Count Numbers with Unique Digits问题及解法

问题描述：

Given a non-negative integer n, count all numbers with unique digits, x, where 0 ≤ x < 10n.

示例：
Given n = 2, return 91. (The answer should be the total numbers in the range of 0 ≤ x < 100, excluding[11,22,33,44,55,66,77,88,99])

问题分析：

我们通过找规律发现如下：

n = 1, res[1] = 10;

n = 2, res[2] = res[1] + 9 * (9) = 91;

n = 3, res[3] = res[2] + 9 *(9 * 8) = 739;

......依此类推

过程详见代码：

class Solution {public:    int countNumbersWithUniqueDigits(int n) {        if (!n) return 1;vector<int> res(n + 1,1);int product = 9, num = 9;res[1] = 10;n = min(10, n);for (int i = 2; i <= n; i++){res[i] = res[i - 1] + product * 9;product *= (--num);}return res[n];    }};