Two Sum II
Detailed guide and Python implementation for the 'Two Sum II' problem.
1. Concept Overview
The 'Two Sum II' problem is a key challenge in the Two Pointers 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 Two Sum II.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Two Sum II 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
Given a 1-indexed array of integers numbers that is already sorted in non-decreasing order, find two numbers such that they add up to a specific target number.
Return the indices of the two numbers, index1 and index2, added by one as an integer array [index1, index2] of length 2.
You may not use the same element twice. Your solution must use only constant extra space.
Write a function twoSum(numbers: List[int], target: int) -> List[int].
- •2 <= len(numbers) <= 3 * 10^4
- •-1000 <= numbers[i] <= 1000
- •numbers is sorted in non-decreasing order
- •-1000 <= target <= 1000
- •Exactly one solution exists
Examples
numbers = [2, 7, 11, 15], target = 9
[1, 2]
2 + 7 = 9. The indices are 1 and 2 (1-indexed).
numbers = [2, 3, 4], target = 6
[1, 3]
2 + 4 = 6. The indices are 1 and 3 (1-indexed).
numbers = [-1, 0], target = -1
[1, 2]
-1 + 0 = -1. The indices are 1 and 2 (1-indexed).
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 two_sum_ii_opt(numbers, target):
l, r = 0, len(numbers) - 1
while l < r:
curSum = numbers[l] + numbers[r]
if curSum > target:
r -= 1
elif curSum < target:
l += 1
else:
return [l + 1, r + 1]
return []Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def two_sum_ii_brute(numbers, target):
for i in range(len(numbers)):
for j in range(i + 1, len(numbers)):
if numbers[i] + numbers[j] == target:
return [i + 1, j + 1]
return []Algorithm Pattern Checklist
When dealing with Two Pointers data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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