博客
关于我
java 牛客:因子个数
阅读量:749 次
发布时间:2019-03-22

本文共 2746 字,大约阅读时间需要 9 分钟。

To solve this problem, we need to determine the number of factors for each given positive integer. The solution involves understanding the prime factorization of a number and using it to compute the total number of factors.

Approach

The approach can be broken down into the following steps:

  • Prime Factorization: Decompose the given number into its prime factors. For example, the number 36 can be decomposed into (2^2 \times 3^2).

  • Exponent Tracking: For each prime factor, determine its exponent in the factorization. For instance, in the case of 36, the exponent of 2 is 2, and the exponent of 3 is also 2.

  • Calculate Factors: The total number of factors of a number can be found by taking the product of each prime factor's exponent incremented by one. For example, using the prime factors of 36, the total number of factors is ((2+1) \times (2+1) = 9).

  • Efficient Looping: Use efficient looping techniques to iterate through potential factors, and stop early when further division isn't possible. This optimization prevents unnecessary computations.

  • Solution Code

    import java.util.Scanner;public class Main {    public static void main(String[] args) {        Scanner scanner = new Scanner(System.in);        while (scanner.hasNextInt()) {            int n = scanner.nextInt();            System.out.println(countFactors(n));        }    }    private static int countFactors(int n) {        if (n <= 1) {            return 1;        }        int factors = 1;        for (int i = 2; i * i <= n; ) {            if (n % i == 0) {                int exponent = 0;                while (n % i == 0) {                    exponent++;                    n /= i;                }                factors *= (exponent + 1);            } else {                i++;            }        }        if (n > 1) {            factors *= 2;        }        return factors;    }}

    Explanation

  • Reading Input: The code reads each integer from the standard input.
  • Handling Special Cases: If the input number is 1, it directly returns 1 as it is the only factor.
  • Prime Factorization Loop: The loop iterates from 2 up to the square root of the number. For each potential factor, it checks if it divides the number. If it does, it counts how many times it divides (the exponent) and then divides the number by this factor until it no longer can.
  • Updating Factors Count: The number of factors is updated by multiplying the product of each exponent incremented by one.
  • Remaining Prime Check: If after processing all factors up to the square root, the remaining number is greater than 1, it means it is a prime factor itself, contributing one more factor.
  • This approach efficiently computes the number of factors for each positive integer, ensuring correct and optimal results.

    转载地址:http://nvewk.baihongyu.com/

    你可能感兴趣的文章
    MySql二进制日志的应用及恢復
    查看>>
    mysql互换表中两列数据方法
    查看>>
    mysql五补充部分:SQL逻辑查询语句执行顺序
    查看>>
    mysql交互式连接&非交互式连接
    查看>>
    MySQL什么情况下会导致索引失效
    查看>>
    Mysql什么时候建索引
    查看>>
    MySql从入门到精通
    查看>>
    MYSQL从入门到精通(一)
    查看>>
    MYSQL从入门到精通(二)
    查看>>
    mysql以下日期函数正确的_mysql 日期函数
    查看>>
    mysql以服务方式运行
    查看>>
    mysql优化--索引原理
    查看>>
    MySQL优化之BTree索引使用规则
    查看>>
    MySQL优化之推荐使用规范
    查看>>
    Webpack Critical CSS 提取与内联教程
    查看>>
    mysql优化概述(范式.索引.定位慢查询)
    查看>>
    MySQL优化的一些需要注意的地方
    查看>>
    mysql优化相关
    查看>>
    MySql优化系列-优化版造数据(存储过程+函数+修改存储引擎)-2
    查看>>
    MySql优化系列-进阶版造数据(load data statment)-3
    查看>>