sudoku using backtraking

1. SUDOKU USING
BACK TRACKING
“PLAY IT THE CODE WAY”
B
Y
Abhishek kumar singh
@Code_do_it_better

2. 2
Sudoku?
A simple but addictive puzzle, invented in the
USA in 1979 and called Number Place;
Became popular in Japan in 1986, where it was
renamed Sudoku (~ “single number”);
First appeared in UK newspapers in 2004, and
became an international craze in 2005.

3. 3
How it’s played ?
The matrix(9*9) is partially filled.
You have to fill it such that:
1-> Each row contains all of 9 digits
from 1 to 9.
2-> Each col contains all of 9 digits
from 1 to 9.
3-> Each (3*3) matrix separated by
Dark lines contains all of 9
digits from 1 to 9.
2 1 3 8
5
7 6
1 3
9 8 1 2 5 7
3 1 8
9 8 2
5 6 9 7 8 4
4 2 5

4. “THAT’S WHAT PEOPLE KNOW ABOUT SUDOKU”
ONLY THING THAT SEPARATE US…….
CODER’S KNOW A BIT MORE.
SO LET’S LEARN TO DO IT OUR WAY.

5. WHAT IS BACKTRACKING ?
•As the name suggests we backtrack to find the solution. We
start with one possible move out of many available moves
and try to solve the problem if we are able to solve the
problem with the selected move then we will print the
solution else we will backtrack and select some other move
and try to solve it. If none if the moves work out we will
claim that there is no solution for the problem.
•Recursion is the key in backtracking
programming.

6. BACKTRACKING ALGORITHM
Find row, column of an unassigned cell If there is none,
return true .
For digits from 1 to 9
a) If there is no conflict for digit at row, column and 3*3
matrix box, assign digit to row, column .
b) Recursively try fill in rest of grid.
c) If recursion successful, return true.
c) Else, remove digit and try another If all digits have
been tried and nothing worked, return false.
We are going to solve the above puzzle using…..

7. Example:
Solve the given Sudoku
problem.

8. 1 1
1 1
4 982
1 4 921 4 92

9. 1 11 1 421 62 4 9 8 1 62 4 98
MOVING THROUGH THE NEXT LINES AND
FOLLOWING THE SAME PROCEDURE WE
WILL BE ABLE TO SOLVE THIS PROBLEM
WITH BACKTRACKING ALGORITHM.

10. 5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9

11. Bool SolveSudoku(grid[N][N])
{
int row, col;
if (!FindUnassignedLocation(grid, row, col))
return true;
do for num = 1 to 9
{
if (isSafe(grid, row, col, num))
{
grid[row][col] = num;
if (SolveSudoku(grid))
return true;
grid[row][col] = UNASSIGNED;
}
}
return false;
}
IMPLEMENTATION

12. Some Important Points
•Backtracking algorithm will search for every possible
solution.
•If You have a proper question, this method will
definitely provide a solution.
•Backtracking always provides a solution but it uses a lot
of time and space to solve it.
•If problem is large enough, backtracking will take a lot
of time and space and it’s worthless to use it.