Search a 2D Matrix

Problem

https://leetcode.com/problems/search-a-2d-matrix/

You are given an m x n integer matrix matrix with the following two properties:

Each row is sorted in non-decreasing order.
The first integer of each row is greater than the last integer of the previous row.

Given an integer target, return true if target is in matrix or false otherwise.

You must write a solution in O(log(m * n)) time complexity.

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
-10:sup:`4`<= matrix[i][j], target <= 10:sup:`4`

Pattern

Array, Binary Search, Matrix

Approaches

Binary Search

Code

def searchMatrix(matrix: list[list[int]], target: int) -> bool:
    m = len(matrix)
    n = len(matrix[0])

    left = 0
    right = m * n - 1
    while left <= right:
        mid = (left + right) // 2

        rows = mid // n
        cols = mid % n

        if matrix[rows][cols] == target:
            return True
        elif matrix[rows][cols] > target:
            right = mid - 1
        else:
            left = mid + 1

    return False

Test

>>> from search_a_2d_matrix__binary_search import searchMatrix
>>> searchMatrix([[1,3,5,7],[10,11,16,20],[23,30,34,60]], 3)
True
>>> searchMatrix([[1,3,5,7],[10,11,16,20],[23,30,34,60]], 13)
False

search_a_2d_matrix__binary_search.searchMatrix(matrix: list[list[int]], target: int) → bool