有人可以解释 Dmitry 是如何计算 NMin 的吗？

Question

原问题位于Project Euler Largest palindrome product下方

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers.

上下文中的问题位于 Dmitry Answering Largest palindrome product - C#. I got the correct answer but did it from min to max instead of max to min so I looked for a more efficient answer to study. I understand what all the code does, but I can't figure out where Dmitry开始求公式从最大被乘数常数求最小被乘数。我正在浏览几个编码挑战网站，为一些技术面试做准备。

这一行：

const int NMin = NMax - (NMax + 1) / 10 + 1;

OF

// Store the maximum palindrome number here:
long maxNumber = 0;

// The maximum multiplicand (typically: 9...9):
const int NMax = 999;
// The minimum multiplicand.
// Obviously, it couldn't be less than 90...0:
const int NMin = NMax - (NMax + 1) / 10 + 1;

for (int i = NMax; i > NMin; i--)
{
    // Starting from i since i * j = j * i for any i, j:
    for (int j = i; j > NMin; j--)
    {
        long number = Math.BigMul(i, j);
        // The fastest condition should be the first in the `if` statement:
        if (number > maxNumber && isPalindome(number))
        {
            maxNumber = number;
            Console.WriteLine("{0} = {1} * {2}", number, i, j);
            break; // Leave the `j` loop, because it's guaranteed that there is
                   // no numbers greater than `number` for the current `i`
        }
    }
}

我浏览过的网站包括：

Advent Of Code
HackerEarth and HackerRank
Leetcode I've been attempting to finish the Comprehensive Study Plans
Project Euler 现在只有问题 #4

Answer 1

如 problem 4 所述，two-digit 个数字乘积的最大回文是 91*99。我相信 Dmitry 认识到对于给定的数字范围（他计算的 3、4 或 5 但实际上是无穷大）的所有最大回文必须是 9x -> 9y（其中 x 代表 0，y代表9）。 x 和 y 所需的数量是 digit - 1 如果你总是想要 最高回文。 这里较低的 90% 根本不值得检查回文，因为它们不会产生最高的乘法。

因此他每次都可以根据他提供的等式计算出最小值：

NMin = NMax - (NMax + 1) / 10 + 1 // NMin = 900 if NMax = 999

在 4 位回文的情况下，这会产生 9,000 -> 9,999 或 90,000 -> 99,999 5.

这里要注意的重要一点是他可以 hard-coded NMin 或者选择一个更大的最小值。

有人可以解释 Dmitry 是如何计算 NMin 的吗？

Can someone explain how Dmitry got the NMin math down?

c#

performance

math