File: form-smallest-number-from-two-digit-arrays/solution.py

Date: 2026-06-06

Time: 16:54

form-smallest-number-from-two-digit-arrays/solution.py

Purpose

This file solves LeetCode 2605: Form Smallest Number From Two Digit Arrays. Given two arrays of unique single digits (1-9), it finds the smallest integer that contains at least one digit from each array. The file is self-contained: solution function + inline unit tests.

Key Components

smallestnumberwithatleastonedigitfromeach_array(nums1, nums2) -> int — The core solver. It handles two distinct cases:

1. Common digit exists: If the arrays share any digit, the answer is simply the smallest shared digit (a single-digit number always beats a two-digit number).

2. No common digit: The answer is a two-digit number formed from the minimum of each array, with the smaller digit in the tens place.

TestSmallestNumber — Seven test cases covering the key partitions: no common digit, common digit, single-element arrays, ordering when the smaller minimum is in nums2, multiple common digits, and fully overlapping arrays.

Patterns

• Set intersection for common-element detection — set(nums1) & set(nums2) is the idiomatic Python approach, O(n+m).
• Greedy construction — When no common digit exists, the two-digit number is built by placing min(a, b) in the tens place and max(a, b) in the ones place: min(a,b) * 10 + max(a,b).
• Inline tests — Tests live in the same file as the solution rather than in a separate test module, with unittest.main() guarded by _name_.

Dependencies

Imports: Only unittest from the standard library — no external dependencies.

Imported by: The test_solution.py file in the same directory, plus hundreds of other test files across the repo import unittest (the "Imported By" list in the prompt is actually listing files that import unittest, not this solution directly).

Flow

1. Compute the set intersection of nums1 and nums2.

2. If non-empty, return min(common) — the smallest shared digit.

3. Otherwise, find a = min(nums1) and b = min(nums2).

4. Return the two-digit number min(a,b) * 10 + max(a,b).

The entire function is branchless after the initial if — no loops beyond what min() and set operations do internally.

Invariants

• Digits are 1-9 — The problem guarantees no zeros, so min(a,b) * 10 + max(a,b) always produces a valid two-digit number (11-99). A zero in either array would break the tens-place assumption.
• Uniqueness within each array — Each array contains unique digits, so set conversion is lossless.
• Common digit always wins — Any single-digit number (1-9) is smaller than any two-digit number (11-99), so checking for a common digit first is correct and sufficient.

Error Handling

None. The function trusts its inputs match the problem constraints (non-empty arrays of unique digits 1-9). Empty arrays would cause min() to raise ValueError.