Question

Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:

Integers in each row are sorted in ascending from left to right.
Integers in each column are sorted in ascending from top to bottom.

Answer 1

To search for a value in an m x n matrix with sorted rows and columns, start from the top right corner and use directional comparisons to move either left or down, ceasing when you find the target value or reach the matrix bounds.

Step-by-step explanation:

The question involves creating an efficient algorithm to search for a value in an m x n matrix, which has sorted integers in each row from left to right and each column from top to bottom. To accomplish this, we can start the search from the top right corner of the matrix. Here's a step-by-step algorithm:

1. Begin at the top right corner of the m x n matrix.
2. Compare the target value with the value at the current position.
3. If the target value is larger, move down to the next row (since all values to the left are smaller).
4. If the target value is smaller, move left to the next column (since all values below are larger).
5. Repeat steps 2-4 until you either find the target value or exhaust the bounds of the matrix.
6. If you find the target value, return its position. If you reach the bounds of the matrix, the target is not present, and you should return an indication of failure.

This approach takes advantage of the sorted order of the matrix's rows and columns, creating an efficient search process. The worst-case time complexity of this algorithm is O(m + n), where 'm' is the number of rows and 'n' is the number of columns, hence it is quite suitable for large matrices.