Approach

To design an efficient algorithm for searching a value in an m x n matrix where each row is sorted in ascending order from left to right and each column is sorted in ascending order from top to bottom, we can utilize a step-wise linear search strategy. This method exploits the sorted properties of the matrix to minimize the number of comparisons.

Thought Process Steps:

1. Identify Starting Point: Begin the search from the top-right corner of the matrix.

2. Comparison Logic:

• If the current element is equal to the target, return its position.

• If the current element is greater than the target, move left (decrease the column index).

• If the current element is less than the target, move down (increase the row index).

• Termination: Continue the process until the indices go out of bounds or the target is found.

Key Points

• Efficiency: This algorithm runs in O(m + n) time complexity, making it suitable for large matrices.

• Early Exit: The method allows for quick exits, avoiding unnecessary comparisons.

• Clear Logic: The structured movement through the matrix based on comparisons simplifies the implementation.

Standard Response

Here’s a sample response to the interview question, detailing the algorithm:

def searchMatrix(matrix, target):
 if not matrix or not matrix[0]:
 return False

 rows, cols = len(matrix), len(matrix[0])
 row, col = 0, cols - 1 # Start from the top-right corner

 while row < rows and col >= 0:
 current = matrix[row][col]
 if current == target:
 return True # Target found
 elif current > target:
 col -= 1 # Move left
 else:
 row += 1 # Move down

 return False # Target not found

Explanation:

• We first check if the matrix is empty.

• We initialize row to 0 and col to the last column.

• In each iteration, we compare the current element with the target:

• If it matches, we return True.

• If it's greater, we move left; if it's smaller, we move down.

• If we exit the loop, the target is not present in the matrix.

Tips & Variations

Common Mistakes to Avoid

• Ignoring Edge Cases: Failing to check if the matrix is empty can lead to errors.

• Inefficient Search: Using a nested loop to search through all elements can drastically reduce performance.

Alternative Ways to Answer

• Binary Search Approach: For interviewers looking for complexity, discuss converting the 2D matrix into a 1D array and applying binary search, though this is less efficient in this specific case.

Role-Specific Variations

• Technical Roles: Emphasize the algorithm's time complexity and space efficiency.

• Managerial Roles: Focus on the problem-solving approach and how you would lead a team in developing this solution.

• Creative Roles: Highlight innovative ways to visualize the search process or user interface design considerations.

Follow-Up Questions

• How would you modify the algorithm for a matrix that is sorted in descending order?

• Can you explain the time complexity in more detail?

• What would you do if the matrix was not guaranteed to be sorted?

Conclusion

By following this structured approach, job seekers can efficiently communicate their problem-solving abilities in technical interviews. Practicing such algorithmic questions not only helps in securing a position but also enhances overall coding proficiency