# Find K Pairs With Smallest Sums Problem

## Description

LeetCode Problem 373.

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 (u_1, v_1), (u_2, v_2), …, (u_k, v_k) with the smallest sums.

Example 1:

``````1
2
3
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:

``````1
2
3
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:

``````1
2
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 <= 10^5
• -10^9 <= nums1[i], nums2[i] <= 10^9
• nums1 and nums2 both are sorted in ascending order.
• 1 <= k <= 1000

## Sample C++ Code

``````1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
class Solution {
public:
vector<vector<int>> kSmallestPairs(vector<int>& nums1, vector<int>& nums2, int k) {
vector<vector<int>> ans;
priority_queue<vector<int>, vector<vector<int>>, greater<vector<int>> > pq;

if (nums1.empty() || nums2.empty())
return ans;

for (int i = 0; i < nums1.size(); i ++) {
for (int j = 0; j < nums2.size(); j ++) {
pq.push({nums1[i]+nums2[j], nums1[i], nums2[j]});
}
}

while (!pq.empty() && k > 0) {
k --;
vector<int> temp;
temp.push_back(pq.top()[1]);
temp.push_back(pq.top()[2]);
ans.push_back(temp);
pq.pop();
}

return ans;
}
};
``````