LeetCode #3731 — EASY

Find Missing Elements

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

The Problem

Problem Statement

You are given an integer array nums consisting of unique integers.

Originally, nums contained every integer within a certain range. However, some integers might have gone missing from the array.

The smallest and largest integers of the original range are still present in nums.

Return a sorted list of all the missing integers in this range. If no integers are missing, return an empty list.

Example 1:

Input: nums = [1,4,2,5]

Output: [3]

Explanation:

The smallest integer is 1 and the largest is 5, so the full range should be [1,2,3,4,5]. Among these, only 3 is missing.

Example 2:

Input: nums = [7,8,6,9]

Output: []

Explanation:

The smallest integer is 6 and the largest is 9, so the full range is [6,7,8,9]. All integers are already present, so no integer is missing.

Example 3:

Input: nums = [5,1]

Output: [2,3,4]

Explanation:

The smallest integer is 1 and the largest is 5, so the full range should be [1,2,3,4,5]. The missing integers are 2, 3, and 4.

Constraints:

2 <= nums.length <= 100
1 <= nums[i] <= 100

Step 01

Brute Force Baseline

Problem summary: You are given an integer array nums consisting of unique integers. Originally, nums contained every integer within a certain range. However, some integers might have gone missing from the array. The smallest and largest integers of the original range are still present in nums. Return a sorted list of all the missing integers in this range. If no integers are missing, return an empty list.

Baseline thinking

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

Pattern signal: Array · Hash Map

Example 1

[1,4,2,5]

Example 2

[7,8,6,9]

Example 3

[5,1]

Step 02

Core Insight

What unlocks the optimal approach

First, find the maximum and minimum elements in the array.
Then, iterate over all the integers in the range <code>[min, max]</code> and check if they are in the array.
If not, add them to the array, and return the sorted array at the end.

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 #3731: Find Missing Elements
class Solution {
    public List<Integer> findMissingElements(int[] nums) {
        int mn = 100, mx = 0;
        Set<Integer> s = new HashSet<>();
        for (int x : nums) {
            mn = Math.min(mn, x);
            mx = Math.max(mx, x);
            s.add(x);
        }
        List<Integer> ans = new ArrayList<>();
        for (int x = mn + 1; x < mx; ++x) {
            if (!s.contains(x)) {
                ans.add(x);
            }
        }
        return ans;
    }
}

// Accepted solution for LeetCode #3731: Find Missing Elements
func findMissingElements(nums []int) (ans []int) {
	mn, mx := 100, 0
	s := make(map[int]bool)
	for _, x := range nums {
        mn = min(mn, x)
        mx = max(mx, x)
		s[x] = true
	}
	for x := mn + 1; x < mx; x++ {
		if !s[x] {
			ans = append(ans, x)
		}
	}
	return
}

# Accepted solution for LeetCode #3731: Find Missing Elements
class Solution:
    def findMissingElements(self, nums: List[int]) -> List[int]:
        mn, mx = min(nums), max(nums)
        s = set(nums)
        return [x for x in range(mn + 1, mx) if x not in s]

// Accepted solution for LeetCode #3731: Find Missing Elements
fn find_missing_elements(nums: Vec<i32>) -> Vec<i32> {
    let mut nums = nums;
    nums.sort_unstable();

    let mut ret = vec![];
    let mut prev = nums[0];
    for n in nums.into_iter().skip(1) {
        if n - prev != 1 {
            for i in (prev + 1)..n {
                ret.push(i);
            }
        }

        prev = n;
    }

    ret
}

fn main() {
    let ret = find_missing_elements(vec![1, 9]);
    println!("ret={ret:?}");
}

#[test]
fn test() {
    assert_eq!(find_missing_elements(vec![1, 4, 2, 5]), [3]);
    assert_eq!(find_missing_elements(vec![7, 8, 6, 9]), []);
    assert_eq!(find_missing_elements(vec![5, 1]), [2, 3, 4]);
}

// Accepted solution for LeetCode #3731: Find Missing Elements
function findMissingElements(nums: number[]): number[] {
    let [mn, mx] = [100, 0];
    const s = new Set<number>();
    for (const x of nums) {
        mn = Math.min(mn, x);
        mx = Math.max(mx, x);
        s.add(x);
    }
    const ans: number[] = [];
    for (let x = mn + 1; x < mx; ++x) {
        if (!s.has(x)) {
            ans.push(x);
        }
    }
    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(n)

Space

O(n)

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.