【POJ 2478】 Farey Sequence

【题目链接】

点击打开链接

【算法】

不难看出，ans = phi(2) + phi(3) + .... + phi(n-1) + phi(n)

线性筛筛出欧拉函数，预处理前缀和，即可

【代码】

#include <algorithm>

#include <bitset>

#include <cctype>

#include <cerrno>

#include <clocale>

#include <cmath>

#include <complex>

#include <cstdio>

#include <cstdlib>

#include <cstring>

#include <ctime>

#include <deque>

#include <exception>

#include <fstream>

#include <functional>

#include <limits>

#include <list>

#include <map>

#include <iomanip>

#include <ios>

#include <iosfwd>

#include <iostream>

#include <istream>

#include <ostream>

#include <queue>

#include <set>

#include <sstream>

#include <stdexcept>

#include <streambuf>

#include <string>

#include <utility>

#include <vector>

#include <cwchar>

#include <cwctype>

#include <stack>

#include <limits.h>

using namespace std;

typedef long long ll;

const ll MAXN = 1e6;

ll i,n,tmp,j,tot;

ll prime[MAXN+10],phi[MAXN+10],sum[MAXN+10],f[MAXN+10];

template <typename T> inline void read(T &x) {

		ll f = 1; x = 0;

		char c = getchar();

		for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; }

		for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';

		x *= f;

}

template <typename T> inline void write(T x) {

		if (x < 0) { x = -x; putchar('-'); }

		if (x > 9) write(x/10);

		putchar(x%10+'0');

}

template <typename T> inline void writeln(T x) {

		write(x);

		puts("");

}

int main() {

	for (i = 2; i <= MAXN; i++) {

			if (!f[i]) {

					prime[++tot] = f[i] = i;

					phi[i] = i - 1;

			}

			for (j = 1; j <= tot; j++) {

					tmp = i * prime[j];

					if (tmp > MAXN) break;

					f[tmp] = prime[j];

					if (prime[j] == f[i]) {

							phi[tmp] = prime[j] * phi[i];

							break;

					}

					phi[tmp] = phi[i] * phi[prime[j]];

			}

	}

	for (i = 2; i <= MAXN; i++) sum[i] = sum[i-1] + phi[i];

	while (true) {

			read(n);

			if (!n) return 0;

			writeln(sum[n]);

	}

	return 0;

}