#PSEUDOCODE FOR SOLVING SUDOKU CODE#

4x4-1: test Quantum solution of 4x4 puzzle missing 1 number.4x4-classic : test classic algorithm on a 4x4 puzzle.You can also choose a specific puzzle to solve by adding the puzzle name as below To run the sample, use the dotnet run command from your terminal. for 9x9 puzzles, 4 bits per color are used but the colors in the solution can only be 0 to 8.constraints on Vertex colors based on initial colors when you start.

#PSEUDOCODE FOR SOLVING SUDOKU CODE#

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. Output: True, when placing the number at position grid is valid.This program demonstrates solving Sudoku puzzle using Grover's algorithm. Input: Row, a column of the grid, and number to check. Output − If the grid is empty, then return true, otherwise false. Beginįor each row r in boxStartRow to next 3 rows, doįor each col r in boxStartCol to next 3 columns, do Output − True when the number is present in the box. Input − The starting row and column of a 3 x 3 box, and the targeted number. IsPresentInBox(boxStartRow, boxStartCol, num) Output − True when the number is present in the given column. Input − The row, and the targeted number. Output − True when the number is present in the given column. IsPresentInCol(col, num) Input: The column, and the targeted number. If the solution does not exist, it will return false. The final matrix (Sudoku grid) filled with numbers. This will take a 9 x 9 matrix as Sudoku grid. If all numbers are checked from 1-9, and no valid digit found to place, it backtracks to the previous option. When it is not valid, it checks for other numbers. When some cell is filled with a digit, it checks whether it is valid or not. Using the backtracking algorithm, we will try to solve the Sudoku problem. One digit cannot be repeated in one row, one column or in one 3 x 3 box. We have to use digits 1 to 9 for solving this problem. Sudoku is a 9 x 9 number grid, and the whole grid are also divided into 3 x 3 boxes There are some rules to solve the Sudoku. In this section, we will try to solve the famous number maze problem called Sudoku.

Pseudocode for solving sudoku