# https://leetcode.com/problems/search-a-2d-matrix/
"""
Write an efficient algorithm that searches for a value target in an m x n integer matrix matrix. This matrix has the following properties:

Integers in each row are sorted from left to right.
The first integer of each row is greater than the last integer of the previous row.

Example 1:
Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 3
Output: true

Example 2:
Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13
Output: false

Constraints:
m == matrix.length
n == matrix[i].length
1 <= m, n <= 100
-104 <= matrix[i][j], target <= 104
"""


def search_matrix(matrix: list[list[int]], target: int) -> bool:
    rows, cols = len(matrix), len(matrix[0])
    left, right = 0, rows * cols - 1
    while left <= right:
        mid = (left + right) // 2
        r, c = divmod(mid, cols)
        if matrix[r][c] == target:
            return True
        if matrix[r][c] > target:
            right = mid - 1
        elif matrix[r][c] < target:
            left = mid + 1
    return False
