Minimum Moves to Capture The Queen

Problem Description

Given a chessboard with a white rook, a white bishop, and a black queen, determine the minimum number of moves required for either the rook or the bishop to capture the queen. The rook can move vertically or horizontally, while the bishop moves diagonally. Neither piece can jump over the other.

Key Insights

• A rook can capture the queen if it is in the same row or column.
• A bishop can capture the queen if it is on the same diagonal.
• Both pieces can move any number of squares but cannot jump over each other.
• The pieces can take multiple moves to reach the queen if they are blocked.

Space and Time Complexity

Time Complexity: O(1)
Space Complexity: O(1)

Solution

To solve the problem, we need to assess the positions of the rook, bishop, and queen. We will check if either piece can capture the queen immediately or if they need to move to an intermediate square to do so.

1. Check if the rook can capture the queen in one move by verifying if they share the same row or column.
2. Check if the bishop can capture the queen in one move by verifying if they are on the same diagonal.
3. If neither can capture the queen directly, check if the rook can move to a position that allows the bishop to capture the queen in one additional move, or vice versa.
4. If no capturing positions are available in one move for either piece, return 2 moves as the maximum.

Code Solutions