LeetCode Top Interview 150

373. Find K Pairs with Smallest Sums

Medium

You are given two integer arrays nums1 and nums2 sorted in ascending order and an integer k.

Define a pair (u, v) which consists of one element from the first array and one element from the second array.

Return the k pairs (u1, v1), (u2, v2), ..., (uk, vk) with the smallest sums.

Example 1:

Input: nums1 = [1,7,11], nums2 = [2,4,6], k = 3

Output: [[1,2],[1,4],[1,6]]

Explanation: The first 3 pairs are returned from the sequence: [1,2],[1,4],[1,6],[7,2],[7,4],[11,2],[7,6],[11,4],[11,6]

Example 2:

Input: nums1 = [1,1,2], nums2 = [1,2,3], k = 2

Output: [[1,1],[1,1]]

Explanation: The first 2 pairs are returned from the sequence: [1,1],[1,1],[1,2],[2,1],[1,2],[2,2],[1,3],[1,3],[2,3]

Example 3:

Input: nums1 = [1,2], nums2 = [3], k = 3

Output: [[1,3],[2,3]]

Explanation: All possible pairs are returned from the sequence: [1,3],[2,3]

Constraints:

• 1 <= nums1.length, nums2.length <= 105
• -109 <= nums1[i], nums2[i] <= 109
• nums1 and nums2 both are sorted in ascending order.
• 1 <= k <= 1000

Solution

import heapq
from typing import List

class Solution:
    def kSmallestPairs(self, nums1: List[int], nums2: List[int], k: int) -> List[List[int]]:
        if not nums1 or not nums2:
            return []
        
        heap = []
        result = []
        
        # Initialize heap with first k pairs from nums1 and first element of nums2
        for i in range(min(len(nums1), k)):
            heapq.heappush(heap, (nums1[i] + nums2[0], i, 0))
        
        # Extract k smallest pairs
        for _ in range(min(k, len(nums1) * len(nums2))):
            if not heap:
                break
            _, i, j = heapq.heappop(heap)
            result.append([nums1[i], nums2[j]])
            
            # Add next pair from nums2 if available
            if j + 1 < len(nums2):
                heapq.heappush(heap, (nums1[i] + nums2[j + 1], i, j + 1))
        
        return result

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