codeforces 424C Magic Formulas

最新推荐文章于 2017-07-23 23:46:58 发布

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在Tomsk地区，人们非常喜爱那些看似神秘的数学公式。文章介绍了一个涉及位运算的公式，并通过一系列步骤解释了如何计算给定整数序列的值Q。文章深入探讨了位操作符在编程语言中的实现，以及如何使用它们来解决实际问题。

Description
People in the Tomskaya region like magic formulas very much. You can see some of them below.

Imagine you are given a sequence of positive integer numbers p1, p2, …, pn. Lets write down some magic formulas:

Here, “mod” means the operation of taking the residue after dividing.

The expression means applying the bitwise xor (excluding “OR”) operation to integers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by “^”, in Pascal — by “xor”.

People in the Tomskaya region like magic formulas very much, but they don’t like to calculate them! Therefore you are given the sequence p, calculate the value of Q.

Input
The first line of the input contains the only integer n (1 ≤ n ≤ 106). The next line contains n integers: p1, p2, …, pn (0 ≤ pi ≤ 2·109).

Output
The only line of output should contain a single integer — the value of Q.

Sample Input
Input
3
1 2 3
Output
3

#include<iostream>
#include<cstdio>
using namespace std;
int a[1000001];
int main()
{
    int n;
    int q,p;
    cin>>n;
    cin>>p;
    q=p;
    for(int i=1; i<n; i++)
    {
        scanf("%d",&p);
        q^=p;
    }
    a[1]=0;
    a[0]=0;
    for(int i=2; i<=n; i++)
    {
        a[i]=a[i-1]^(i-1);
    }
    for(int i=1; i<=n; i++)
    {
        int num=n/i;
        int r=n%i;
        if(num&1)
        q^=a[i];
        q^=a[r];
        q^=r;
    }
    cout<<q<<endl;
    return 0;
}