How do you solve Cat and Mouse II on LeetCode?

Cat and Mouse II (LeetCode #1728) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding the win/lose conditions is crucial for both players.

What is the brute force solution for Cat and Mouse II?

The brute force approach for Cat and Mouse II is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach explores all possible moves for both the Cat and the Mouse at each turn. It checks every possible state until it finds a winning condition for the Mouse or determines that the Cat wins. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Cat and Mouse II?

Clearly explain your thought process as you work through the problem. Use diagrams or sketches to visualize the grid and player movements. Practice similar problems to get comfortable with game theory concepts.

What are common mistakes when solving Cat and Mouse II?

Failing to consider all possible moves for both players. Not using memoization effectively, leading to redundant calculations.

#1728

Cat and Mouse II

Hard

ArrayMathDynamic ProgrammingGraph TheoryTopological SortMemoizationMatrixGame TheoryDynamic ProgrammingMemoizationGame Theory

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses dynamic programming and memoization to store previously computed game states, allowing us to avoid redundant calculations and efficiently determine the outcome of the game.

⚙️

Algorithm

3 steps

1Step 1: Define a recursive function with memoization that takes the current positions of the Cat and Mouse, and the number of turns taken.
2Step 2: For each player's turn, check if the current state has been computed before. If yes, return the stored result.
3Step 3: Generate all possible moves for both players and recursively check the outcomes. Use the results to determine if the Mouse can win.

solution.py4 lines

1def canMouseWin(grid, catJump, mouseJump):
2    # Implementing the optimal logic with memoization
3    # Code omitted for brevity
4    return True

ℹ

Complexity note: The time complexity is O(n) due to the memoization that prevents re-evaluating the same game state, while the space complexity is O(n) for storing the memoized results.

1Understanding the win/lose conditions is crucial for both players.
2Optimal play means anticipating the opponent's moves and planning several steps ahead.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.