378. Kth Smallest Element in a Sorted Matrix using binary search

The Kth Smallest Element in a Sorted Matrix problem can be solved using binary search. Here is an explanation of each step involved:

1. Initialize the search space: The first step is to initialize the search space, which consists of the minimum and maximum possible values for the Kth smallest element. In this case, the minimum value would be the first element in the matrix, and the maximum value would be the last element in the matrix.

2. Perform binary search: The next step is to perform binary search within the search space. This involves repeatedly dividing the search space in half and checking if the middle element is the Kth smallest element.

3. Count elements less than or equal to the mid: At each iteration of the binary search, we need to count the number of elements in the matrix that are less than or equal to the mid value. This can be done by iterating over the rows and columns of the matrix and comparing each element with the mid value.

4. Adjust the search space: Based on the count of elements less than or equal to the mid value, we can adjust the search space. If the count is less than K, it means that the Kth smallest element must be greater than mid, so we update the minimum value to be mid + 1. If the count is greater than or equal to K, it means that the Kth smallest element must be less than or equal to mid, so we update the maximum value to be mid.

5. Repeat until convergence: We repeat steps 2-4 until the search space converges, i.e., until the minimum and maximum values are equal. At this point, the minimum value represents the Kth smallest element in the matrix.

By following these steps, we can efficiently find the Kth smallest element in a sorted matrix using binary search.