0074-Search-a-2D-Matrix.py

'''
Write an efficient algorithm that searches for a value in an m x n 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, 50]
]
target = 3
Output: true
Example 2:

Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 13
Output: false
'''
class Solution:
    def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
        if not matrix:
            return False

        rows, cols = len(matrix), len(matrix[0])
        low, high = 0, rows * cols - 1
        
        while low <= high:
            mid = (low + high) // 2
            num = matrix[mid // cols][mid % cols]

            if num == target: return True
            elif num < target: low = mid + 1
            else: high = mid - 1
        
        return False