Plus One
Detailed guide and Python implementation for the 'Plus One' problem.
1. Concept Overview
The 'Plus One' problem is a key challenge in the Math & Geometry section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Plus One.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Plus One carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
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.
- •1 <= digits.length <= 100
- •0 <= digits[i] <= 9
- •digits does not contain any leading 0's
Examples
[1,2,3]
[1,2,4]
The array represents the integer 123. Incrementing by one gives 124.
[4,3,2,1]
[4,3,2,2]
The array represents the integer 4321. Incrementing by one gives 4322.
[9]
[1,0]
The array represents the integer 9. Incrementing by one gives 10, which is [1,0].
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def plus_one_opt(digits: list[int]) -> list[int]:
for i in range(len(digits) - 1, -1, -1):
if digits[i] < 9:
digits[i] += 1
return digits
digits[i] = 0
return [1] + digitsBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def plus_one_brute(digits: list[int]) -> list[int]:
num = int("".join(map(str, digits))) + 1
return [int(i) for i in str(num)]Algorithm Pattern Checklist
When dealing with Math & Geometry data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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