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

SOLUTION:

class Solution:
    def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
        m = len(matrix)
        n = len(matrix[0])
        beg = 0
        end = m * n - 1
        while beg <= end:
            mid = (beg + end) // 2
            i = mid // n
            j = mid % n
            if matrix[i][j] == target:
                return True
            elif beg == end:
                break
            elif matrix[i][j] < target:
                beg = mid + 1
            else:
                end = mid
        return False