poj-2478 Farey Sequence(dp,歐拉函數)

題目鏈接：

Farey Sequence

Time Limit:?1000MS	?	Memory Limit:?65536K
Total Submissions:?14230	?	Accepted:?5624

Description

The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few are?
F2 = {1/2}?
F3 = {1/3, 1/2, 2/3}?
F4 = {1/4, 1/3, 1/2, 2/3, 3/4}?
F5 = {1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5}?

You task is to calculate the number of terms in the Farey sequence Fn.

Input

There are several test cases. Each test case has only one line, which contains a positive integer n (2 <= n <= 10⁶). There are no blank lines between cases. A line with a single 0 terminates the input.

Output

For each test case, you should output one line, which contains N(n) ---- the number of terms in the Farey sequence Fn.?

Sample Input

2
3
4
5
0

Sample Output

1
3
5
9
題意：問滿足a/b with 0 < a < b <= n and gcd(a,b) = 1,的數對有多少個;
思路：dp[i]=dp[i-1]+n的歐拉函數;
AC代碼：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int N=1e6+2;
long long dp[N],a[N];
int get_a()
{memset(a,0,sizeof(a));for(int i=2;i<N;i++){if(!a[i]){for(int j=i;j<N;j+=i){if(!a[j])a[j]=j;a[j]=a[j]/i*(i-1);}}}}
int fun()
{get_a();dp[1]=0;dp[2]=1;for(int i=3;i<N;i++){dp[i]=dp[i-1]+a[i];}
}
int main()
{int n;fun();while(1){scanf("%d",&n);if(!n)break;cout<<dp[n]<<"\n";}return 0;
}

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