HDU 2824 求区间欧拉函数和

最新推荐文章于 2021-09-26 22:33:14 发布

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最新推荐文章于 2021-09-26 22:33:14 发布

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分类专栏：数论文章标签：欧拉函数

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本文介绍了一种计算欧拉函数区间求和的有效算法，并通过一个具体的编程实例展示了如何实现该算法。输入两个整数L和R，程序将输出从L到R之间的所有整数的欧拉函数值之和。

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题目链接
The Euler function

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 5799 Accepted Submission(s): 2455

Problem Description
The Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are smaller than n and coprime to n, and this function has a lot of beautiful characteristics. Here comes a very easy question: suppose you are given a, b, try to calculate (a)+ (a+1)+….+ (b)

Input
There are several test cases. Each line has two integers a, b (2< a < b <3000000).

Output
Output the result of (a)+ (a+1)+….+ (b)

Sample Input
3 100

Sample Output
3042

Source
2009 Multi-University Training Contest 1 - Host by TJU

题意：
输入L，R，输出φ(l)+φ(l+1)+…+φ(r)

#include<iostream>
#include<cstdio>
#include<cmath>

using namespace std;

#define N 3000001

int phi[N];

void init() {
    int i, j;
    for (i = 1; i < N; i++)
        phi[i] = i;
    for (i = 2; i < N; i++)
        if (i == phi[i]) //此时i为素数
            for (j = i; j < N; j += i)  //j累加i
                phi[j] = (phi[j] / i) * (i - 1); //j有因子i,而且i是素数,正是欧拉函数
}

int main() {
    init();
    int a, b;
    while (scanf("%d%d", &a, &b) != EOF) {
        __int64 ans = 0;
        for (int i = a; i <= b; i++)
            ans += phi[i];
        printf("%I64d\n", ans);
    }
    return 0;
}