Leetcode 378. Kth Smallest Element in a Sorted Matrix (Medium) (cpp)

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本文提供了一种解决LeetCode上第378题“有序矩阵中第K小的元素”的有效方法。该题要求在一个每行每列都按升序排列的n×n矩阵中找到第K小的元素。解决方案利用了二分查找和上界查找方法来高效地解决问题。

Leetcode 378. Kth Smallest Element in a Sorted Matrix (Medium) (cpp)

Tag: Binary Search, Heap

Difficulty: Medium

/*

378. Kth Smallest Element in a Sorted Matrix (Medium)

Given a n x n matrix where each of the rows and columns are sorted in ascending order, find the kth smallest element in the matrix.

Note that it is the kth smallest element in the sorted order, not the kth distinct element.

Example:

matrix = [
   [ 1,  5,  9],
   [10, 11, 13],
   [12, 13, 15]
],
k = 8,

return 13.
Note: 
You may assume k is always valid, 1 ≤ k ≤ n2.

*/
class Solution {
public:
    int kthSmallest(vector<vector<int>>& matrix, int k) {
        int r = matrix.size() - 1, min = matrix[0][0], max = matrix[r][r];
        while (min < max) {
            int cnt = 0, mid = (min + max) / 2;
            for (int i = 0; i <= r && matrix[i][0] <= mid; i++)
                cnt += upper_bound(matrix[i].begin(), matrix[i].end(), mid) - matrix[i].begin();
            k <= cnt ? max = mid : min = mid + 1;
        }
        return min;
    }
};