2048. Next Greater Numerically Balanced Number
Description
An integer x
is numerically balanced if for every digit d
in the number x
, there are exactly d
occurrences of that digit in x
.
Given an integer n
, return the smallest numerically balanced number strictly greater than n
.
Example 1:
Input: n = 1 Output: 22 Explanation: 22 is numerically balanced since: - The digit 2 occurs 2 times. It is also the smallest numerically balanced number strictly greater than 1.
Example 2:
Input: n = 1000 Output: 1333 Explanation: 1333 is numerically balanced since: - The digit 1 occurs 1 time. - The digit 3 occurs 3 times. It is also the smallest numerically balanced number strictly greater than 1000. Note that 1022 cannot be the answer because 0 appeared more than 0 times.
Example 3:
Input: n = 3000 Output: 3133 Explanation: 3133 is numerically balanced since: - The digit 1 occurs 1 time. - The digit 3 occurs 3 times. It is also the smallest numerically balanced number strictly greater than 3000.
Constraints:
0 <= n <= 106
Solutions
Solution 1: Enumeration
We note that the range of $n$ in the problem is $[0, 10^6]$, and one of the balanced numbers greater than $10^6$ is $1224444$. Therefore, we directly enumerate $x \in [n + 1, ..]$ and then judge whether $x$ is a balanced number. The enumerated $x$ will definitely not exceed $1224444$.
The time complexity is $O(M - n)$, where $M = 1224444$. The space complexity is $O(1)$.
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