Search a 2D Matrix
Given an m x n matrix where each row is sorted and the first element of each row is greater than the last element of the previous row, determine if a target value exists.
Input: matrix rows comma-separated, then target on last line.
Example:
1,3,5,7 10,11,16,20 23,30,34,60 3
True
- The input matrix is: 1, 3, 5, 7 10, 11, 16, 20 23, 30, 34, 60
- We treat the 2D matrix as a 1D sorted array: 1, 3, 5, 7, 10, 11, 16, 20, 23, 30, 34, 60
- To find the target value 3, we can use a binary search algorithm, which has a time complexity of O(log(mn))
- Since 3 is present in the sorted array, the output is True
Constraints:
- 1 <= m, n <= 100
- -10^4 <= matrix[i][j], target <= 10^4
Background Knowledge
The problem involves searching for a target value in a 2D matrix where each row is sorted. This is a classic example of a searching problem, which is a fundamental concept in computer science. To tackle this problem, it's essential to understand the properties of the given matrix. Since each row is sorted and the first element of each row is greater than the last element of the previous row, we can consider the matrix as a sorted array if we were to flatten it.
The concept of sorted arrays and searching algorithms is crucial here. In a sorted array, elements are arranged in a specific order, either ascending or descending. This ordering allows for efficient searching using algorithms like binary search, which has a time complexity of O(logn). However, the matrix structure adds an extra layer of complexity, requiring us to adapt our searching strategy.
Understanding the relationship between the rows and columns in the matrix is vital. Since each row is sorted and the first element of each row is greater than the last element of the previous row, we can think of the matrix as a series of connected sorted arrays. This relationship can be leveraged to develop an efficient searching algorithm.
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