<p>You are given an <code>m x n</code> matrix <code>mat</code> that has its rows sorted in non-decreasing order and an integer <code>k</code>.</p>

<p>You are allowed to choose <strong>exactly one element</strong> from each row to form an array.</p>

<p>Return <em>the </em><code>k<sup>th</sup></code><em> smallest array sum among all possible arrays</em>.</p>

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

<pre>
<strong>Input:</strong> mat = [[1,3,11],[2,4,6]], k = 5
<strong>Output:</strong> 7
<strong>Explanation:</strong> Choosing one element from each row, the first k smallest sum are:
[1,2], [1,4], [3,2], [3,4], [1,6]. Where the 5th sum is 7.
</pre>

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

<pre>
<strong>Input:</strong> mat = [[1,3,11],[2,4,6]], k = 9
<strong>Output:</strong> 17
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> mat = [[1,10,10],[1,4,5],[2,3,6]], k = 7
<strong>Output:</strong> 9
<strong>Explanation:</strong> Choosing one element from each row, the first k smallest sum are:
[1,1,2], [1,1,3], [1,4,2], [1,4,3], [1,1,6], [1,5,2], [1,5,3]. Where the 7th sum is 9.  
</pre>

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

<ul>
	<li><code>m == mat.length</code></li>
	<li><code>n == mat.length[i]</code></li>
	<li><code>1 &lt;= m, n &lt;= 40</code></li>
	<li><code>1 &lt;= mat[i][j] &lt;= 5000</code></li>
	<li><code>1 &lt;= k &lt;= min(200, n<sup>m</sup>)</code></li>
	<li><code>mat[i]</code> is a non-decreasing array.</li>
</ul>


struct CustomCompare {
    bool operator()(const std::pair<long long, std::vector<int>>& a, 
                    const std::pair<long long, std::vector<int>>& b) {
        // 比较规则：优先级由 pair 的第一个元素（long long）决定
        // 默认是最大堆，这里实现从大到小排序
        return a.first > b.first; 
    }
};

class Solution {
public:
    int kthSmallest(vector<vector<int>>& mat, int k)
    {
        if(mat.size() == 0 || mat[0].size() == 0) return 0;
        int row = mat.size();
        int col = mat[0].size();
        // priority_queue<pair<long long, vector<int>>, vector<pair<long long, vector<int>>>, decltype(&myCompare)> minHeap;
        priority_queue<pair<long long, vector<int>>, vector<pair<long long, vector<int>>>, CustomCompare> minHeap;
        vector<int> ptrsV(row, 0);
        // vector<long long> sumsV(row, 0);
        set<string> sumkeyS;
        string sumKey = "";
        long long sum = 0;
        for(int i = 0; i < row; i++)
        {
            sumKey += '0';
            sum += mat[i][0];
        }
        pair<long long, vector<int>> p;
        p.first = sum;
        p.second = ptrsV;
        minHeap.push(p);
        sumkeyS.insert(sumKey);
        int cnt = 0;
        pair<long long, vector<int>> topP;
        while(cnt <= k)
        {
            topP = minHeap.top();
            minHeap.pop();
            cnt++;
            if(cnt >= k) break;
            vector<int> ptrsV = topP.second;
            for(int i = 0; i < row; i++)
            {
                vector<int> v = ptrsV;
                if(v[i] < col - 1)
                {
                    v[i] += 1;
                    sumKey = "";
                    sum = 0;
                    for(int j = 0; j < row; j++)
                    {
                        sumKey += '0' + v[j];
                    }
                    if(sumkeyS.find(sumKey) == sumkeyS.end())
                    {
                        for(int k = 0; k < row; k++)
                        {
                            sum += mat[k][v[k]];
                        }
                        pair<long long, vector<int>> p;
                        p.first = sum;
                        p.second = v;
                        minHeap.push(p);
                        sumkeyS.insert(sumKey);
                    }
                }
            }
        }   
        return topP.first;
    }
};
61726