373. Find K Pairs with Smallest Sums

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

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 <= 104

🧠 Thuật Toán & Kỹ Thuật

Heap / Priority Queue (Heap / Hàng đợi ưu tiên)
⏱️ Thời gian O(n)
💾 Không gian O(n)

💻 Lời Giải

Python 0373-find-k-pairs-with-smallest-sums.py 
class Solution:
    def kSmallestPairs(self, nums1: List[int], nums2: List[int], k: int) -> List[List[int]]:
        n, m = len(nums1), len(nums2)
        heap = [(nums1[0] + nums2[0], 0, 0)]
        ans = []
        
        while len(heap) and len(ans) < k:
            _, i, j = heappop(heap)
            ans.append([nums1[i], nums2[j]])
            
            if i < n and j + 1 < m:
                heappush(heap, (nums1[i] + nums2[j + 1], i, j + 1))
                
            if j == 0 and i + 1 < n and j < m:
                heappush(heap, (nums1[i + 1] + nums2[j], i + 1, j))
                
        return ans