projectEuler Problem 12.Highly divisible triangular number_the sequence of triangle numbers is generated by a-优快云博客

本文探讨了如何找到第一个拥有超过500个因数的三角形数。通过分解质因数的方法，实现了一个高效的算法来解决这个问题。文章详细介绍了算法的实现过程，并提供了一段使用C++编写的代码示例。

题目链接：12.Highly divisible triangular number

题意：

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28

What is the value of the first triangle number to have over five hundred divisors?

求哪个值有 500个因数

解题思路：
分解质因数

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

ll sum(ll i) {  // 求 triangle number
	if(i % 2 == 0) {
		return i / 2 * (i + 1);
	}
	return (i+1) / 2 * i;
}
int solve(ll n) {
	int num = 0, i;
	for(i = 1; i * i < n; i++) {  // 分解质因数
		if(n % i == 0) { // 如果能整除，那么他就有两个因数
			num += 2;
		}
	}
	if(i * i == n) {  // 平方等于n，因数加1
		num++;
	}
	return num;
}
int main() {
	ll ans = 1;
	while(solve(sum(ans)) < 500) {
		ans++;
	}
	cout << sum(ans) << endl;
	return 0;
}