Write an efficient algorithm that searches for a target value in an m x n integer matrix. The matrix has the following properties:

Integers in each row are sorted in ascending from left to right.
Integers in each column are sorted in ascending from top to bottom.

Example 1:

Input: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 5
Output: true

Example 2:

Input: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 20
Output: false

Constraints:

m == matrix.length
n == matrix[i].length
1 <= n, m <= 300
-10^9 <= matix[i][j] <= 10^9
All the integers in each row are sorted in ascending order.
All the integers in each column are sorted in ascending order.
-10^9 <= target <= 10^9

Solution

Time complexity : O(m+n)
Space complexity : O(1)

class Solution {
public:
    bool searchMatrix(vector<vector<int>>& matrix, int target) {
        const int rows = matrix.size(), cols = matrix[0].size();
        int r = 0, c = cols-1;
        while (r < rows && 0 <= c) {
            if (matrix[r][c] == target) return true;
            matrix[r][c] < target ? ++r : --c;
        }
        return false;
    }
};