├── .gitignore ├── LICENSE ├── README.md ├── requirements.txt ├── simulate.py ├── solver.py ├── tests.py └── visualize.py /.gitignore: -------------------------------------------------------------------------------- 1 | venv/ 2 | __pycache__/ 3 | .idea/ 4 | output.cast -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # battleship 2 | This is project code accompanies this [blog post](https://www.nulliq.dev/posts/battleship/). 3 | 4 | ## solver.py 5 | See the solver in action! Run this file to see a GUI of where you should shoot next. 6 | 7 | ## visualize.py 8 | Script used to generate asciinema cast files for the blog post. 9 | 10 | ## solver.py 11 | TODO: Script used to test a strategy against randomly generated boards. -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | cycler==0.11.0 2 | fonttools==4.30.0 3 | kiwisolver==1.3.2 4 | matplotlib==3.5.1 5 | mplcursors==0.5.1 6 | numpy==1.22.3 7 | packaging==21.3 8 | pandas==1.4.1 9 | Pillow==9.0.1 10 | pyparsing==3.0.7 11 | python-dateutil==2.8.2 12 | pytz==2021.3 13 | scipy==1.8.0 14 | seaborn==0.11.2 15 | six==1.16.0 16 | -------------------------------------------------------------------------------- /simulate.py: -------------------------------------------------------------------------------- 1 | """This file generates random boards and tests strategies.""" 2 | 3 | 4 | def main(): 5 | """Program entry point""" 6 | raise NotImplementedError 7 | 8 | 9 | if __name__ == "__main__": 10 | main() 11 | -------------------------------------------------------------------------------- /solver.py: -------------------------------------------------------------------------------- 1 | """ 2 | Messy incomplete implementation of strategy described in: https://www.nulliq.dev/posts/battleship/ 3 | """ 4 | import math 5 | from typing import List, Dict, Tuple 6 | import numpy as np 7 | import matplotlib 8 | import matplotlib.pyplot as plt 9 | from matplotlib.colors import LinearSegmentedColormap 10 | from matplotlib.widgets import Button 11 | from scipy import signal 12 | import seaborn as sns 13 | import mplcursors 14 | 15 | SHIPS: Dict[int, int] = {4: 1, 3: 2, 2: 3, 1: 4} 16 | 17 | GRID: np.array = np.array([[0 for _ in range(10)] for _ in range(10)]) 18 | 19 | PLOT: matplotlib.pyplot = plt 20 | 21 | 22 | def main(): 23 | """Program entry point""" 24 | # It's recommended to not enable exhaustive search until mid to late game. 25 | heatdata, _, _ = solve(exhaustive=True) 26 | init_plot(heatdata) 27 | 28 | 29 | def ship_fits(i, j, ship, board=None) -> (int, int): 30 | """Does this size ship fit at these coordinates?""" 31 | if board is None: 32 | board = GRID 33 | 34 | i_fits = True 35 | j_fits = True 36 | 37 | if i + ship <= len(board): 38 | for k in range(i, i + ship): 39 | if board[k][j] != 0: 40 | i_fits = False 41 | else: 42 | i_fits = False 43 | 44 | if j + ship <= len(board[i]): 45 | for k in range(j, j + ship): 46 | if board[i][k] != 0: 47 | j_fits = False 48 | else: 49 | j_fits = False 50 | 51 | if ship == 1: 52 | j_fits = False 53 | 54 | return i_fits, j_fits 55 | 56 | 57 | def info_sum( 58 | ship: int, i: int, j: int, singles: np.array, spine: np.array, vert: bool 59 | ) -> int: 60 | """Add together the surrounding cells for the given ship position""" 61 | last_i = i 62 | last_j = j 63 | 64 | if vert: 65 | last_j += ship - 1 66 | else: 67 | last_i += ship - 1 68 | 69 | if ship == 1: 70 | return singles[i][j] 71 | if ship == 2: 72 | # Add up two ends of ship and delete the double-counted center spines 73 | return ( 74 | singles[i][j] 75 | + singles[last_i][last_j] 76 | - spine[math.floor((i + last_i) / 2)][math.floor((j + last_j) / 2)] 77 | - spine[math.ceil((i + last_i) / 2)][math.ceil((j + last_j) / 2)] 78 | ) 79 | if ship == 3: 80 | # Add up two ends of ship and delete the double-counted center spine 81 | return ( 82 | singles[i][j] 83 | + singles[last_i][last_j] 84 | - spine[(i + last_i) // 2][(j + last_j) // 2] 85 | ) 86 | if ship == 4: 87 | # Add up two ends of ship 88 | return singles[i][j] + singles[last_i][last_j] 89 | 90 | # Unsupported ship len 91 | raise NotImplementedError 92 | 93 | 94 | def count_occurances(grid: np.array, ships: Dict[int, int]) -> List[List[int]]: 95 | """Count how many different ships can fit into each cell on the grid.""" 96 | res = [[0 for _ in range(len(grid[0]))] for _ in range(len(grid))] 97 | 98 | for i in range(len(grid)): 99 | for j in range(len(grid[i])): 100 | for ship, count in ships.items(): 101 | fits = ship_fits(i, j, ship) 102 | if fits[0]: # fits with horizontal orientation 103 | for k in range(i, i + ship): 104 | res[k][j] += count 105 | if fits[1]: # fits vertically 106 | for k in range(j, j + ship): 107 | res[i][k] += count 108 | 109 | return res 110 | 111 | 112 | def place_ship(i: int, j: int, ship: int, grid: np.array, vert: bool) -> np.array: 113 | """Increment the cells that could not contain another ship if the ship occupied the given coords.""" 114 | # Effective values 115 | e_i = i - 1 116 | e_j = j - 1 117 | if vert: 118 | e_i_delta = ship + 2 119 | e_j_delta = 3 120 | else: 121 | e_i_delta = 3 122 | e_j_delta = ship + 2 123 | 124 | if e_i < 0: 125 | e_i_delta -= 1 126 | e_i += 1 127 | if e_i + e_i_delta > len(grid): 128 | e_i_delta -= 1 129 | 130 | if e_j < 0: 131 | e_j += 1 132 | e_j_delta -= 1 133 | if e_j + e_j_delta > len(grid[i]): 134 | e_j_delta -= 1 135 | 136 | add_grid = np.ones((e_i_delta, e_j_delta)) 137 | 138 | add_grid = np.pad(add_grid, ((e_i, len(grid)-e_i_delta-e_i), (e_j, len(grid[i])-e_j_delta-e_j)), 'constant') 139 | 140 | return np.add(grid, add_grid) 141 | 142 | 143 | def permutate_board(GRID: np.array, SHIPS: dict): 144 | """Exhaustively count valid board configurations - See github issue #1""" 145 | all_prob = np.zeros_like(GRID) 146 | 147 | # Base case 148 | if len(SHIPS.keys()) == 0: 149 | return all_prob 150 | 151 | # Place largest ship 152 | ship = max(SHIPS.keys()) 153 | ships = SHIPS.copy() 154 | if ships[ship] == 1: 155 | ships.pop(ship) 156 | else: 157 | ships[ship] -= 1 158 | 159 | for i in range(len(GRID)): 160 | for j in range(len(GRID[i])): 161 | # Place ship 162 | vert, hor = ship_fits(i, j, ship, GRID) 163 | 164 | vert_prob = None 165 | if vert: 166 | grid = GRID.copy() 167 | grid = place_ship(i, j, ship, grid, vert=True) 168 | 169 | # Recursively call self 170 | vert_prob = permutate_board(grid, ships) 171 | if vert_prob is not None: 172 | for k in range(i, i + ship): 173 | vert_prob[k][j] += 1 174 | 175 | hor_prob = None 176 | if hor: 177 | grid = GRID.copy() 178 | 179 | grid = place_ship(i, j, ship, grid, vert=False) 180 | # Recursively call self 181 | hor_prob = permutate_board(grid, ships) 182 | if hor_prob is not None: 183 | for k in range(j, j + ship): 184 | hor_prob[i][k] += 1 185 | 186 | # Sum up probability counts 187 | if vert_prob is not None and hor_prob is not None: 188 | res = np.add(vert_prob, hor_prob) 189 | all_prob = np.add(all_prob, res) 190 | elif vert_prob is not None: 191 | all_prob = np.add(all_prob, vert_prob) 192 | elif hor_prob is not None: 193 | all_prob = np.add(all_prob, hor_prob) 194 | 195 | # If there weren't any valid placements, return None 196 | if all_prob.sum() == 0: 197 | return None 198 | 199 | return all_prob 200 | 201 | 202 | def solve(exhaustive=False) -> Tuple[np.array, np.array, np.array]: 203 | """Generate the heatmap data using the methods described in the blogpost""" 204 | if exhaustive: 205 | prob = permutate_board(GRID, SHIPS) 206 | else: 207 | prob = count_occurances(GRID, SHIPS) 208 | 209 | matrix = np.array(prob) 210 | 211 | size = 3 212 | 213 | kernel = np.ones((size, size)) 214 | result = signal.convolve(matrix, kernel, method="direct").astype(int) 215 | singles = result[ 216 | (size - 1) // 2 : -(size - 1) // 2, (size - 1) // 2 : -(size - 1) // 2 217 | ] 218 | singles = np.where(matrix != 0, singles, 0) 219 | 220 | kernel = np.array([[0, 1, 0], [0, 1, 0], [0, 1, 0]]) 221 | result = signal.convolve(matrix, kernel, method="direct").astype(int) 222 | vert = result[ 223 | (size - 1) // 2 : -(size - 1) // 2, (size - 1) // 2 : -(size - 1) // 2 224 | ] 225 | vert = np.where(matrix != 0, vert, 0) 226 | 227 | kernel = np.array([[0, 0, 0], [1, 1, 1], [0, 0, 0]]) 228 | result = signal.convolve(matrix, kernel, method="direct").astype(int) 229 | hor = result[(size - 1) // 2 : -(size - 1) // 2, (size - 1) // 2 : -(size - 1) // 2] 230 | hor = np.where(matrix != 0, hor, 0) 231 | 232 | print("vert/hor:") 233 | print(vert) 234 | print(hor) 235 | 236 | weighted_info = np.array( 237 | [[0 for i in range(len(GRID[0]))] for j in range(len(GRID))] 238 | ) 239 | total_lens = np.array([[0 for i in range(len(GRID[0]))] for j in range(len(GRID))]) 240 | 241 | for i in range(len(GRID)): 242 | for j in range(len(GRID[i])): 243 | for ship, count in SHIPS.items(): 244 | fits = ship_fits(i, j, ship) 245 | if fits[0]: # fits with horizontal orientation 246 | total_lens[i][j] += ship * count 247 | wsum = info_sum(ship, i, j, singles, hor, vert=False) 248 | for k in range(i, i + ship): 249 | weighted_info[k][j] += wsum * count 250 | if fits[1]: # fits vertically 251 | total_lens[i][j] += ship * count 252 | wsum = info_sum(ship, i, j, singles, vert, vert=True) 253 | for k in range(j, j + ship): 254 | weighted_info[i][k] += wsum * count 255 | 256 | # If we used the exhaustive search, we know for a fact that the zeros cannot contain a ship. 257 | if exhaustive: 258 | weighted_info = np.where(matrix != 0, weighted_info, 0) 259 | vert = np.where(matrix != 0, vert, 0) 260 | hor = np.where(matrix != 0, hor, 0) 261 | 262 | return weighted_info, vert, hor 263 | 264 | 265 | def init_plot(data): 266 | """Generate a matplotlib seaborn heatmap""" 267 | 268 | cdict = { 269 | "red": [(0.0, 0.129, 0.129), (1.0, 0.933, 1.0)], 270 | "green": [(0.0, 0.125, 0.125), (1.0, 0.447, 1.0)], 271 | "blue": [(0.0, 0.173, 0.173), (1.0, 0.945, 1.0)], 272 | } 273 | 274 | cmap = LinearSegmentedColormap("test", cdict) 275 | 276 | ax = sns.heatmap(data, linewidth=0.5, cmap=cmap) 277 | 278 | max_coords = data.argmax() 279 | 280 | dummy_image = ax.imshow(data, zorder=-1, aspect="auto") 281 | cursor = mplcursors.cursor(dummy_image, hover=False) 282 | cursor.connect("add", toggle_square) 283 | 284 | plt.title(f"Hit the red ({max_coords % len(GRID)}, {max_coords // len(GRID[0])})") 285 | 286 | vaxes = plt.axes([0.81, 0.000001, 0.1, 0.075]) 287 | bvert = Button(vaxes, "Vert", color="yellow") 288 | bvert.on_clicked(vert_plot) 289 | 290 | haxes = plt.axes([0.70, 0.000001, 0.1, 0.075]) 291 | bhor = Button(haxes, "Horiz", color="yellow") 292 | bhor.on_clicked(hor_plot) 293 | 294 | plt.show() 295 | 296 | 297 | def search_plot(press): 298 | """ 299 | Broken, haven't gotten around to figuring out how to update matplotlib seaborn figures 300 | without closing the window. 301 | """ 302 | update_plot(solve()[0]) 303 | 304 | 305 | def vert_plot(press): 306 | """ 307 | Broken, haven't gotten around to figuring out how to update matplotlib seaborn figures 308 | without closing the window. 309 | """ 310 | update_plot(solve()[1]) 311 | 312 | 313 | def hor_plot(press): 314 | """ 315 | Broken, haven't gotten around to figuring out how to update matplotlib seaborn figures 316 | without closing the window. 317 | """ 318 | update_plot(solve()[2]) 319 | 320 | 321 | def update_plot(data: np.array): 322 | """It's a hack. Definitely a better way to do this, but hey, this works.""" 323 | PLOT.close() 324 | 325 | init_plot(data) 326 | 327 | 328 | def toggle_data(cell_x: int, cell_y: int): 329 | """Toggle a grid cell""" 330 | if GRID[cell_y][cell_x] == 0: 331 | GRID[cell_y][cell_x] = 1 332 | elif GRID[cell_y][cell_x] == 1: 333 | GRID[cell_y][cell_x] = 2 334 | elif GRID[cell_y][cell_x] == 2: 335 | GRID[cell_y][cell_x] = 0 336 | 337 | print(repr(GRID)) 338 | 339 | 340 | def toggle_square(press): 341 | """Translate a click event and toggle a square""" 342 | cell_x = int(press.target[0]) 343 | cell_y = int(press.target[1]) 344 | 345 | toggle_data(cell_x, cell_y) 346 | data = solve()[0] 347 | update_plot(data=data) 348 | 349 | 350 | if __name__ == "__main__": 351 | main() 352 | -------------------------------------------------------------------------------- /tests.py: -------------------------------------------------------------------------------- 1 | import unittest 2 | 3 | import numpy as np 4 | 5 | import solver 6 | 7 | 8 | class TestExhaustiveProb(unittest.TestCase): 9 | 10 | def test_invalid(self): 11 | board = np.zeros((1, 2)) 12 | pmap = solver.permutate_board(board, {1: 2}) 13 | self.assertIsNone(pmap) 14 | 15 | def test_basic(self): 16 | board = np.zeros((1, 3)) 17 | pmap = solver.permutate_board(board, {1: 2}) 18 | self.assertTrue(np.array_equal(pmap, np.array([[2, 0, 2]]))) 19 | 20 | def test_example(self): 21 | board = np.zeros((3, 3)) 22 | pmap = solver.permutate_board(board, {3: 1, 1: 2}) 23 | self.assertTrue(np.array_equal(pmap, np.array([[6, 1, 6], [1, 0, 1], [6, 1, 6]]))) 24 | 25 | 26 | if __name__ == '__main__': 27 | unittest.main() 28 | -------------------------------------------------------------------------------- /visualize.py: -------------------------------------------------------------------------------- 1 | """ 2 | Generate (unoptimized) asciinema replay files for the blog post. 3 | """ 4 | import time 5 | from typing import List, TextIO 6 | 7 | from solver import ship_fits, count_occurances 8 | 9 | FILE: TextIO = open(r"output.cast", "w+", encoding="UTF8") 10 | TIMESTAMP: int = 0 11 | 12 | 13 | def write(output: str): 14 | """Write a line to the cast file""" 15 | global TIMESTAMP 16 | 17 | output = output.replace("\n", "\\n") 18 | 19 | FILE.write(f'[{TIMESTAMP}, "o", "{output}"]\n') 20 | 21 | TIMESTAMP += 0.5 22 | 23 | 24 | def print_board(board): 25 | """Write a board to the cast file""" 26 | board_str = "" 27 | for row in board: 28 | for cell in row: 29 | board_str += print_pos(cell) 30 | board_str = board_str.strip() 31 | # board_str += "\n" 32 | 33 | # print(board_str, end="") 34 | write(board_str) 35 | 36 | 37 | def print_num_board(board): 38 | """Write a zero-padded board to the cast file""" 39 | board_str = "" 40 | for row in board: 41 | for cell in row: 42 | board_str += str(cell).zfill(5) + " " 43 | board_str = board_str.strip() 44 | # board_str += "\n" 45 | 46 | # print(board_str, end="") 47 | write(board_str) 48 | 49 | 50 | def print_pos(cell: int) -> str: 51 | """Return the symbol associated with the cell type""" 52 | if cell == 0: 53 | return ". " 54 | if cell == 1: 55 | return "- " 56 | if cell == 2: 57 | return "X " 58 | 59 | raise NotImplementedError 60 | 61 | 62 | def solo_ship_board(i, j, ship, horizontal) -> List[List[int]]: 63 | """Board containing single ship""" 64 | board = [[1 for _ in range(10)] for _ in range(10)] 65 | if horizontal: 66 | for k in range(j, j + ship): 67 | board[i][k] = 2 68 | else: 69 | for k in range(i, i + ship): 70 | board[k][j] = 2 71 | 72 | return board 73 | 74 | 75 | def enumerate_positions(ships, board): 76 | """Enumerate over every possible ship position""" 77 | 78 | for i in range(len(board)): 79 | for j in range(len(board[i])): 80 | for ship, _ in ships.items(): 81 | i_fits, j_fits = ship_fits(i, j, ship, board) 82 | 83 | if i_fits: 84 | print_board(solo_ship_board(i, j, ship, False)) 85 | if j_fits: 86 | print_board(solo_ship_board(i, j, ship, True)) 87 | 88 | 89 | def enumerate_num_positions(ships, board): 90 | """Enumerate over every possible position and add the ship occurrences at each cell""" 91 | res = [[0 for _ in range(len(board[0]))] for _ in range(len(board))] 92 | 93 | for i in range(len(board)): 94 | for j in range(len(board[i])): 95 | for ship, count in ships.items(): 96 | i_fits, j_fits = ship_fits(i, j, ship, board) 97 | 98 | if i_fits: 99 | for k in range(i, i + ship): 100 | res[k][j] += count 101 | print_num_board(res) 102 | time.sleep(0.01) 103 | if j_fits: 104 | for k in range(j, j + ship): 105 | res[i][k] += count 106 | print_num_board(res) 107 | time.sleep(0.01) 108 | 109 | 110 | def sum_row(i, j, size, source): 111 | """Add all the cells in a row/col""" 112 | if i < 0 or i >= len(source): 113 | return 0 114 | if j < 0 or j + size > len(source): 115 | return 0 116 | 117 | if j == 0: 118 | size += 1 119 | else: 120 | j -= 1 121 | size += 2 122 | 123 | return sum(source[i][j : j + size]) 124 | 125 | 126 | def position_sum(i, j, ship, vert, source): 127 | """Sum up the cells surrounding a position""" 128 | psum = 0 129 | 130 | if vert: 131 | for k in range(ship + 2): 132 | psum += sum_row(i, j + k - 1, 1, source) 133 | else: 134 | for k in range(3): 135 | psum += sum_row(i, j + k - 1, ship, source) 136 | 137 | return psum 138 | 139 | 140 | def enumerate_smart_sum(ships, board): 141 | """ 142 | Enumerate over every possible position and add the 143 | sum of this cell plus surrounding ship occurrences 144 | """ 145 | result = count_occurances(board, ships) 146 | 147 | res = [[0 for _ in range(10)] for _ in range(10)] 148 | 149 | for i in range(len(board)): 150 | for j in range(len(board)): 151 | for ship, _ in ships.items(): 152 | i_fits, j_fits = ship_fits(i, j, ship, board) 153 | 154 | if i_fits: 155 | count = position_sum(i, j, ship, True, result) 156 | print("i", ship, i, j, count) 157 | print(res) 158 | for k in range(i, i + ship): 159 | res[k][j] += count 160 | print_num_board(res) 161 | if j_fits: 162 | count = position_sum(i, j, ship, False, result) 163 | print(ship, i, j, count) 164 | print(res) 165 | for k in range(j, j + ship): 166 | res[i][k] += count 167 | print_num_board(res) 168 | 169 | print(result) 170 | print(res) 171 | 172 | 173 | def visualize(): 174 | """Write an enumeration to a cast file""" 175 | FILE.write( 176 | '{"version": 2, "width": 29, "height": 10, "timestamp": 0, ' 177 | '"env": {"SHELL": "/bin/bash", "TERM": "xterm-256color"}}\n' 178 | ) 179 | print("Hi!") 180 | board = [[0 for _ in range(10)] for _ in range(10)] 181 | 182 | enumerate_smart_sum({4: 1, 3: 2, 2: 3, 1: 4}, board) 183 | 184 | 185 | if __name__ == "__main__": 186 | visualize() 187 | --------------------------------------------------------------------------------