# 0373-find-k-pairs-with-smallest-sums


Try it on <a href='https://leetcode.com/problems/0373-find-k-pairs-with-smallest-sums'>leetcode</a>

## Description
<div class="description">
<p>You are given two integer arrays <code>nums1</code> and <code>nums2</code> sorted in <strong>non-decreasing&nbsp;order</strong> and an integer <code>k</code>.</p>

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

<p>Return <em>the</em> <code>k</code> <em>pairs</em> <code>(u<sub>1</sub>, v<sub>1</sub>), (u<sub>2</sub>, v<sub>2</sub>), ..., (u<sub>k</sub>, v<sub>k</sub>)</code> <em>with the smallest sums</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [1,7,11], nums2 = [2,4,6], k = 3
<strong>Output:</strong> [[1,2],[1,4],[1,6]]
<strong>Explanation:</strong> 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]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [1,1,2], nums2 = [1,2,3], k = 2
<strong>Output:</strong> [[1,1],[1,1]]
<strong>Explanation:</strong> 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]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums1.length, nums2.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= nums1[i], nums2[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>nums1</code> and <code>nums2</code> both are sorted in <strong>non-decreasing order</strong>.</li>
	<li><code>1 &lt;= k &lt;= 10<sup>4</sup></code></li>
	<li><code>k &lt;=&nbsp;nums1.length *&nbsp;nums2.length</code></li>
</ul>

</div>

## Solution(Python)
```Python
import heapq
class Solution:
    def kSmallestPairs(self, nums1: List[int], nums2: List[int], k: int) -> List[List[int]]:
        m = len(nums1)
        n = len(nums2)

        minHeap = [(nums1[0]+nums2[0] , (0,0))]
        heapq.heapify(minHeap)
        visited = set()
        visited.add((0,0))
        res = []
        while k > 0:
            cur_sum, (i,j) = heapq.heappop(minHeap)
            res.append([nums1[i],nums2[j]])
            

            if i + 1 < m and (i+1,j) not in visited:
                heapq.heappush(minHeap, ( nums1[i+1]+nums2[j],(i+1,j)))
                visited.add((i+1,j))
            if j+ 1 < n and (i,j + 1) not in visited:
                heapq.heappush(minHeap,( nums1[i]+nums2[j+1],(i,j+1)))
                visited.add((i,j+1))

            if i + 1 < m and j+ 1 < n and (i+1,j+1) not in visited:
                heapq.heappush(minHeap,( nums1[i+1]+nums2[j+1],(i+1,j+1)))
                visited.add((i+1,1+j))
            k-=1

        return res
```