完美的正方形与否？ [英] Perfect square or not?

问题描述

这是用于检查数字是否为正整数的代码。它为什么起作用？

This is a code to check if a number is perfect square or not. Why does it work ?

static bool IsSquare(int n)
{
    int i = 1;
    for (; ; )
    {
        if (n < 0)
            return false;
        if (n == 0)
            return true;
        n -= i;
        i += 2;
    }
}

推荐答案

因为所有理想平方都是连续奇数的和：

Because all perfect squares are sums of consecutive odd numbers:

• 1 = 1


• 4 = 1 + 3


• 9 = 1 + 3 + 5


• 16 = 1 + 3 + 5 + 7

• 1 = 1
• 4 = 1 + 3
• 9 = 1 + 3 + 5
• 16 = 1 + 3 + 5 + 7

，依此类推。您的程序尝试从 n 中减去连续的奇数，然后看它是否降为零或变为负数。

and so on. Your program attempts to subtract consecutive odd numbers from n, and see if it drops to zero or goes negative.

您可以通过绘制边为 {1,2,3,4，...} 的正方形并观察构造一个<$ c $正方形 k 中的c> k + 1 需要添加 2k + 1 单位正方形。

You can make an informal proof of this by drawing squares with sides of {1,2,3,4,...} and observe that constructing a square k+1 from square k requires adding 2k+1 unit squares.

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