What is the brute force solution for Smallest Missing Integer Greater Than Sequential Prefix Sum?

The brute force approach for Smallest Missing Integer Greater Than Sequential Prefix Sum is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every prefix of the array to find the longest sequential prefix and then calculates its sum. This method is straightforward but inefficient as it involves checking each prefix multiple times. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Smallest Missing Integer Greater Than Sequential Prefix Sum?

Smallest Missing Integer Greater Than Sequential Prefix Sum uses the following concepts: Array, Hash Table, Sorting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Smallest Missing Integer Greater Than Sequential Prefix Sum?

Always clarify the problem statement and constraints before diving into coding. Think about edge cases, such as arrays with only one element or all elements being sequential. Discuss your thought process and approach with the interviewer before writing code.

What are common mistakes when solving Smallest Missing Integer Greater Than Sequential Prefix Sum?

Failing to correctly identify when the sequential prefix ends. Not utilizing efficient data structures like sets for quick lookups.

#2996

Smallest Missing Integer Greater Than Sequential Prefix Sum

Easy

ArrayHash TableSortingHash 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 approach efficiently finds the longest sequential prefix in a single pass and uses a set to track existing numbers, allowing for quick checks for the smallest missing integer.

⚙️

Algorithm

3 steps

1Step 1: Initialize a set to store the numbers in the array for quick lookup.
2Step 2: Iterate through the array to find the longest sequential prefix and calculate its sum.
3Step 3: After determining the sum, check for the smallest integer greater than or equal to this sum that is not in the set.

solution.py23 lines

1# Full working Python code
2
3def smallest_missing_integer(nums):
4    num_set = set(nums)
5    max_sum = 0
6    current_sum = 0
7
8    for i in range(len(nums)):
9        if i == 0 or nums[i] == nums[i - 1] + 1:
10            current_sum += nums[i]
11        else:
12            max_sum = max(max_sum, current_sum)
13            current_sum = nums[i]
14
15    max_sum = max(max_sum, current_sum)
16
17    missing = max_sum
18    while missing in num_set:
19        missing += 1
20    return missing
21
22# Example usage
23print(smallest_missing_integer([1, 2, 3, 2, 5]))  # Output: 6

ℹ

Complexity note: The time complexity is O(n) because we only make a single pass through the array to find the longest sequential prefix and another pass to find the missing integer. The space complexity is O(n) due to the set used for quick lookups.

1The longest sequential prefix can be found in a single pass through the array.
2Using a set allows for O(1) average time complexity for checking existence of numbers.

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