What is the time complexity of Smallest Missing Non-negative Integer After Operations?

The optimal solution for Smallest Missing Non-negative Integer After Operations runs in O(n) time and uses O(n) space. The time complexity is linear because we traverse the list once to populate the set and then check for MEX in a linear manner.

What is the brute force solution for Smallest Missing Non-negative Integer After Operations?

The brute force approach for Smallest Missing Non-negative Integer After Operations is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible integer starting from 0 to see if we can form it using the operations allowed. This is straightforward but inefficient as it checks each integer sequentially. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Smallest Missing Non-negative Integer After Operations?

Smallest Missing Non-negative Integer After Operations uses the following concepts: Array, Hash Table, Math, Greedy. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Smallest Missing Non-negative Integer After Operations?

Always clarify the constraints and edge cases before diving into coding. Think about how you can reduce the number of checks needed — look for patterns. Practice explaining your thought process as you code; it helps solidify your understanding.

What are common mistakes when solving Smallest Missing Non-negative Integer After Operations?

Not considering negative numbers properly when calculating MEX. Overcomplicating the problem by trying to simulate every operation instead of using mathematical properties.

#2598

Smallest Missing Non-negative Integer After Operations

Medium

ArrayHash TableMathGreedyHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution leverages modular arithmetic to determine which integers can be formed. By grouping numbers based on their remainder when divided by `value`, we can efficiently find the maximum MEX.

⚙️

Algorithm

3 steps

1Step 1: Create a set to store the reachable integers based on their remainders when divided by `value`.
2Step 2: For each number in `nums`, calculate its effective value as `num % value` and add it to the set if it is non-negative.
3Step 3: Iterate from 0 upwards, checking if each integer is in the set. The first integer not found is the maximum MEX.

solution.py12 lines

1# Full working Python code
2
3def max_mex(nums, value):
4    reachable = set()
5    for num in nums:
6        if num >= 0:
7            reachable.add(num % value)
8    mex = 0
9    while mex in reachable:
10        mex += 1
11    return mex
12

ℹ

Complexity note: The time complexity is linear because we traverse the list once to populate the set and then check for MEX in a linear manner.

1Using modular arithmetic allows us to efficiently determine which integers can be formed.
2The MEX is determined by checking sequentially from 0 upwards, making it easy to find the first missing integer.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.