LeetCode 74: Search a 2D Matrix

Problem Description

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
-10⁴ <= matrix[i][j], target <= 10⁴

Difficulty: Medium

Tags: array, binary search, matrix

Rating: 97.41%

Solution

Here’s my Python solution to this problem:

class Solution:
    def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
        if not matrix or not matrix[0]:
            return False

        m, n = len(matrix), len(matrix[0])
        l, r = 0, m*n - 1

        while l <= r:
            mid = l + (r - l) // 2
            row = mid // n
            col = mid % n

            if matrix[row][col] == target:
                return True
            elif matrix[row][col] > target:
                r = mid - 1
            else:
                l = mid + 1
        return False