Smallest Missing Integer Greater Than Sequential Prefix Sum Python/Java solution

Python and Java implementations typically compute the sequential prefix sum with a loop, store elements in a set or HashSet, and increment the candidate value until it is not present. Both languages achieve O(n) time complexity with O(n) additional space.

What is the best approach for Smallest Missing Integer Greater Than Sequential Prefix Sum?

The most efficient approach computes the longest sequential prefix, calculates its sum, and stores all array values in a hash set. Starting from the prefix sum, increment until a value is not found in the set. Hash lookups are O(1), so the overall complexity is O(n) time with O(n) space.

Is Smallest Missing Integer Greater Than Sequential Prefix Sum asked at Google/Amazon/Meta?

This problem follows common patterns seen in technical interviews: prefix processing, hash set membership checks, and missing-number detection. Similar problems appear in interviews at companies like Amazon and Google where candidates must combine array traversal with hash-based lookups.

What data structure is used in Smallest Missing Integer Greater Than Sequential Prefix Sum?

A hash set is the primary data structure used in the optimal solution. It provides constant-time membership checks when searching for the smallest integer that does not appear in the array. The array itself is scanned to detect the sequential prefix.

What is the time complexity of Smallest Missing Integer Greater Than Sequential Prefix Sum?

The optimal solution runs in O(n) time. One pass identifies the longest sequential prefix and builds a hash set of values, and additional checks for the missing integer are constant-time lookups. Space complexity is O(n) due to storing the elements in a hash set.

Description Hints 1 Solution Video 5:15

2996. Smallest Missing Integer Greater Than Sequential Prefix Sum

Q: Is Smallest Missing Integer Greater Than Sequential Prefix Sum easy or hard?

The problem is classified as Easy. It mainly tests careful array traversal and efficient lookup using a hash set. Once the sequential prefix condition is recognized, the remaining step is a straightforward missing-number search.

Q: How to solve Smallest Missing Integer Greater Than Sequential Prefix Sum in O(n)?

First iterate from the beginning of the array while elements increase by exactly one to determine the sequential prefix and compute its sum. Insert all numbers into a hash set. Starting from the prefix sum, repeatedly check if the value exists in the set and increment until a missing number appears. This keeps the entire process linear.

Easy49.8% acceptance2 companies

You are given a 0-indexed array of integers nums.

A prefix nums[0..i] is sequential if, for all 1 <= j <= i, nums[j] = nums[j - 1] + 1. In particular, the prefix consisting only of nums[0] is sequential.

Return the smallest integer x missing from nums such that x is greater than or equal to the sum of the longest sequential prefix.

Example 1:

Input: nums = [1,2,3,2,5]
Output: 6
Explanation: The longest sequential prefix of nums is [1,2,3] with a sum of 6. 6 is not in the array, therefore 6 is the smallest missing integer greater than or equal to the sum of the longest sequential prefix.

Example 2:

Input: nums = [3,4,5,1,12,14,13]
Output: 15
Explanation: The longest sequential prefix of nums is [3,4,5] with a sum of 12. 12, 13, and 14 belong to the array while 15 does not. Therefore 15 is the smallest missing integer greater than or equal to the sum of the longest sequential prefix.

Constraints:

1 <= nums.length <= 50
1 <= nums[i] <= 50

Asked at 2 companies

Microsoft

Google

Topics

Hints open one at a time

Hint 1

To find the longest sequential prefix, iterate from left to right. For a fixed i, if nums[i] != nums[i - 1] + 1 then the longest sequential prefix ends at i - 1.

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