分解质因数-白红宇的个人博客

分解质因数

发布日期：2021-05-15 08:58:18 浏览次数：21 分类：精选文章

本文共 1568 字，大约阅读时间需要 5 分钟。

Here's an optimized version of the code along with the step-by-step explanation:

#include 
   
    
#include 
    
     
int main() {
    int n, a = 2;
    std::cin >> n;
    while (n != 1) {
        if (n % a == 0) {
            std::cout << a << " ";
            n /= a;
        } else {
            if (a == 2) {
                a = 3;
            } else {
                a += 2; // Check only odd numbers after 2
            }
            if (a * a > n) {
                std::cout << n << " ";
                n = 1;
            }
        }
    }
    return 0;
}

Explanation:

Initialization:

Read the integer n from the input.

Initialize a to 2, the smallest prime number.

While Loop:

Continue the loop until n is reduced to 1.

This ensures all factors are processed until n is completely divided.

Check Divisibility:

For each a, check if n is divisible by a.

If yes, print a and divide n by a. Continue this to factorize n completely.

Handle Even and Odd Numbers:

After checking for 2, handle all subsequent factors by incrementing a by 2. This optimizes by skipping even numbers, reducing the number of checks.

Optimization Check:

If a squared exceeds n, it means n has no more factors apart from itself. If n is greater than 1, print it as a prime factor.

Set n to 1 to terminate the loop.

Termination:

Once n becomes 1, the loop exits, and the function returns 0, indicating all prime factors have been processed.

This version optimizes the code by minimizing unnecessary checks and improving efficiency, ensuring it's both effective and easy to understand.

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