_357.java

package com.fishercoder.solutions;

public class _357 {

    public static class Solution1 {
        /**
         * reference: https://discuss.leetcode.com/topic/47983/java-dp-o-1-solution Following the hint.
         * Let f(n) = count of number with unique digits of length n. f(1) = 10. (0, 1, 2, 3, ...., 9)
         * f(2) = 9 * 9. Because for each number i from 1, ..., 9, we can pick j to form a 2-digit
         * number ij and there are 9 numbers that are different from i for j to choose from. f(3) = f(2)
         * * 8 = 9 * 9 * 8. Because for each number with unique digits of length 2, say ij, we can pick
         * k to form a 3 digit number ijk and there are 8 numbers that are different from i and j for k
         * to choose from. Similarly f(4) = f(3) * 7 = 9 * 9 * 8 * 7.... ... f(10) = 9 * 9 * 8 * 7 * 6 *
         * ... * 1 f(11) = 0 = f(12) = f(13).... any number with length > 10 couldn't be unique digits
         * number. The problem is asking for numbers from 0 to 10^n. Hence return f(1) + f(2) + .. +
         * f(n) As @4acreg suggests, There are only 11 different ans. You can create a lookup table for
         * it. This problem is O(1) in essence.
         */
        public int countNumbersWithUniqueDigits(int n) {
            if (n == 0) {
                return 1;
            }
            int res = 10;
            int uniqueDigits = 9;
            int availableNumber = 9;
            while (n-- > 1 && availableNumber > 0) {
                uniqueDigits = uniqueDigits * availableNumber;
                res += uniqueDigits;
                availableNumber--;
            }
            return res;
        }
    }

}