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
Explanation: 3 is found in the matrix at row 0, column 1.
Example 2:
Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13
Output: false
Explanation: 13 is not present in the matrix.
Examples
Example 1
Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 3
Output: true
Explanation: 3 is found in the matrix at row 0, column 1.
Example 2
Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13
Output: false
Explanation: 13 is not present in the matrix.
Example 3
Input: matrix = [[1]], target = 1
Output: true
Explanation: The matrix has a single element which equals the target.
Constraints
- -m == matrix.length
- -n == matrix[i].length
- -1 <= m, n <= 100
- --10^4 <= matrix[i][j], target <= 10^4
Optimal Complexity
Time
O(log(m * n))
Space
O(1)
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