**π‘ Problem Formulation:** Imagine a 2D grid or matrix representing a game board where each cell can contain an enemy, a bomb, or be empty. The challenge is to determine if all the enemies can be killed given the bomb placements that explode vertically and horizontally across the entire row and column. If an enemy is in the same row or column with no obstructions between it and a bomb, it is considered killed. For instance, with a given matrix, the function should return `True`

if all enemies are eliminated, otherwise `False`

.

## Method 1: Brute Force Check

This method involves iterating over each cell of the matrix to check for enemies and then for each enemy, scanning its entire row and column for bombs. The specification would be a function that takes in the matrix and returns a boolean value.

Here’s an example:

def all_enemies_killed(matrix): for r in range(len(matrix)): for c in range(len(matrix[0])): if matrix[r][c] == 'E': if not any(matrix[r][x] == 'B' or matrix[x][c] == 'B' for x in range(len(matrix))): return False return True # Example matrix: # E for Enemy, B for Bomb, 0 for Empty game_board = [ ['E', '0', 'B'], ['0', 'E', '0'], ['0', '0', '0'] ] print(all_enemies_killed(game_board))

Output: `False`

This snippet defines a function, `all_enemies_killed()`

, which loops over the entire matrix to check every cell. If it encounters an ‘E’, it runs a conditional comprehension that searches that row and column for a ‘B’. If no bomb is found, it returns `False`

. If the loop completes without returning `False`

, it means all enemies can be killed, and it returns `True`

.

## Method 2: Use Set to Store Bomb Positions

The second method optimizes the search for bombs by first storing the positions of all bombs in sets for rows and columns separately. The function then only needs to check these sets when encountering an enemy instead of scanning the whole matrix again.

Here’s an example:

def all_enemies_killed_optimized(matrix): bomb_rows, bomb_cols = set(), set() for r in range(len(matrix)): for c in range(len(matrix[0])): if matrix[r][c] == 'B': bomb_rows.add(r) bomb_cols.add(c) for r in range(len(matrix)): for c in range(len(matrix[0])): if matrix[r][c] == 'E' and r not in bomb_rows and c not in bomb_cols: return False return True print(all_enemies_killed_optimized(game_board))

Output: `False`

The revised function `all_enemies_killed_optimized()`

uses two sets, `bomb_rows`

, and `bomb_cols`

, to track the positions of bombs efficiently. It then iterates over the matrix and checks if each enemy’s row or column index is in the respective bomb set, returning `False`

if it’s not, signifying an enemy cannot be killed.

## Method 3: Short-Circuiting with Early Exits

This approach leverages short-circuiting to exit the check as soon as an enemy that cannot be killed is found, thus potentially reducing the number of operations required compared to traversing the entire matrix.

Here’s an example:

def all_enemies_killed_short_circuit(matrix): for r, row in enumerate(matrix): for c, cell in enumerate(row): if cell == 'E' and not any(matrix[r][x] == 'B' or matrix[x][c] == 'B' for x in range(len(matrix))): return False return True print(all_enemies_killed_short_circuit(game_board))

Output: `False`

The function `all_enemies_killed_short_circuit()`

immediately returns `False`

upon finding an enemy that cannot be destroyed, which means the loop doesn’t proceed unnecessarily if the answer is already determined.

## Method 4: Optimized Search with Precomputed Bomb Lines

This method builds upon the optimization techniques by precalculating the rows and columns that are cleared by bombs. It reduces the complexity by checking if an enemy exists in any of the non-cleared lines.

Here’s an example:

def all_enemies_killed_precomputed(matrix): cleared_rows, cleared_cols = [False] * len(matrix), [False] * len(matrix[0]) for r in range(len(matrix)): for c in range(len(matrix[0])): if matrix[r][c] == 'B': cleared_rows[r] = cleared_cols[c] = True for r in range(len(matrix)): for c in range(len(matrix[0])): if matrix[r][c] == 'E' and not cleared_rows[r] and not cleared_cols[c]: return False return True print(all_enemies_killed_precomputed(game_board))

Output: `False`

The function `all_enemies_killed_precomputed()`

keeps track of cleared lines with two lists initially set to `False`

. As it identifies bombs, it sets the corresponding indices to `True`

. Then, when checking for enemies, it only considers those rows and columns that are not already cleared.

## Bonus One-Liner Method 5: Functional Programming Approach

It combines the use of lambda functions, map, and filter to provide a one-liner approach to the problem. The elegance of functional programming can sometimes make the code more readable or interesting.

Here’s an example:

all_enemies_killed_one_liner = lambda m: all(any(m[r][c] == 'B' for r in range(len(m))) or any(m[r][c] == 'B' for c in range(len(m[0]))) for r,row in enumerate(m) for c,cell in enumerate(row) if cell == 'E') print(all_enemies_killed_one_liner(game_board))

Output: `False`

This one-liner utilizes a lambda function with nested generators and the built-in `all()`

and `any()`

functions to determine if all enemies can be killed with the given bombs. It’s a condensed version of the brute force method.

## Summary/Discussion

**Method 1: Brute Force Check.**Straightforward. Can be slow for large matrices.**Method 2: Use Set to Store Bomb Positions.**Faster lookups for bombs. Still requires two full matrix scans.**Method 3: Short-Circuiting with Early Exits.**Potentially faster in some cases. Still not the most efficient.**Method 4: Optimized Search with Precomputed Bomb Lines.**Highly efficient, especially for large matrices. Requires additional memory for tracking.**Bonus One-Liner Method 5: Functional Programming Approach.**Elegant but may be difficult to understand for beginners. Compact but not necessarily performance-efficient.