Search in row wise sorted matrix

Given a row-wise sorted matrix mat[][] and an integer x, the task is to check if x is present in mat[][] or not. Note that there is no ordering among column elements.

Examples:

Input: x = 9, mat[][] = [[3, 4, 9],
[2, 5, 6],
[9, 25, 27]]
Output: true
Explanation: mat[0][2] is equal to 9.

Input: x = 56, mat[][] = [[19, 22, 27, 38, 55, 67]]
Output: false
Explanation: 56 is not present in mat[][].

[Naive Approach] Comparing with all elements – O(n*m) Time and O(1) Space

The simple idea is to traverse the complete matrix and search for the target element. If the target element is found, return true. Otherwise, return false. Please refer to Searching Algorithms for 2D Arrays (Matrix) to know more about the implementation.

[Expected Approach] Using Binary Search - O(n * log(m)) Time and O(1) Space

The idea is simple, we traverse through the matrix and apply binary search on each row to find the element.

true

Time Complexity: O(n*logm), where n is the number of rows and m is the number of columns.
Auxiliary Space: O(1)