LeetCode #2605 — EASY

Form Smallest Number From Two Digit Arrays

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

Problem Statement

Given two arrays of unique digits nums1 and nums2, return the smallest number that contains at least one digit from each array.

Example 1:

Input: nums1 = [4,1,3], nums2 = [5,7]
Output: 15
Explanation: The number 15 contains the digit 1 from nums1 and the digit 5 from nums2. It can be proven that 15 is the smallest number we can have.

Example 2:

Input: nums1 = [3,5,2,6], nums2 = [3,1,7]
Output: 3
Explanation: The number 3 contains the digit 3 which exists in both arrays.

Constraints:

1 <= nums1.length, nums2.length <= 9
1 <= nums1[i], nums2[i] <= 9
All digits in each array are unique.

Step 01

Brute Force Baseline

Problem summary: Given two arrays of unique digits nums1 and nums2, return the smallest number that contains at least one digit from each array.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Hash Map

Example 1

[4,1,3]
[5,7]

Example 2

[3,5,2,6]
[3,1,7]

Step 02

Core Insight

What unlocks the optimal approach

How many digits will the resulting number have at most?
The resulting number will have either one or two digits. Try to find when each case is possible.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2605: Form Smallest Number From Two Digit Arrays
class Solution {
    public int minNumber(int[] nums1, int[] nums2) {
        int ans = 100;
        for (int a : nums1) {
            for (int b : nums2) {
                if (a == b) {
                    ans = Math.min(ans, a);
                } else {
                    ans = Math.min(ans, Math.min(a * 10 + b, b * 10 + a));
                }
            }
        }
        return ans;
    }
}

// Accepted solution for LeetCode #2605: Form Smallest Number From Two Digit Arrays
func minNumber(nums1 []int, nums2 []int) int {
	ans := 100
	for _, a := range nums1 {
		for _, b := range nums2 {
			if a == b {
				ans = min(ans, a)
			} else {
				ans = min(ans, min(a*10+b, b*10+a))
			}
		}
	}
	return ans
}

# Accepted solution for LeetCode #2605: Form Smallest Number From Two Digit Arrays
class Solution:
    def minNumber(self, nums1: List[int], nums2: List[int]) -> int:
        ans = 100
        for a in nums1:
            for b in nums2:
                if a == b:
                    ans = min(ans, a)
                else:
                    ans = min(ans, 10 * a + b, 10 * b + a)
        return ans

// Accepted solution for LeetCode #2605: Form Smallest Number From Two Digit Arrays
impl Solution {
    pub fn min_number(nums1: Vec<i32>, nums2: Vec<i32>) -> i32 {
        let mut ans = 100;

        for &a in &nums1 {
            for &b in &nums2 {
                if a == b {
                    ans = std::cmp::min(ans, a);
                } else {
                    ans = std::cmp::min(ans, std::cmp::min(a * 10 + b, b * 10 + a));
                }
            }
        }

        ans
    }
}

// Accepted solution for LeetCode #2605: Form Smallest Number From Two Digit Arrays
function minNumber(nums1: number[], nums2: number[]): number {
    let ans = 100;
    for (const a of nums1) {
        for (const b of nums2) {
            if (a === b) {
                ans = Math.min(ans, a);
            } else {
                ans = Math.min(ans, a * 10 + b, b * 10 + a);
            }
        }
    }
    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(m × n)

Space

O(1)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.