链接：LintCode 炼码 - ChatGPT！更高效的学习体验！

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class Solution {
public:
    /**
     * @param matrix: a matrix of integers
     * @param k: An integer
     * @return: the kth smallest number in the matrix
     */
class Node {
public:
    Node(int v, int i):val(v),index(i) {

    }
    bool operator < (const Node& node) const {
        return val > node.val ? true : false;
    }
    int val;
    int index;
};
    int kthSmallest(vector<vector<int>> &matrix, int k) {
        // write your code here
        int m = matrix.size();
        if (m <= 0) {
            return 0;
        }
        int n = matrix[0].size();
        if (n <= 0) {
            return 0;
        }
        std::vector<bool> distance(m*n, false);
        distance[0] = true;
        std::priority_queue<Node> que;
        que.push(Node(matrix[0][0], 0)); 
        int i = 1;
        std::vector<std::vector<int>> direction{{0, 1}, {1, 0}};
        while (!que.empty()) {
            auto f = que.top();
            que.pop();
            if (i >= k) {
                return f.val;
            }
            for (int j = 0; j < direction.size(); ++j) {
                int next_row = f.index / n + direction[j][0];
                int next_col = f.index % n + direction[j][1];
                if (next_row < 0 || next_col < 0 || next_row >= m || next_col >= n) {
                    continue;
                }
                int node = next_row * n + next_col;
                if (distance[node]) {
                    continue;
                }
                que.push(Node(matrix[next_row][next_col], node));
                distance[node] = true;
            }
            ++i;
        }
        return -1;
    }
};