array（2019CCPC网络预选赛 hdu6703主席树+set）主席树求大于等于k的最小值
Problem Description
You are given an array a1,a2,…,an(∀i∈[1,n],1≤ai≤n). Initially, each element of the array is unique.
Moreover, there are m instructions.
Each instruction is in one of the following two formats:
- (1,pos),indicating to change the value of apos to apos+10,000,000;
- (2,r,k),indicating to ask the minimum value which is not equal to any ai ( 1≤i≤r ) and **not less ** than k.
Please print all results of the instructions in format 2.
Input
The first line of the input contains an integer T(1≤T≤10), denoting the number of test cases.
In each test case, there are two integers n(1≤n≤100,000),m(1≤m≤100,000) in the first line, denoting the size of array a and the number of instructions.
In the second line, there are n distinct integers a1,a2,…,an (∀i∈[1,n],1≤ai≤n),denoting the array.
For the following m lines, each line is of format (1,t1) or (2,t2,t3).
The parameters of each instruction are generated by such way :
For instructions in format 1 , we defined pos=t1⊕LastAns . (It is promised that 1≤pos≤n)
For instructions in format 2 , we defined r=t2⊕LastAns,k=t3⊕LastAns. (It is promised that 1≤r≤n,1≤k≤n )
(Note that ⊕ means the bitwise XOR operator. )
Before the first instruction of each test case, LastAns is equal to 0 .After each instruction in format 2, LastAns will be changed to the result of that instruction.
(∑n≤510,000,∑m≤510,000 )
Output
For each instruction in format 2, output the answer in one line.
Sample Input
3
5 9
4 3 1 2 5
2 1 1
2 2 2
2 6 7
2 1 3
2 6 3
2 0 4
1 5
2 3 7
2 4 3
10 6
1 2 4 6 3 5 9 10 7 8
2 7 2
1 2
2 0 5
2 11 10
1 3
2 3 2
10 10
9 7 5 3 4 10 6 2 1 8
1 10
2 8 9
1 12
2 15 15
1 12
2 1 3
1 9
1 12
2 2 2
1 9
Sample Output
1
5
2
2
5
6
1
6
7
3
11
10
11
4
8
11
Hint
note:
After the generation procedure ,the instructions of the first test case are :
2 1 1, in format 2 and r=1 , k=1
2 3 3, in format 2 and r=3 , k=3
2 3 2, in format 2 and r=3 , k=2
2 3 1, in format 2 and r=3 , k=1
2 4 1, in format 2 and r=4 , k=1
2 5 1, in format 2 and r=5 , k=1
1 3 , in format 1 and pos=3
2 5 1, in format 2 and r=5 , k=1
2 5 2, in format 2 and r=5 , k=2
the instructions of the second test case are :
2 7 2, in format 2 and r=7 , k=2
1 5 , in format 1 and pos=5
2 7 2, in format 2 and r=7 , k=2
2 8 9, in format 2 and r=8 , k=9
1 8 , in format 1 and pos=8
2 8 9, in format 2 and r=8 , k=9
the instructions of the third test case are :
1 10 , in format 1 and pos=10
2 8 9 , in format 2 and r=8 , k=9
1 7 , in format 1 and pos=7
2 4 4 , in format 2 and r=4 , k=4
1 8 , in format 1 and pos=8
2 5 7 , in format 2 and r=5 , k=7
1 1 , in format 1 and pos=1
1 4 , in format 1 and pos=4
2 10 10, in format 2 and r=10 , k=10
1 2 , in format 1 and pos=2
昨天卡了很久的一个题，你开始线段树+set一直超时，后来改了主席树，但是还是卡了很久。。
题意：要找出一个数，这个数在1~r中不能出现过，并且还要不小于k。并且读入的数据还都要异或上上一次的答案。
一开始理解错了，以为必须是数组里的数才行。但是第一个样例中就有一个数不是数组里的数，除此之外，题目中有说所有的数都是独一无二的。在执行操作1的时候，一个数加上1e7之后，就相当于作废了。因为数组中所有的数字都是不大于1e5的，所以异或之后的值也是不大于1e5的。这样的话，在加上1e7之后，就相当于这个值在1~r中删除了，又可以再用了。那这样我们把这样的值存到一个set里面，r+1到n的值用主席树去求。主席树是好多权值线段树的集合，是按着权值来的，存的是每个数的出现的个数。用主席树去求r+1 ~ n中大于等于k最小的数。
代码如下：
#include昨天写的超时的代码（线段树+set）当个借鉴吧
代码如下：
#include努力加油a啊，(o)/~