0 or 1
Time Limit: 6000/2000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 1934 Accepted Submission(s): 477
Problem Description
Solving problem is a interesting thing. Yifenfei like to slove different problem,because he think it is a way let him more intelligent. But as we know,yifenfei is weak in math. When he come up against a difficult math problem, he always try to get a hand. Now
the problem is coming! Let we
define T(n) as the sum of all numbers which are positive integers can divied n. and S(n) = T(1) + T(2) + T(3)…..+T(n).
define T(n) as the sum of all numbers which are positive integers can divied n. and S(n) = T(1) + T(2) + T(3)…..+T(n).
Input
The first line of the input contains an integer T which means the number of test cases. Then T lines follow, each line consists of only one positive integers n. You may assume the integer will not exceed 2^31.
Output
For each test case, you should output one lines of one integer S(n) %2. So you may see the answer is always 0 or 1 .
Sample Input
3 1 2 3
Sample Output
1 0 0首先在此膜拜那些用数论或者打表推出规律的大神刚看这题毫无思路,百度题解原来思路是那么的巧妙分析在代码中/* 分析:假设数n=2^k*p1^s1*p2^s2*p3^s3*...*pi^si;//k,s1...si>=0,p1..pi为n的素因子 所以T[n]=(2^0+2^1+...+2^k)*(p1^0+p1^1+...+p1^s1)*...*(pi^0+pi^1+...+pi^si); 显然(2^0+2^1+...+2^k)%2=1,所以T[n]是0或1就取决于(p1^0+p1^1+...+p1^s1)*...*(pi^0+pi^1+...+pi^si) 而p1...pi都是奇数(除2之外的素数一定是奇数),所以(pi^0+pi^1+...+pi^si)只要有一个si为奇数(i=1...i) 则(pi^0+pi^1+...+pi^si)%2=0,则T[n]%2=0//若si为奇数,则pi^si+1为偶数,pi^1+pi^2+...+pi^(si-1)为偶数(偶数个奇数和为偶数) 所以要T[n]%2=1,则所有的si为偶数,则n=2^(k%2)*m^2;//m=2^(k/2)*p1^(s1/2)*p2^(s2/2)*...*pi^(si/2) 所以只要n为某个数的平方或者某个数的平方和则T[n]%2=1,只要统计n的个数即可 */ #include<iostream> #include<cstdio> #include<cstdlib> #include<cstring> #include<string> #include<queue> #include<algorithm> #include<map> #include<cmath> #include<iomanip> #define INF 99999999 using namespace std; const int MAX=10; int main(){ int t,n; cin>>t; while(t--){ cin>>n; int sum=(int)sqrt(n*1.0)+(int)sqrt(n*1.0/2); cout<<sum%2<<endl; } return 0; }
作者:xingyeyongheng 发表于2013-8-11 0:25:04 原文链接
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