<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>

class Compare {
    public:
       bool operator()(std::pair<int, int>& lhs, std::pair<int, int>& rhs){
          return (lhs.first + lhs.second) < (rhs.first + rhs.second);
      }
};

class Solution {
public:
    vector<vector<int>> kSmallestPairs(vector<int>& nums1, vector<int>& nums2, int k) {
       // Lesson1: Compare should be a class in which we define a bool operator.
       // for maxheap (max on top), use <. For minheap (min on top) use >
        std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int>>, Compare> pairs;

        // At this point the maximum sum should be at the top.
        // bool done  = false;
        for (int i = 0; i < nums1.size(); i++) {
            for (int j = 0;j < nums2.size(); j++) {
                if (k > 0) {
                    pairs.push({nums1[i], nums2[j]});
                    k--;
                    continue;
                } else if (nums1[i] + nums2[j] < (pairs.top().first + pairs.top().second)) {
                    // remove the max and replace with current pair
                    pairs.pop(); 
                    pairs.push({nums1[i], nums2[j]});
                }  else break;
            }
        }

        // construct the vector
        std::vector<std::vector<int>> final;
        while(!pairs.empty()) {
             final.push_back({pairs.top().first, pairs.top().second});
             pairs.pop();
        }

        return final;
    }
};
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