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
    mysql5.7免费下载地址
    查看>>
    mysql5.7命令总结
    查看>>
    mysql5.7安装
    查看>>
    mysql5.7性能调优my.ini
    查看>>
    MySQL5.7新增Performance Schema表
    查看>>
    Mysql5.7深入学习 1.MySQL 5.7 中的新增功能
    查看>>
    Webpack 之 basic chunk graph
    查看>>
    Mysql5.7版本单机版my.cnf配置文件
    查看>>
    mysql5.7的安装和Navicat的安装
    查看>>
    mysql5.7示例数据库_Linux MySQL5.7多实例数据库配置
    查看>>
    Mysql8 数据库安装及主从配置 | Spring Cloud 2
    查看>>
    mysql8 配置文件配置group 问题 sql语句group不能使用报错解决 mysql8.X版本的my.cnf配置文件 my.cnf文件 能够使用的my.cnf配置文件
    查看>>
    MySQL8.0.29启动报错Different lower_case_table_names settings for server (‘0‘) and data dictionary (‘1‘)
    查看>>
    MYSQL8.0以上忘记root密码
    查看>>
    Mysql8.0以上重置初始密码的方法
    查看>>
    mysql8.0新特性-自增变量的持久化
    查看>>
    Mysql8.0注意url变更写法
    查看>>
    Mysql8.0的特性
    查看>>
    MySQL8修改密码报错ERROR 1819 (HY000): Your password does not satisfy the current policy requirements
    查看>>
    MySQL8修改密码的方法
    查看>>