项目欧拉45 [英] Project euler 45

问题描述

我还不是一个熟练的程序员，但我认为这是一个有趣的问题，我想我会试一试。

I'm not yet a skilled programmer but I thought this was an interesting problem and I thought I'd give it a go.

三角形，五角形和六角形
数字由以下
公式生成：

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

• 三角形T_（n ）= n（n + 1）/ 2
  1,3,6,10,15，......


• 五角形P_（n）= n（3n-1） / 2 1,5,12,22,35，
  ...


• 六边形H_（n）= n（2n-1）1，
  6， 15,28,45，...

可以验证T_（285）=
P_（165） = H_（143）= 40755。

It can be verified that T_(285) = P_(165) = H_(143) = 40755.

找到下一个三角形数字，即
，也是五边形和六边形。

Find the next triangle number that is also pentagonal and hexagonal.

是任务描述。

我知道六边形数字是三角形数字的子集，这意味着你只需要找到Hn = Pn的数字。
但我似乎无法让我的代码工作。我只知道java语言，这就是为什么我在网络上找不到解决方案的原因。无论如何希望有人可以帮忙。这是我的代码

I know that Hexagonal numbers are a subset of triangle numbers which means that you only have to find a number where Hn=Pn. But I can't seem to get my code to work. I only know java language which is why I'm having trouble finding a solution on the net womewhere. Anyway hope someone can help. Here's my code

public class NextNumber {

    public NextNumber() {
    next();
    }

    public void next() {


int n = 144;
int i = 165;
int p = i * (3 * i - 1) / 2;
int h = n * (2 * n - 1);
        while(p!=h) {
            n++;
           h = n * (2 * n - 1);

            if (h == p) {
                System.out.println("the next triangular number is" + h);
            } else {
                while (h > p) {
                    i++;
                    p = i * (3 * i - 1) / 2;
                }
                if (h == p) {
                    System.out.println("the next triangular number is" + h); break;
                    }
                 else if (p > h) {
                    System.out.println("bummer");
                }
            }

            }

    }
}

我意识到它可能是一个非常缓慢且无效的代码，但这并不关心我此时我只关心找到下一个数字，即使它需要我的计算机多年。

I realize it's probably a very slow and ineffecient code but that doesn't concern me much at this point I only care about finding the next number even if it would take my computer years.

推荐答案

我们知道T ₂₈₅ = P ₁₆₅ = H < sub> 143 = 40755.我们从 nt = 286 开始， np = 166 和 nh = 144 并计算出相应的三角形，五边形和六边形数字。无论结果数量最小，我们都会提高其 n 值。继续执行此操作，直到所有数字相等并且您有答案。

We know that T₂₈₅ = P₁₆₅ = H₁₄₃ = 40755. We start with nt=286, np=166 and nh=144 and work out the respective triangle, pentagonal, and hexagonal numbers. Whichever resulting number is smallest, we bump up its n value. Continue doing this until all numbers are equal and you have your answer.

此算法的Python实现在我的计算机上运行0.1秒。

A Python implementation of this algorithm runs in 0.1 seconds on my computer.

代码问题是溢出。虽然答案适合32位 int ，但临时值 i *（3 * i - 1）溢出之前得到答案。使用64位 long 值可修复您的代码。

The problem with your code is overflow. While the answer fits into a 32 bit int, the temporary values i * (3 * i - 1) overflows before reaching the answer. Using 64 bit long values fixes your code.

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