<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 Solution {
public:
    struct compare {
        bool operator()(vector<int>& a, vector<int>& b) {
            return a[2] > b[2];
        }
    };

    vector<vector<int>> kSmallestPairs(vector<int>& nums1, vector<int>& nums2, int k) {
        int i = 0, j = 0;
        // min heap
        priority_queue<vector<int>, vector<vector<int>>, compare> pq;
        pq.push({0, 0, nums1[0] + nums2[0]});
        vector<vector<int>> res;
        set<pair<int, int>> visited;
        while (k > 0) {
            int cur1 = pq.top()[0];
            int cur2 = pq.top()[1];
            pq.pop();
            res.push_back({nums1[cur1], nums2[cur2]});
            k--;
            if (k == 0) {
                break;
            }
            int curNum1 = cur1 + 1;
            if (curNum1 < nums1.size() && !visited.count({curNum1, cur2})) {
                pq.push({curNum1, cur2, nums1[curNum1] + nums2[cur2]});
                visited.insert({curNum1, cur2});
            }
            int curNum2 = cur2 + 1;
            if (curNum2 < nums2.size() && !visited.count({cur1, curNum2})) {
                pq.push({cur1, curNum2, nums1[cur1] + nums2[curNum2]});
                visited.insert({cur1, curNum2});
            }
        }
        return res;
    }
};
145546