![]() ![]() The graph coloring code is based on the Graph Coloring Kata with the following changes: However, trying to use more than 8 qubits (2 empty squares) in a simulation becomes very slow, so here we only run it for 1 or 2 missing squares in a 9x9 puzzle. The code can also solve 9x9 Sudoku puzzles using 4 qubits per number. This allows a 4x4 puzzle to be solved using 2 qubits per missing number. The numbers are changed to 0 to 3 and 0 to 8 and then converted back. However, when solving this using a quantum program and encoding these values into qubits, Note that the puzzles are initially defined in C# using numbers from 1 to 4, or 1 to9. Similarly, startingNumberConstraints is the array of (Cell#, constraint).įor example, the constraint that empty cell 0 can't have value 1 or 3 is encoded as startingNumberConstraints =. A list of constraints on empty squares to the initial numbers in the puzzle (starting numbers)įor example, for the row above the empty squares have indices: _Īnd emptySquareEdges is the array of edges.įor example, cell 0 can't have the same number (color) as cell 1, so emptySquareEdges =.A list of edges connecting empty squares.We define the puzzle using 2 data structures. To reduce the number of qubits, we only use qubits for empty squares.Įach empty square gets 2 qubits to encode the numbers 0 to 3. In the above example, the constraints for the top row are _ Graph edges are the constraints preventing squares from having the same values. In our case, graph nodes are puzzle squares and colors are the Sudoku numbers. Sudoku is a graph coloring problem where graph edges must connect nodes of different colors. ![]() The numbers 0 to 3 may only appear once per row, column and 2x2 sub squares. The code supports both 4x4 and 9x9 Sudoku puzzles. It’s also called the brute force algorithm way to solve the sudoku puzzle.This program demonstrates solving Sudoku puzzle using Grover's algorithm. We use this principle of backtracking to implement the sudoku algorithm. Backtracking means switching back to the previous step as soon as we determine that our current solution cannot be continued into a complete one. We’ll use the backtracking method to create our sudoku solver in Python. As our assumption was wrong, we discard the assigned num and then we go for the next assumption with a different num value.Later we check for the next possibility with the next column. After checking if it is a safe place, we move to the next column and then assign the num in the current (row, col) position of the grid.Further now we see if the current position of the grid has a value greater than 0, then we iterate for the next column.Next, we will check if the column value becomes 9 then we move to the next row and column.Then we will check if we have reached the 8th row and 9th column and return true for stopping further backtracking.If we find the same num in the same row or same column or in the specific 3*3 matrix, ‘false’ will be returned.Later it will assign num to the row and col.Then we assign the utility function (puzzle) to print the grid.In this method for solving the sudoku puzzle, first, we assign the size of the 2D matrix to a variable M (M*M).Steps to solve the Sudoku Puzzle in Python The lesser the clues, the higher the chances of multiple solutions. It is unknown whether or not there exists a well-formed puzzle with only 16 clues. Well-formed Sudoku with 17 symbols exists. Another challenging research problem is to determine how few boxes need to be filled for a Sudoku puzzle to be well-formed. A Sudoku puzzle is believed to be well-formed if it has a unique solution. The Sudoku puzzles which are published for entertainment have unique solutions. ![]()
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