implement the easiest algorithm to see if it works: ""import tkinter as tk
import time
import random
import heapq
from queue import Queue, LifoQueue
import numpy as np

# Define constants for the board
BOARD_SIZE = 5  # Example size, 5x5 grid
PIECES = {
    'line': {
        'chars': ['─', '│', '─', '│'],
        'connections': [
            [0, 1, 0, 1],  # 0°, horizontal
            [1, 0, 1, 0],  # 90°, vertical
            [0, 1, 0, 1],  # 180°, horizontal
            [1, 0, 1, 0],  # 270°, vertical
        ]
    },
    'curve': {
        'chars': ['└', '┌', '┐', '┘'],
        'connections': [
            [1, 1, 0, 0],  # 0°, connects Top and Right
            [0, 1, 1, 0],  # 90°, connects Right and Bottom
            [0, 0, 1, 1],  # 180°, connects Bottom and Left
            [1, 0, 0, 1],  # 270°, connects Left and Top
        ]
    },
    't': {
        'chars': ['┬', '┤', '┴', '├'],
        'connections': [
            [1, 1, 0, 1],  # 0°, connects Top, Right, Left
            [1, 1, 1, 0],  # 90°, connects Top, Right, Bottom
            [0, 1, 1, 1],  # 180°, connects Right, Bottom, Left
            [1, 0, 1, 1],  # 270°, connects Top, Bottom, Left
        ]
    },
    'cross': {
        'chars': ['┼', '┼', '┼', '┼'],
        'connections': [
            [1, 1, 1, 1],
            [1, 1, 1, 1],
            [1, 1, 1, 1],
            [1, 1, 1, 1],
        ]
    }
}

class Piece:
    def __init__(self, piece_type, rotation=0):
        self.piece_type = piece_type
        self.rotation = rotation
    
    def rotate(self):
        self.rotation = (self.rotation + 1) % 4

    def get_connections(self):
        return PIECES[self.piece_type]['connections'][self.rotation]

    def get_char(self):
        return PIECES[self.piece_type]['chars'][self.rotation]

class PipePuzzle:
    def __init__(self, board_size=BOARD_SIZE):
        self.board_size = board_size
        self.board = self.generate_board()

    def generate_board(self):
        board = []
        piece_types = list(PIECES.keys())
        for _ in range(self.board_size):
            row = [Piece(random.choice(piece_types), random.randint(0, 3)) for _ in range(self.board_size)]
            board.append(row)
        return board

    def display_board(self):
        for row in self.board:
            print(" ".join([piece.get_char() for piece in row]))

    def solve_with_dfs(self):
        # Implement depth-first search (DFS)
        print("Solving with DFS...")
        pass

    def solve_with_bfs(self):
        # Implement breadth-first search (BFS)
        print("Solving with BFS...")
        pass

    def solve_with_astar(self):
        # Implement A* algorithm
        print("Solving with A*...")
        pass

    def solve_with_genetic(self):
        # Implement genetic algorithm
        print("Solving with Genetic Algorithm...")
        pass

    def benchmark(self, algorithm):
        start_time = time.time()
        algorithm()
        end_time = time.time()
        print(f"Execution time: {end_time - start_time} seconds")
        # You can further enhance this with memory usage, etc.

class PipePuzzleGUI:
    def __init__(self, root, board_size=BOARD_SIZE):
        self.root = root
        self.board_size = board_size
        self.puzzle = PipePuzzle(board_size)
        self.create_widgets()

    def create_widgets(self):
        self.canvas = tk.Canvas(self.root, width=500, height=500)
        self.canvas.grid(row=0, column=0, columnspan=4)
        self.update_board()

        # Buttons to trigger different algorithms
        self.dfs_button = tk.Button(self.root, text="Solve with DFS", command=self.solve_with_dfs)
        self.dfs_button.grid(row=1, column=0)

        self.bfs_button = tk.Button(self.root, text="Solve with BFS", command=self.solve_with_bfs)
        self.bfs_button.grid(row=1, column=1)

        self.astar_button = tk.Button(self.root, text="Solve with A*", command=self.solve_with_astar)
        self.astar_button.grid(row=1, column=2)

        self.genetic_button = tk.Button(self.root, text="Solve with GA", command=self.solve_with_genetic)
        self.genetic_button.grid(row=1, column=3)

    def update_board(self):
        self.canvas.delete("all")
        cell_size = 500 // self.board_size
        for i, row in enumerate(self.puzzle.board):
            for j, piece in enumerate(row):
                x0 = j * cell_size
                y0 = i * cell_size
                x1 = x0 + cell_size
                y1 = y0 + cell_size
                self.canvas.create_rectangle(x0, y0, x1, y1, fill="white", outline="black")
                self.canvas.create_text(x0 + cell_size//2, y0 + cell_size//2, text=piece.get_char(), font=("Helvetica", 24))

    def solve_with_dfs(self):
        self.puzzle.benchmark(self.puzzle.solve_with_dfs)
        self.update_board()

    def solve_with_bfs(self):
        self.puzzle.benchmark(self.puzzle.solve_with_bfs)
        self.update_board()

    def solve_with_astar(self):
        self.puzzle.benchmark(self.puzzle.solve_with_astar)
        self.update_board()

    def solve_with_genetic(self):
        self.puzzle.benchmark(self.puzzle.solve_with_genetic)
        self.update_board()

if __name__ == "__main__":
    root = tk.Tk()
    root.title("Pipe Puzzle Game")
    app = PipePuzzleGUI(root)
    root.mainloop()""