README_EN.md

378. Kth Smallest Element in a Sorted Matrix

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Description

Given an n x n matrix where each of the rows and columns are sorted in ascending order, return 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 1:

Input: matrix = [[1,5,9],[10,11,13],[12,13,15]], k = 8
Output: 13
Explanation: The elements in the matrix are [1,5,9,10,11,12,13,13,15], and the 8th smallest number is 13

Example 2:

Input: matrix = [[-5]], k = 1
Output: -5

 

Constraints:

• n == matrix.length
• n == matrix[i].length
• 1 <= n <= 300
• -109 <= matrix[i][j] <= 109
• All the rows and columns of matrix are guaranteed to be sorted in non-decreasing order.
• 1 <= k <= n2

Solutions

Binary search.

Python3

class Solution:
    def kthSmallest(self, matrix: List[List[int]], k: int) -> int:
        def check(matrix, mid, k, n):
            count = 0
            i, j = n - 1, 0
            while i >= 0 and j < n:
                if matrix[i][j] <= mid:
                    count += (i + 1)
                    j += 1
                else:
                    i -= 1
            return count >= k

        n = len(matrix)
        left, right = matrix[0][0], matrix[n - 1][n - 1]
        while left < right:
            mid = (left + right) >> 1
            if check(matrix, mid, k, n):
                right = mid
            else:
                left = mid + 1
        return left

Java

class Solution {
    public int kthSmallest(int[][] matrix, int k) {
        int n = matrix.length;
        int left = matrix[0][0], right = matrix[n - 1][n - 1];
        while (left < right) {
            int mid = (left + right) >>> 1;
            if (check(matrix, mid, k, n)) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }

    private boolean check(int[][] matrix, int mid, int k, int n) {
        int count = 0;
        int i = n - 1, j = 0;
        while (i >= 0 && j < n) {
            if (matrix[i][j] <= mid) {
                count += (i + 1);
                ++j;
            } else {
                --i;
            }
        }
        return count >= k;
    }
}

C++

class Solution {
public:
    int kthSmallest(vector<vector<int>>& matrix, int k) {
        int n = matrix.size();
        int left = matrix[0][0], right = matrix[n - 1][n - 1];
        while (left < right) {
            int mid = left + right >> 1;
            if (check(matrix, mid, k, n)) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }

private:
    bool check(vector<vector<int>>& matrix, int mid, int k, int n) {
        int count = 0;
        int i = n - 1, j = 0;
        while (i >= 0 && j < n) {
            if (matrix[i][j] <= mid) {
                count += (i + 1);
                ++j;
            } else {
                --i;
            }
        }
        return count >= k;
    }
};

Go

func kthSmallest(matrix [][]int, k int) int {
	n := len(matrix)
	left, right := matrix[0][0], matrix[n-1][n-1]
	for left < right {
		mid := (left + right) >> 1
		if check(matrix, mid, k, n) {
			right = mid
		} else {
			left = mid + 1
		}
	}
	return left
}

func check(matrix [][]int, mid, k, n int) bool {
	count := 0
	i, j := n-1, 0
	for i >= 0 && j < n {
		if matrix[i][j] <= mid {
			count += (i + 1)
			j++
		} else {
			i--
		}
	}
	return count >= k
}

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