Leetcode: Count Numbers with Unique Digits

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

Example:
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])

Analysis:

A number of unique digits is a number which is a combination of unrepeated digits. So, we can calculate the total number. for number with n digits, like 100-999 or 1000-9999, the total numbers with unique digits equals to 9*9*8...*(11-n). because the highest digit cannot be 0.

Here is DP. dp[i] is the count of all i-digit numbers with unique digits, dp[i] = dp[i-1]*(11-i) for i from 2 to n

public static int countNumbersWithUniqueDigits(int n) {
    if (n == 0) {
        return 1;
    }
    int ans = 10, base = 9;
    for (int i = 2; i <= n && i <= 10; i++) {
        base = base * (11 - i);
        ans += base;
    }
    return ans;
}

第一遍backtracking做法：

public class Solution {
    public int countNumbersWithUniqueDigits(int n) {
        if (n == 0) return 1;
        if (n == 1) return 10;
        int res = 10;
        for (int i=2; i<=n && i<=10; i++) {
            int count = 1;
            int bit = 9;
            for (int j=0; j<i; j++) {
                count *= bit;
                if (j != 0) bit--;
            }
            res += count;
        }
        return res;
    }
}