2094. Finding 3-Digit Even Numbers
Description
You are given an integer array digits
, where each element is a digit. The array may contain duplicates.
You need to find all the unique integers that follow the given requirements:
- The integer consists of the concatenation of three elements from
digits
in any arbitrary order. - The integer does not have leading zeros.
- The integer is even.
For example, if the given digits
were [1, 2, 3]
, integers 132
and 312
follow the requirements.
Return a sorted array of the unique integers.
Example 1:
Input: digits = [2,1,3,0] Output: [102,120,130,132,210,230,302,310,312,320] Explanation: All the possible integers that follow the requirements are in the output array. Notice that there are no odd integers or integers with leading zeros.
Example 2:
Input: digits = [2,2,8,8,2] Output: [222,228,282,288,822,828,882] Explanation: The same digit can be used as many times as it appears in digits. In this example, the digit 8 is used twice each time in 288, 828, and 882.
Example 3:
Input: digits = [3,7,5] Output: [] Explanation: No even integers can be formed using the given digits.
Constraints:
3 <= digits.length <= 100
0 <= digits[i] <= 9
Solutions
Solution 1: Counting + Enumeration
First, we count the occurrence of each digit in $\textit{digits}$, recording it in an array or hash table $\textit{cnt}$.
Then, we enumerate all even numbers in the range $[100, 1000)$, checking if each digit of the even number does not exceed the corresponding digit's count in $\textit{cnt}$. If so, we add this even number to the answer array.
Finally, we return the answer array.
The time complexity is $O(k \times 10^k)$, where $k$ is the number of digits of the target even number, which is $3$ in this problem. Ignoring the space consumed by the answer, the space complexity is $O(1)$.
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