LeetCode 357. Count Numbers with Unique Digits C++

357. Count Numbers with Unique Digits

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

Example:

Input: 2
Output: 91 
Explanation: The answer should be the total numbers in the range of 0 ≤ x < 100, 
             excluding 11,22,33,44,55,66,77,88,99

Approach

1. 这是一道很纯粹的数学题，需要用到排列组合的知识，直接看代码吧。

Code

class Solution {
public:
    vector<int> cache;
    int fact(int n) {
        if (n>1&&cache[n]==0) {
            cache[n] = fact(n - 1)*n;
        }
        return cache[n];
    }
    int C(int a, int b) {
        return fact(a) / (fact(b)*fact(a - b));
    }
    int A(int a,int b) {
        return fact(a) / fact(a - b);
    }
    int countNumbersWithUniqueDigits(int n) {
        cache = vector<int>(10, 0);
        cache[0] = 1;
        cache[1] = 1;
        int res = 0;
        if (n >= 1)res += 9;
        for (int i = 2; i <= n; i++) {
            res += C(9, 1)*C(9, i - 1)*A(i - 1, i - 1);//第一位不能为零
        }
        return res;
    }
};