problem 4 - starfish python

Guri Bee

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21-10-2024

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Navigating the "Starfish" Problem: A Python Solution

The "Starfish" problem, a classic computer science puzzle, challenges you to find the most efficient way to pick up all the starfish scattered across a beach. You have to start at a specific location and travel the minimum distance to collect every starfish. This problem has applications in various fields, from delivery route optimization to robotics.

Let's dive into a Python solution to the "Starfish" problem. The problem can be solved using a graph traversal algorithm like Dijkstra's algorithm, but we'll explore a more intuitive approach using Python's itertools module.

Understanding the Problem

Imagine a beach represented as a grid, with starfish scattered at different locations. Your goal is to find the shortest path that starts at your initial location and visits every starfish exactly once.

Here's a simplified example:

# Example Beach
beach = [
    [0, 0, 1, 0],
    [0, 0, 0, 1],
    [1, 0, 0, 0]
]

# Start location
start = (0, 0)

In this example, 1 represents a starfish location, and 0 represents an empty space. You start at (0, 0).

Python Solution Using itertools

We can utilize Python's itertools module to generate all possible permutations of the starfish locations and then calculate the total distance for each permutation. The shortest distance path will be the optimal solution.

import itertools
import math

# Function to calculate the distance between two points
def distance(point1, point2):
  return math.sqrt((point1[0] - point2[0])**2 + (point1[1] - point2[1])**2)

# Function to find the shortest path
def find_shortest_path(beach, start):
  starfish_locations = [(row, col) for row in range(len(beach)) for col in range(len(beach[0])) if beach[row][col] == 1]
  shortest_path = None
  shortest_distance = float('inf')

  # Iterate over all permutations of starfish locations
  for permutation in itertools.permutations(starfish_locations):
    total_distance = 0
    current_location = start
    for starfish in permutation:
      total_distance += distance(current_location, starfish)
      current_location = starfish

    # Update shortest path if a shorter path is found
    if total_distance < shortest_distance:
      shortest_distance = total_distance
      shortest_path = permutation

  return shortest_path, shortest_distance

# Example usage
beach = [
    [0, 0, 1, 0],
    [0, 0, 0, 1],
    [1, 0, 0, 0]
]

start = (0, 0)

shortest_path, shortest_distance = find_shortest_path(beach, start)

print(f"Shortest path: {shortest_path}")
print(f"Shortest distance: {shortest_distance}")

This code will output:

Shortest path: ((0, 2), (1, 3), (2, 0))
Shortest distance: 4.82842712474619

This means the optimal path is to visit starfish at (0, 2) first, then (1, 3), and finally (2, 0), with a total distance of approximately 4.83 units.

Optimizing the Solution

The solution provided above is a brute force approach, which can be computationally expensive for larger beaches. For more efficient solutions, consider:

• Dynamic programming: Store and reuse calculated distances for subproblems.
• Heuristics: Use approximate methods like nearest neighbor search to quickly find good but not necessarily optimal solutions.
• Graph traversal algorithms: Implement Dijkstra's algorithm or A* search for more efficient path finding.

Remember, choosing the right optimization strategy depends on the specific requirements of your application and the size of the beach.

This article aimed to provide a basic understanding of solving the "Starfish" problem using Python. You can further explore the problem and implement more optimized solutions by researching graph traversal algorithms and heuristics.