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Battleships in a Board

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Raymond Chen edited this page Mar 21, 2023 · 6 revisions

Problem Highlights

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

  • Established a set (2-3) of test cases to verify their own solution later.
  • Established a set (1-2) of edge cases to verify their solution handles complexities.
  • Have fully understood the problem and have no clarifying questions.
  • Have you verified any Time/Space Constraints for this problem?
  • Can the input board be blank?
    • Let’s assume the board is not blank. We don’t need to consider empty inputs.
  • Can battleships be attached to one another?
    • There will always be at least one horizontal or vertical cell separating two battleships.
  • What is the time and space constraints?
    • Time complexity should be O(m*n), m being the rows of the matrix and n being the columns of matrix. Space complexity should be O(1), excluding the recursive stack.
HAPPY CASE
Input: board = [["X",".",".","X"],[".",".",".","X"],[".",".",".","X"]]
Output: 2
Explanation: The answer is not 11, because the island must be connected 4-directionally.

Image1

Input: board = [["."]]
Output: 0

EDGE CASE
Input: board = [["X"]]
Output: 1

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

For 2D-Array, common solution patterns include:

  • Perform a BFS/DFS Search through the 2D Array

    • A search through the 2D Array (either BFS or DFS) can help us find each battleship. Which of these two traversals will better help us locate the battleship?

  • Hash the 2D Array in some way to help with the Strings

    • Hashing would not directly help us find islands. However, we could hash where certain 1's are in the 2D Array to jumpstart searches (BFS/DFS) faster.

  • Create/Utilize a Trie

    • A Trie would not help us much in this problem since we are not trying to determine anything about a sequence of characters.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Knowing that a ship can only be horizontal or vertical, we can count the head of ships. A head of ship is where the left side and the up side is ocean or boarder

1) Initialize a variable to keep track of the number of battleships
2) Iterate over the board
3) If a 'X' is seen and if the left side and the up side is ocean or at the boarder, then it's the head of a ship and add one to the count.
4) Return number of battleships

⚠️ Common Mistakes

  • We can optimize this solution when we reduce the need to follow the route of common solution patterns

4: I-mplement

Implement the code to solve the algorithm.

class Solution:
    def countBattleships(self, board: List[List[str]]) -> int:
        # Initialize a variable to keep track of the number of battleships
        numberOfBattleships = 0
        
        # Iterate over the board
        for i, row in enumerate(board):
            for j, cell in enumerate(row):
                # If a 'X' is seen and if the left side and the up side is ocean or at the boarder, then it's the head of a ship and add one to the count.
                if cell == "X":
                    if (i == 0 or board[i - 1][j] == ".") and\
                       (j == 0 or board[i][j - 1] == "."):
                            numberOfBattleships += 1
        
        # Return number of battleships
        return numberOfBattleships

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

  • Trace through your code with an input to check for the expected output
  • Catch possible edge cases and off-by-one errors

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

Assume N represents the number of rows in 2D-array. AssumeM represents the number of columns in 2D-array.

  • Time Complexity: O(N * M) we need to view each item in the 2D-Array
  • Space Complexity: O(1), we only need to store the number of battlships
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