【Codeforces Round 367 (Div 2) D】【字典树典型题】Vasiliy's Multiset

D. Vasiliy's Multiset

time limit per test
4 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

Author has gone out of the stories about Vasiliy, so here is just a formal task description.
You are given q queries
and a multiset A, initially containing only integer 0.
There are three types of queries:

"+ x" — add integer x to
multiset A.

"- x" — erase one occurrence of integer x from
multiset A. It's guaranteed that at least one x is
present in the multiset A before this query.

"? x" — you are given integer x and
need to compute the value 

,
i.e. the maximum value of bitwise exclusive OR (also know as XOR) of integer x and
some integer y from the multiset A.
Multiset is a set, where equal elements are allowed.

Input
The first line of the input contains a single integer q (1 ≤ q ≤ 200 000) —
the number of queries Vasiliy has to perform.
Each of the following q lines
of the input contains one of three characters '+', '-'
or '?' and an integer xi (1 ≤ xi ≤ 109).
It's guaranteed that there is at least one query of the third type.
Note, that the integer 0 will always
be present in the set A.

Output
For each query of the type '?' print one integer — the maximum value of bitwise
exclusive OR (XOR) of integer xi and
some integer from the multiset A.

Example

input

10
+ 8
+ 9
+ 11
+ 6
+ 1
? 3
- 8
? 3
? 8
? 11

output

11
10
14
13

Note
After first five operations multiset A contains
integers 0, 8, 9, 11, 6 and 1.
The answer for the sixth query is integer 

 —
maximum among integers 

, 

, 

, 

 and 

.

#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
void fre() { freopen("c://test//input.in", "r", stdin); freopen("c://test//output.out", "w", stdout); }
#define MS(x,y) memset(x,y,sizeof(x))
#define MC(x,y) memcpy(x,y,sizeof(x))
#define MP(x,y) make_pair(x,y)
#define ls o<<1
#define rs o<<1|1
typedef long long LL;
typedef unsigned long long UL;
typedef unsigned int UI;
template <class T1, class T2>inline void gmax(T1 &a, T2 b) { if (b>a)a = b; }
template <class T1, class T2>inline void gmin(T1 &a, T2 b) { if (b<a)a = b; }
const int N = 1e7 + 10, M = 0, Z = 1e9 + 7, ms63 = 0x3f3f3f3f;
int nxt
[2], id;
int num
;
void ins(int x, int val)
{
int k = 0;
for (int i = 29; ~i; --i)
{
int y = x >> i & 1;
if (nxt[k][y] == 0)nxt[k][y] = ++id;
k = nxt[k][y];
num[k] += val;
}
}
int check(int x)
{
int ret = 0;
int k = 0;
for (int i = 29; ~i; --i)
{
int y = x >> i & 1;
if (nxt[k][y] == 0 || num[nxt[k][y]] == 0)y ^= 1;
else ret |= 1 << i;
k = nxt[k][y];
}
return ret;
}
int main()
{
int n;
while (~scanf("%d", &n))
{
MS(nxt, 0); id = 0;
MS(num, 0);
ins(0, 1);
while (n--)
{
char ch; int x;
scanf(" %c%d", &ch, &x);
if (ch == '+')ins(x, 1);
else if (ch == '-')ins(x, -1);
else printf("%d\n", check(~x));
}
}
return 0;
}