K Pairs with smallest sum
Detailed guide and Python implementation for the 'K Pairs with smallest sum' problem.
1. Concept Overview
The 'K Pairs with smallest sum' problem is a key challenge in the Arrays 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 K Pairs with smallest sum.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for K Pairs with smallest sum 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
Write a function k_smallest_pairs(nums1, nums2, k) that takes two sorted integer arrays nums1 and nums2 and an integer k. Return the first k pairs [u, v] with the smallest sums, where u is from nums1 and v is from nums2, sorted by their sum in ascending order.
- •1 <= len(nums1), len(nums2) <= 10^4
- •1 <= k <= 1000
Examples
nums1 = [1, 7, 11], nums2 = [2, 4, 6], k = 3
[[1, 2], [1, 4], [1, 6]]
The smallest sum pairs are (1,2) sum=3, (1,4) sum=5, (1,6) sum=7.
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
import heapq
def k_smallest_pairs_opt(nums1, nums2, k):
res = []; minH = [[nums1[0] + nums2[0], 0, 0]]
visit = set([(0, 0)])
while minH and len(res) < k:
s, i, j = heapq.heappop(minH)
res.append([nums1[i], nums2[j]])
if i + 1 < len(nums1) and (i + 1, j) not in visit:
heapq.heappush(minH, [nums1[i+1] + nums2[j], i + 1, j])
visit.add((i + 1, j))
if j + 1 < len(nums2) and (i, j + 1) not in visit:
heapq.heappush(minH, [nums1[i] + nums2[j+1], i, j + 1])
visit.add((i, j + 1))
return resBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def k_smallest_pairs_brute(nums1, nums2, k):
res = []
for n1 in nums1:
for n2 in nums2: res.append([n1, n2])
res.sort(key=lambda x: x[0] + x[1])
return res[:k]Algorithm Pattern Checklist
When dealing with Arrays data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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