├── .circleci └── config.yml ├── .devcontainer └── devcontainer.json ├── LICENSE ├── README.md ├── problem.txt ├── requirements.txt ├── sudoku.py └── tests ├── __init__.py ├── test_integration.py └── test_sudoku.py /.circleci/config.yml: -------------------------------------------------------------------------------- 1 | version: 2.1 2 | 3 | orbs: 4 | dwave: dwave/orb-examples@2 5 | 6 | workflows: 7 | version: 2.1 8 | tests: 9 | jobs: 10 | - dwave/test-linux 11 | - dwave/test-osx 12 | - dwave/test-win 13 | 14 | weekly: 15 | triggers: 16 | - schedule: 17 | cron: "0 21 * * 0" 18 | filters: 19 | branches: 20 | only: 21 | - master 22 | - main 23 | jobs: 24 | - dwave/test-linux: 25 | integration-tests: "canary" 26 | - dwave/test-osx: 27 | integration-tests: "skip" 28 | - dwave/test-win: 29 | integration-tests: "skip" 30 | -------------------------------------------------------------------------------- /.devcontainer/devcontainer.json: -------------------------------------------------------------------------------- 1 | // For format details, see https://aka.ms/devcontainer.json. For config options, see the 2 | // README at: https://github.com/devcontainers/templates/tree/main/src/debian 3 | { 4 | "name": "Ocean Development Environment", 5 | 6 | // python 3.11 on debian, with latest Ocean and optional packages 7 | // source repo: https://github.com/dwavesystems/ocean-dev-docker 8 | "image": "docker.io/dwavesys/ocean-dev:latest", 9 | 10 | // install repo requirements on create and content update 11 | "updateContentCommand": "pip install -r requirements.txt", 12 | 13 | // forward/expose container services (relevant only when run locally) 14 | "forwardPorts": [ 15 | // dwave-inspector web app 16 | 18000, 18001, 18002, 18003, 18004, 17 | // OAuth connect redirect URIs 18 | 36000, 36001, 36002, 36003, 36004 19 | ], 20 | 21 | "portsAttributes": { 22 | "18000-18004": { 23 | "label": "D-Wave Problem Inspector", 24 | "requireLocalPort": true 25 | }, 26 | "36000-36004": { 27 | "label": "OAuth 2.0 authorization code redirect URI", 28 | "requireLocalPort": true 29 | } 30 | }, 31 | 32 | // Configure tool-specific properties. 33 | "customizations": { 34 | // Configure properties specific to VS Code. 35 | "vscode": { 36 | // Set *default* container specific settings.json values on container create. 37 | "settings": { 38 | "workbench": { 39 | "editorAssociations": { 40 | "*.md": "vscode.markdown.preview.editor" 41 | }, 42 | "startupEditor": "readme" 43 | } 44 | }, 45 | "extensions": [ 46 | "ms-python.python", 47 | "ms-toolsai.jupyter" 48 | ] 49 | } 50 | } 51 | } 52 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. 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We also recommend that a 185 | file or class name and description of purpose be included on the 186 | same "printed page" as the copyright notice for easier 187 | identification within third-party archives. 188 | 189 | Copyright [yyyy] [name of copyright owner] 190 | 191 | Licensed under the Apache License, Version 2.0 (the "License"); 192 | you may not use this file except in compliance with the License. 193 | You may obtain a copy of the License at 194 | 195 | http://www.apache.org/licenses/LICENSE-2.0 196 | 197 | Unless required by applicable law or agreed to in writing, software 198 | distributed under the License is distributed on an "AS IS" BASIS, 199 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 200 | See the License for the specific language governing permissions and 201 | limitations under the License. 202 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | [![Open in GitHub Codespaces]( 2 | https://img.shields.io/badge/Open%20in%20GitHub%20Codespaces-333?logo=github)]( 3 | https://codespaces.new/dwave-examples/sudoku?quickstart=1) 4 | [![Linux/Mac/Windows build status]( 5 | https://circleci.com/gh/dwave-examples/sudoku.svg?style=shield)]( 6 | https://circleci.com/gh/dwave-examples/sudoku) 7 | 8 | # Sudoku 9 | 10 | A demo on how to solve a Sudoku puzzle with D-Wave Ocean. 11 | 12 | ## Usage 13 | 14 | ``` 15 | python sudoku.py 16 | ``` 17 | 18 | For example, 19 | 20 | ``` 21 | python sudoku.py problem.txt 22 | ``` 23 | 24 | ## Code Overview 25 | 26 | The idea is to describe the Sudoku puzzle as a set of constraints that our 27 | solution needs to satisfy (i.e. we are posing the puzzle as a constraint 28 | satisfaction problem). By laying down these constraints, we can get our solver 29 | to optimize over them and hopefully return a solution that satisfies all 30 | our constraints. 31 | 32 | There are several constraints in Sudoku: 33 | 34 | * Each cell in the Sudoku array must contain one digit 35 | * No row may have duplicate digits 36 | * No column may have duplicate digits 37 | * No sub-square may have duplicate digits 38 | 39 | ## Code Specifics 40 | 41 | ### Input 42 | 43 | The code takes as its input a text file containing a Sudoku puzzle in 44 | the following format: 45 | 46 | * Rows of the puzzle are represented as a sequence of lines, one per row 47 | * Cells in each row of the puzzle are represented as space-separated integers 48 | * Empty cells are represented by zeros 49 | * The file should not contain any additional lines (e.g. headers) or comments 50 | 51 | For example, 52 | 53 | ``` 54 | 8 2 0 9 1 0 0 0 7 55 | 9 0 0 7 0 6 8 1 2 56 | 0 1 7 8 0 0 0 9 0 57 | 0 8 0 0 0 0 9 7 0 58 | 0 5 2 0 9 3 1 8 0 59 | 6 0 0 1 8 7 0 0 0 60 | 0 7 8 0 0 9 0 5 0 61 | 3 0 0 2 5 0 7 6 0 62 | 5 0 9 3 0 1 2 0 8 63 | ``` 64 | 65 | ### Comments on the variables 66 | 67 | * A Sudoku puzzle with `n` by `n` cells requires that each 68 | row, column, and sub-square have `n` unique values. Since the 69 | sub-square is a square matrix with `n` items, it means that `n` 70 | must be a square number (i.e. for a sub-square of size `m` by `m`, 71 | `m * m = n`). Hence in the code, the variables `n` and `m` 72 | represent: 73 | 74 | ``` 75 | n == number of rows == number of columns 76 | m == sqrt(n) == number of sub-square rows == number of sub-square columns 77 | ``` 78 | 79 | ### Comments on the solver 80 | 81 | * We are using a hybrid solver called Kerberos (specifically, 82 | `hybrid.reference.KerberosSampler`). It is a hybrid solver because it 83 | combines classical and quantum resources together 84 | * We are using Kerberos because it can break down our problem into smaller 85 | chunks that could then be solved by our quantum computer. The quantum 86 | and classical solutions are then combined together, resulting in our final 87 | solution 88 | 89 | ## License 90 | 91 | Released under the Apache License 2.0. See [LICENSE](LICENSE) file. 92 | -------------------------------------------------------------------------------- /problem.txt: -------------------------------------------------------------------------------- 1 | 8 2 0 9 1 0 0 0 7 2 | 9 0 0 7 0 6 8 1 2 3 | 0 1 7 8 0 0 0 9 0 4 | 0 8 0 0 0 0 9 7 0 5 | 0 5 2 0 9 3 1 8 0 6 | 6 0 0 1 8 7 0 0 0 7 | 0 7 8 0 0 9 0 5 0 8 | 3 0 0 2 5 0 7 6 0 9 | 5 0 9 3 0 1 2 0 8 -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | dwave-ocean-sdk>=3.3.0 2 | -------------------------------------------------------------------------------- /sudoku.py: -------------------------------------------------------------------------------- 1 | # Copyright 2019 D-Wave Systems Inc. 2 | # 3 | # Licensed under the Apache License, Version 2.0 (the "License"); 4 | # you may not use this file except in compliance with the License. 5 | # You may obtain a copy of the License at 6 | # 7 | # http://www.apache.org/licenses/LICENSE-2.0 8 | # 9 | # Unless required by applicable law or agreed to in writing, software 10 | # distributed under the License is distributed on an "AS IS" BASIS, 11 | # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 | # See the License for the specific language governing permissions and 13 | # limitations under the License. 14 | 15 | from __future__ import print_function 16 | 17 | import dimod 18 | import math 19 | import sys 20 | import copy 21 | 22 | from dimod.generators.constraints import combinations 23 | from hybrid.reference import KerberosSampler 24 | 25 | 26 | def get_label(row, col, digit): 27 | """Returns a string of the cell coordinates and the cell value in a 28 | standard format. 29 | """ 30 | return "{row},{col}_{digit}".format(**locals()) 31 | 32 | def get_matrix(filename): 33 | """Return a list of lists containing the content of the input text file. 34 | 35 | Note: each line of the text file corresponds to a list. Each item in 36 | the list is from splitting the line of text by the whitespace ' '. 37 | """ 38 | with open(filename, "r") as f: 39 | content = f.readlines() 40 | 41 | lines = [] 42 | for line in content: 43 | new_line = line.rstrip() # Strip any whitespace after last value 44 | 45 | if new_line: 46 | new_line = list(map(int, new_line.split(' '))) 47 | lines.append(new_line) 48 | 49 | return lines 50 | 51 | def is_correct(matrix): 52 | """Verify that the matrix satisfies the Sudoku constraints. 53 | 54 | Args: 55 | matrix(list of lists): list contains 'n' lists, where each of the 'n' 56 | lists contains 'n' digits. 57 | """ 58 | n = len(matrix) # Number of rows/columns 59 | m = int(math.sqrt(n)) # Number of subsquare rows/columns 60 | unique_digits = set(range(1, n+1)) # Digits in a solution 61 | 62 | # Verifying rows 63 | for row in matrix: 64 | if set(row) != unique_digits: 65 | print("Error in row: ", row) 66 | return False 67 | 68 | # Verifying columns 69 | for j in range(n): 70 | col = [matrix[i][j] for i in range(n)] 71 | if set(col) != unique_digits: 72 | print("Error in col: ", col) 73 | return False 74 | 75 | # Verifying subsquares 76 | subsquare_coords = [(i, j) for i in range(m) for j in range(m)] 77 | for r_scalar in range(m): 78 | for c_scalar in range(m): 79 | subsquare = [matrix[i + r_scalar * m][j + c_scalar * m] for i, j 80 | in subsquare_coords] 81 | if set(subsquare) != unique_digits: 82 | print("Error in sub-square: ", subsquare) 83 | return False 84 | 85 | return True 86 | 87 | def build_bqm(matrix): 88 | """Build BQM using Sudoku constraints""" 89 | # Set up 90 | n = len(matrix) # Number of rows/columns in sudoku 91 | m = int(math.sqrt(n)) # Number of rows/columns in sudoku subsquare 92 | digits = range(1, n+1) 93 | 94 | bqm = dimod.BinaryQuadraticModel({}, {}, 0.0, dimod.SPIN) 95 | 96 | # Constraint: Each node can only select one digit 97 | for row in range(n): 98 | for col in range(n): 99 | node_digits = [get_label(row, col, digit) for digit in digits] 100 | one_digit_bqm = combinations(node_digits, 1) 101 | bqm.update(one_digit_bqm) 102 | 103 | # Constraint: Each row of nodes cannot have duplicate digits 104 | for row in range(n): 105 | for digit in digits: 106 | row_nodes = [get_label(row, col, digit) for col in range(n)] 107 | row_bqm = combinations(row_nodes, 1) 108 | bqm.update(row_bqm) 109 | 110 | # Constraint: Each column of nodes cannot have duplicate digits 111 | for col in range(n): 112 | for digit in digits: 113 | col_nodes = [get_label(row, col, digit) for row in range(n)] 114 | col_bqm = combinations(col_nodes, 1) 115 | bqm.update(col_bqm) 116 | 117 | # Constraint: Each sub-square cannot have duplicates 118 | # Build indices of a basic subsquare 119 | subsquare_indices = [(row, col) for row in range(m) for col in range(m)] 120 | 121 | # Build full sudoku array 122 | for r_scalar in range(m): 123 | for c_scalar in range(m): 124 | for digit in digits: 125 | # Shifts for moving subsquare inside sudoku matrix 126 | row_shift = r_scalar * m 127 | col_shift = c_scalar * m 128 | 129 | # Build the labels for a subsquare 130 | subsquare = [get_label(row + row_shift, col + col_shift, digit) 131 | for row, col in subsquare_indices] 132 | subsquare_bqm = combinations(subsquare, 1) 133 | bqm.update(subsquare_bqm) 134 | 135 | # Constraint: Fix known values 136 | for row, line in enumerate(matrix): 137 | for col, value in enumerate(line): 138 | if value > 0: 139 | # Recall that in the "Each node can only select one digit" 140 | # constraint, for a given cell at row r and column c, we 141 | # produced 'n' labels. Namely, 142 | # ["r,c_1", "r,c_2", ..., "r,c_(n-1)", "r,c_n"] 143 | # 144 | # Due to this same constraint, we can only select one of these 145 | # 'n' labels (achieved by 'generators.combinations(..)'). 146 | # 147 | # The 1 below indicates that we are selecting the label 148 | # produced by 'get_label(row, col, value)'. All other labels 149 | # with the same 'row' and 'col' will be discouraged from being 150 | # selected. 151 | bqm.fix_variable(get_label(row, col, value), 1) 152 | 153 | return bqm 154 | 155 | def solve_sudoku(bqm, matrix): 156 | """Solve BQM and return matrix with solution.""" 157 | solution = KerberosSampler().sample(bqm, 158 | max_iter=10, 159 | convergence=3, 160 | qpu_params={'label': 'Example - Sudoku'}) 161 | best_solution = solution.first.sample 162 | solution_list = [k for k, v in best_solution.items() if v == 1] 163 | 164 | result = copy.deepcopy(matrix) 165 | 166 | for label in solution_list: 167 | coord, digit = label.split('_') 168 | row, col = map(int, coord.split(',')) 169 | 170 | if result[row][col] > 0: 171 | # the returned solution is not optimal and either tried to 172 | # overwrite one of the starting values, or returned more than 173 | # one value for the position. In either case the solution is 174 | # likely incorrect. 175 | continue 176 | 177 | result[row][col] = int(digit) 178 | 179 | return result 180 | 181 | if __name__ == "__main__": 182 | # Read user input 183 | if len(sys.argv) > 1: 184 | filename = sys.argv[1] 185 | else: 186 | filename = "problem.txt" 187 | print("Warning: using default problem file, '{}'. Usage: python " 188 | "{} ".format(filename, sys.argv[0])) 189 | 190 | # Read sudoku problem as matrix 191 | matrix = get_matrix(filename) 192 | 193 | # Solve BQM and update matrix 194 | bqm = build_bqm(matrix) 195 | result = solve_sudoku(bqm, matrix) 196 | 197 | # Print solution 198 | for line in result: 199 | print(*line, sep=" ") # Print list without commas or brackets 200 | 201 | # Verify 202 | if is_correct(result): 203 | print("The solution is correct") 204 | else: 205 | print("The solution is incorrect") 206 | -------------------------------------------------------------------------------- /tests/__init__.py: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/dwave-examples/sudoku/c0a62a384fb5ef5aaa2674b235003ad636bd5610/tests/__init__.py -------------------------------------------------------------------------------- /tests/test_integration.py: -------------------------------------------------------------------------------- 1 | # Copyright 2020 D-Wave Systems Inc. 2 | # 3 | # Licensed under the Apache License, Version 2.0 (the "License"); 4 | # you may not use this file except in compliance with the License. 5 | # You may obtain a copy of the License at 6 | # 7 | # http://www.apache.org/licenses/LICENSE-2.0 8 | # 9 | # Unless required by applicable law or agreed to in writing, software 10 | # distributed under the License is distributed on an "AS IS" BASIS, 11 | # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 | # See the License for the specific language governing permissions and 13 | # limitations under the License. 14 | 15 | import subprocess 16 | import unittest 17 | import os 18 | import sys 19 | 20 | project_dir = os.path.dirname(os.path.dirname(os.path.abspath(__file__))) 21 | 22 | class IntegrationTests(unittest.TestCase): 23 | @unittest.skipIf(os.getenv('SKIP_INT_TESTS'), "Skipping integration test.") 24 | def test_sudoku(self): 25 | demo_file = os.path.join(project_dir, 'sudoku.py') 26 | problem_file = os.path.join(project_dir, 'problem.txt') 27 | output = subprocess.check_output([sys.executable, demo_file, problem_file]) 28 | output = str(output).upper() 29 | if os.getenv('DEBUG_OUTPUT'): 30 | print("Example output \n" + output) 31 | 32 | with self.subTest(msg="Verify if output contains 'THE SOLUTION IS CORRECT' \n"): 33 | self.assertIn("THE SOLUTION IS CORRECT".upper(), output) 34 | with self.subTest(msg="Verify if error string contains in output \n"): 35 | self.assertNotIn("ERROR", output) 36 | with self.subTest(msg="Verify if warning string contains in output \n"): 37 | self.assertNotIn("WARNING", output) 38 | 39 | if __name__ == '__main__': 40 | unittest.main() -------------------------------------------------------------------------------- /tests/test_sudoku.py: -------------------------------------------------------------------------------- 1 | # Copyright 2020 D-Wave Systems Inc. 2 | # 3 | # Licensed under the Apache License, Version 2.0 (the "License"); 4 | # you may not use this file except in compliance with the License. 5 | # You may obtain a copy of the License at 6 | # 7 | # http://www.apache.org/licenses/LICENSE-2.0 8 | # 9 | # Unless required by applicable law or agreed to in writing, software 10 | # distributed under the License is distributed on an "AS IS" BASIS, 11 | # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 | # See the License for the specific language governing permissions and 13 | # limitations under the License. 14 | 15 | import sys 16 | import unittest 17 | from unittest.mock import patch 18 | from io import StringIO 19 | 20 | from sudoku import is_correct, build_bqm, solve_sudoku 21 | 22 | class TestSudoku(unittest.TestCase): 23 | def test_is_correct(self): 24 | bad_matrix = [[1,2,3,2], 25 | [3,2,1,4], 26 | [4,1,2,3], 27 | [2,3,4,1]] 28 | 29 | with patch('sys.stdout', new_callable=StringIO) as mock_stdout: 30 | self.assertFalse(is_correct(bad_matrix)) 31 | self.assertIn("Error in row: [1, 2, 3, 2]", mock_stdout.getvalue()) 32 | 33 | good_matrix = [[1,4,3,2], 34 | [3,2,1,4], 35 | [4,1,2,3], 36 | [2,3,4,1]] 37 | 38 | self.assertTrue(is_correct(good_matrix)) 39 | 40 | def test_solve_sudoku(self): 41 | matrix = [[1,0,0,0], 42 | [0,0,0,4], 43 | [0,0,2,0], 44 | [0,3,0,0]] 45 | 46 | target = [[1,4,3,2], 47 | [3,2,1,4], 48 | [4,1,2,3], 49 | [2,3,4,1]] 50 | 51 | bqm = build_bqm(matrix) 52 | result = solve_sudoku(bqm, matrix) 53 | 54 | self.assertEqual(result, target) 55 | --------------------------------------------------------------------------------