartesian coordinate system on it as follows: point (0, 0) is located in the bottom-left corner, Ox axis is directed right, Oy axis is directed up. Pete gives Bob requests of three types:

add x y — on the sheet of paper Bob marks a point with coordinates (x, y). For each request of this type it’s guaranteed that point (x, y) is not yet marked on Bob’s sheet at the time of the request.
remove x y — on the sheet of paper Bob erases the previously marked point with coordinates (x, y). For each request of this type it’s guaranteed that point (x, y) is already marked on Bob’s sheet at the time of the request.
find x y — on the sheet of paper Bob finds all the marked points, lying strictly above and strictly to the right of point (x, y). Among these points Bob chooses the leftmost one, if it is not unique, he chooses the bottommost one, and gives its coordinates to Pete.
Bob managed to answer the requests, when they were 10, 100 or 1000, but when their amount grew up to 2·105, Bob failed to cope. Now he needs a program that will answer all Pete’s requests. Help Bob, please!

Input
The first input line contains number n (1 ≤ n ≤ 2·105) — amount of requests. Then there follow n lines — descriptions of the requests. add x y describes the request to add a point, remove x y — the request to erase a point, find x y — the request to find the bottom-left point. All the coordinates in the input file are non-negative and don’t exceed 109.

Output
For each request of type find x y output in a separate line the answer to it — coordinates of the bottommost among the leftmost marked points, lying strictly above and to the right of point (x, y). If there are no points strictly above and to the right of point (x, y), output -1.

Sample test(s)
input
7
add 1 1
add 3 4
find 0 0
remove 1 1
find 0 0
add 1 1
find 0 0
output
1 1
3 4
1 1
input
13
add 5 5
add 5 6
add 5 7
add 6 5
add 6 6
add 6 7
add 7 5
add 7 6
add 7 7
find 6 6
remove 7 7
find 6 6
find 4 4
output
7 7
-1
5 5

#include <iostream>
#include <cstdio>
#include <set>
#include <cstring>
#include <algorithm>
#include <cassert>
using namespace std ;

typedef pair<int , int > PII ;
const int N = 2e5 + 11 ;

int num[N] ; int cnt ;
int oper[N][3] ;
int n ;

int at(int x) {
    return lower_bound(num , num+cnt , x)-num+1 ;
}

struct Segment {
    set<int> sset[N] ;
    int fmax[N<<2] ;
    int x1 , y1 ;
    int ansx , ansy ;
    int n ;

    void init(int x) {
        n = x ;
        build(1 , 1 , n) ;
    }

    void up(int u) {
        fmax[u] = max(fmax[u<<1] , fmax[u<<1|1]) ;
    }

    void build(int u , int l , int r) {
        if(l == r) {
            fmax[u] = -1 ;
            sset[r].clear() ;
            return ;
        }
        int mid = (l+r)>>1 ;
        build(u<<1 , l , mid) ;
        build(u<<1|1 , mid+1 , r) ;
        up(u) ;
    }

    PII find(int a , int b) {
        ansx = -1 , ansy = -1 ;
        a = at(a+1) ; ++b ;
        x1 = a , y1 = n ;
        _find(1 , 1 , n , b) ;
        return make_pair(ansx , ansy) ;
    }

    void query(int u ,int l ,int r, int d) {
        if(l == r) {
            ansx = num[r-1] ;
            ansy = *sset[r].lower_bound(d) ;
            return ;
        }
        int mid = (l+r)>>1 ;
        if(fmax[u<<1] >= d) query(u<<1 , l , mid , d) ;
        else query(u<<1|1 , mid+1 , r , d) ;
    }

    void _find(int u , int l , int r , int d) {
        if(x1 <= l && r <= y1) {
            if(fmax[u] >= d) {
                query(u ,l , r , d) ;
            }
            return ;
        }
        int mid = (l+r)>>1 ;
        if(x1 <= mid && fmax[u] >= d) _find(u<<1 , l , mid , d) ;
        if(ansx == -1 && y1 > mid && fmax[u<<1|1] >= d) _find(u<<1|1 , mid+1 , r , d) ;
    }

    void add(int a , int b) {
        x1 = y1 = at(a) ;
        _add(1 , 1 , n , b) ;
    }

    void _add(int u , int l , int r , int b) {
        if(x1 <= l && r <= y1) {
            sset[r].insert(b) ;
            fmax[u] = *sset[r].rbegin() ;
            return ;
        }
        int mid = (l+r)>>1 ;
        if(x1 <= mid) _add(u<<1 , l , mid , b ) ;
        if(y1 > mid) _add(u<<1|1 , mid+1 , r , b) ;
        up(u) ;
    }

    void del(int a , int b) {
        x1 = y1 = at(a) ;
        _del(1 , 1 , n , b) ;
    }

    void _del(int u , int l ,int r , int b) {
        if(x1 <= l && r <= y1) {
            sset[r].erase(b) ;
            if(sset[r].size() == 0) fmax[u] = -1 ;
            else fmax[u] = *(sset[r].rbegin()) ;
            return ;
        }
        int mid = (l+r)>>1 ;
        if(x1 <= mid) _del(u<<1 , l , mid , b) ;
        if(y1 > mid) _del(u<<1|1 , mid+1 , r , b) ;
        up(u) ;
    }
};

Segment seg ;

void init() {
    char str[10] ;
    for(int i = 0 ; i < n ; ++i) {
        scanf("%s%d%d" , str , &oper[i][1] , &oper[i][2]) ;
        if(str[0] == 'a') oper[i][0] = 0 ;
        else if(str[0] == 'r') oper[i][0] = 1 ;
        else if(str[0] == 'f') oper[i][0] = 2 ;
        num[i] = oper[i][1] ;
    }
    sort(num , num+n) ;
    cnt = unique(num  , num+n)-num ;
}

void work() {
    seg.init(cnt) ;
    for(int i = 0 ; i < n ; ++i) {
        if(oper[i][0] == 0) {
            seg.add(oper[i][1] , oper[i][2]) ;
        }else if(oper[i][0] == 1) {
            seg.del(oper[i][1] , oper[i][2]) ;
        }else if(oper[i][0] == 2) {
            PII ans = seg.find(oper[i][1] , oper[i][2]) ;
            if(ans.first != -1) printf("%d %d\n" , ans.first  , ans.second) ;
            else printf("-1\n") ;
        }
    }
}

int  main() {
    //freopen("data.in" , "r" , stdin) ;
    while(scanf("%d" ,&n)==1) {
        init() ;
        work() ;
    }
}