What is the optimal time complexity of solving Plus One?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Plus One?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Plus One?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Plus One?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Plus One

Learn how to solve the 'Plus One' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

You are given a large integer represented as an integer array digits, where each digits[i] is the ith digit of the integer. The digits are ordered from most significant to least significant in left-to-right order. The large integer does not contain any leading 0's.

Increment the large integer by one and return the resulting array of digits.

Implement a function plusOne(digits: list) -> list.

Constraints

•1 <= digits.length <= 100
•0 <= digits[i] <= 9
•digits does not contain any leading 0's

Examples

Example 1

Input

[1,2,3]

Output

[1,2,4]

Explanation

The array represents the integer 123. Incrementing by one gives 124.

Example 2

Input

[4,3,2,1]

Output

[4,3,2,2]

Explanation

The array represents the integer 4321. Incrementing by one gives 4322.

Example 3

Input

[9]

Output

[1,0]

Explanation

The array represents the integer 9. Incrementing by one gives 10, which is [1,0].

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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