Finding 3-Digit Even Numbers - Video Solutions

Problem Overview: You receive an array of digits (0–9). Use these digits to construct all unique 3-digit even numbers. Each digit can only be used as many times as it appears in the array. The result must contain every valid number exactly once and be returned in sorted order.

Approach 1: Using a Hash Map (Digit Frequency) (Time: O(450 * 10) ≈ O(1), Space: O(10))

Create a frequency map of digits using a small array or hash table. Then enumerate every possible 3-digit even number from 100 to 998. For each candidate number, extract the hundreds, tens, and units digits. The key check: verify the units digit is even and ensure the digit frequency in the candidate does not exceed the available frequency in the input map. This works because there are only 450 possible 3-digit even numbers, so enumeration is effectively constant time. The approach relies on fast frequency comparison rather than generating permutations, which avoids duplicate work.

Use this method when the domain of valid numbers is small and bounded. Instead of exploring combinations from the array, you validate candidates against available digits. This pattern appears frequently in hash table and array counting problems.

Approach 2: Sorting and Linear Enumeration (Time: O(n^3), Space: O(1) extra)

Sort the digits first. Then iterate over all triples of indices i, j, and k to form numbers using three distinct positions. Skip invalid combinations early: the first digit cannot be 0, and the last digit must be even. Sorting allows easy duplicate control because identical digits appear next to each other, so you can skip repeated combinations during iteration. Construct the number as 100*a + 10*b + c and store unique results.

This approach directly generates candidate numbers from the input digits rather than validating against a fixed range. Sorting simplifies duplicate handling and is a common pattern in sorting-based enumeration problems. It is slightly slower asymptotically but still efficient since the input size is small (digits length ≤ 10).

Recommended for interviews: The hash map enumeration approach is usually preferred. It demonstrates awareness of constraints and converts the problem into constant-size validation rather than combinatorial generation. Interviewers appreciate recognizing the small search space (only 3-digit even numbers). The sorting + enumeration method still shows solid reasoning about duplicates and index usage, so it remains a good fallback when the range-based insight does not immediately come to mind.