UVA160 Factors and Factorials【筛选法】

The factorial of a number N (written N!) is defined as the product of all the integers from 1 to N. It is often defined recursively as follows:

1! = 1

N! = N ∗ (N − 1)!

Factorials grow very rapidly — 5! = 120, 10! = 3, 628, 800. One way of specifying such large numbers is by specifying the number of times each prime number occurs in it, thus 825 could be specified as (0 1 2 0 1) meaning no twos, 1 three, 2 fives, no sevens and 1 eleven.

Write a program that will read in a number N (2 ≤ N ≤ 100) and write out its factorial in terms of the numbers of the primes it contains.

Input

Input will consist of a series of lines, each line containing a single integer N. The file will be terminated by a line consisting of a single ‘0’.

Output

Output will consist of a series of blocks of lines, one block for each line of the input. Each block will start with the number N, right justified in a field of width 3, and the characters ‘!’, space, and ‘=’. This will be followed by a list of the number of times each prime number occurs in N!.

These should be right justified in fields of width 3 and each line (except the last of a block, which may be shorter) should contain fifteen numbers. Any lines after the first should be indented.

Follow the layout of the example shown below exactly.

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Sample Input

Sample Output

5! = 3 1 1

53! = 49 23 12 8 4 4 3 2 2 1 1 1 1 1 1

问题链接：UVA160 Factors and Factorials

问题简述：

求出n！的所有素数因子个数，按照 2 ，3，5，7...的顺序输出因子个数。

问题分析：

筛选法是必要的，先找出素数。

输出格式比较麻烦。

需要主要的一点是，需要多算一个素数！

程序说明：（略）

题记：（略）

参考链接：（略）

AC的C＋＋语言程序如下：

/* UVA160 Factors and Factorials */

#include <iostream>
#include <math.h>
#include <string.h>

using namespace std;

const int N = 100 + 2;
const int SQRTN = ceil(sqrt((double) N));
bool isnotPrime[N + 1];
int prime[N / 2], pcnt;
int ans[N + 1];

// Eratosthenes筛选法
void esieve(void)
{
    memset(isnotPrime, false, sizeof(isnotPrime));

    isnotPrime[0] = isnotPrime[1] = true;
    for(int i=2; i<=SQRTN; i++) {
        if(!isnotPrime[i]) {
            for(int j=i*i; j<=N; j+=i)  //筛选
                isnotPrime[j] = true;
        }
    }

    pcnt = 0;
    for(int i = 2; i <= N; i++)
        if(!isnotPrime[i])
            prime[pcnt++] = i;
}

int main()
{
    esieve();

    int n;
    while(cin >> n && n) {
        memset(ans, 0, sizeof(ans));

        for(int i = 2; i <= n; i++) {
            int m = i, now = 0;
            while(m > 1) {
                while(m % prime[now] == 0) {
                    ans[now]++;   //质因子加1
                    m /= prime[now];
                }
                now++;
            }
        }

        // 输出结果
        printf("%3d! =", n);
        for(int j = 0; prime[j] <= n; j++) {
            printf("%3d", ans[j]);
            if((j + 1) % 15 == 0) {     // 每行输出15个，
                printf("\n");
                if(prime[j + 1] <= n)   // 后面还有数的话，输出下一行前置空格
                    printf("      ");
            }
        }
        if(prime[14] > n || prime[15] <= n)     // 判断是否需要换行
            printf("\n");
    }

    return 0;
}

UVA160 Factors and Factorials【筛选法】

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