Find K Pairs with Smallest Sums

Find K Pairs with Smallest Sums

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.

Examples

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 with smallest sums are:
  (1, 2), (1, 4), (1, 6)

Example 2:

Input: nums1 = [1, 1, 2], nums2 = [1, 2, 3], k = 2
Output: [[1, 1], [1, 1]]
Explanation: The first 2 pairs with smallest sums are:
  (1, 1), (1, 1)

Example 3:

Input: nums1 = [1, 2], nums2 = [3], k = 3
Output: [[1, 3], [2, 3]]
Explanation: All possible pairs are (1, 3) and (2, 3). Only 2 pairs exist.

Constraints

• 1 <= nums1.length, nums2.length <= 10^5
• -10^9 <= nums1[i], nums2[i] <= 10^9
• nums1 and nums2 are sorted in non-decreasing order.
• 1 <= k <= 10^4
• k <= nums1.length * nums2.length

Expected Complexity

• Time: O(k log k)
• Space: O(k)