373. Find K Pairs with Smallest Sums

Problem Link

Description

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You are given two integer arrays nums1 and nums2 sorted in non-decreasing 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]

 

Constraints:

• 1 <= nums1.length, nums2.length <= 105
• -109 <= nums1[i], nums2[i] <= 109
• nums1 and nums2 both are sorted in non-decreasing order.
• 1 <= k <= 104
• k <= nums1.length * nums2.length

Solution

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Python3

class Solution:
    def kSmallestPairs(self, nums1: List[int], nums2: List[int], k: int) -> List[List[int]]:
        M, N = len(nums1), len(nums2)
        pq = []
        res = []
 
        for i in range(min(M, k)):
            heappush(pq, (nums1[i] + nums2[0], i, 0))
        
        for _ in range(k):
            if not pq: break
 
            _, i, j = heappop(pq)
            res.append([nums1[i], nums2[j]])
            if j == N - 1: continue
            heappush(pq, (nums1[i] + nums2[j + 1], i, j + 1))
        
        return res