Sasha and a Bit of Relax（前缀异或和+二维数组+思维）

最新推荐文章于 2024-11-12 17:19:00 发布

转载最新推荐文章于 2024-11-12 17:19:00 发布 · 197 阅读

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原文链接：http://www.cnblogs.com/Staceyacm/p/10781801.html

本文介绍了一个算法问题，目标是计算给定数组中所有满足特定条件的区间数量，这些区间长度为偶数且左半部分与右半部分的异或和相等。通过使用前缀异或和与二维数组优化计算过程。

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Sasha likes programming. Once, during a very long contest, Sasha decided that he was a bit tired and needed to relax. So he did. But since Sasha isn't an ordinary guy, he prefers to relax unusually. During leisure time Sasha likes to upsolve unsolved problems because upsolving is very useful.

Therefore, Sasha decided to upsolve the following problem:

You have an array aa with n integers. You need to count the number of funny pairs (l,r) (l≤r). To check if a pair (l,r)is a funny pair, take mid=(l+r−1)/2, then if r−l+1 is an even number and al⊕al+1⊕…⊕amid=amid+1⊕amid+2⊕…⊕aral⊕al+1⊕…⊕amid=amid+1⊕amid+2⊕…⊕ar, then the pair is funny. In other words, ⊕ of elements of the left half of the subarray from ll to rr should be equal to ⊕⊕ of elements of the right half. Note that ⊕ denotes the bitwise XOR operation.

It is time to continue solving the contest, so Sasha asked you to solve this task.

Input

The first line contains one integer nn (2≤n≤3⋅10^5) — the size of the array.

The second line contains nn integers a1,a2,…,an (0≤ai<2^20) — array itself.

Output

Print one integer — the number of funny pairs. You should consider only pairs where r−l+1r−l+1 is even number.

Examples

input

Copy

5
1 2 3 4 5

output

Copy

input

Copy

6
3 2 2 3 7 6

output

Copy

input

Copy

3
42 4 2

output

Copy

Note

Be as cool as Sasha, upsolve problems!

In the first example, the only funny pair is (2,5)(2,5), as 2⊕3=4⊕5=12⊕3=4⊕5=1.

In the second example, funny pairs are (2,3)(2,3), (1,4)(1,4), and (3,6)(3,6).

In the third example, there are no funny pairs.

题意：求有多少个异或和相等的偶数区间

思路：先求出前缀异或和，再用二维数组来进行加的运算，因为后面的可以表示奇数和偶数的而来的，之前的会被总结到，要注意单独一个相邻区间的情况，所以我们把b[0][0]=1

代码：

#include<cstdio>
#include<cstring>
#include<queue>
#include<iostream>
#include<algorithm>
#include<stack>
#include<set>
#include<vector>
#include<cmath>
#define MAX 3000005


typedef long long ll;

using namespace std;
int b[MAX][2];
int a[MAX];
ll sum=0;
int main()
{
	int n;
	cin>>n;
	b[0][0]=1;
	for(int t=1;t<=n;t++)
	{
		scanf("%d",&a[t]);
		a[t]^=a[t-1];
	}
	for(int t=1;t<=n;t++)
	{
		sum+=b[a[t]][t&1];
	    b[a[t]][t&1]++;
	}
	cout<<sum<<endl;
	return 0;
 }

转载于:https://www.cnblogs.com/Staceyacm/p/10781801.html