Our project is a software that can solve Kenken game with any board size using backtracking, backtracking with forward checking, or backtracking with arc consistency.
The goal of this project is to create a software that solves the KENKEN puzzle. This is a constrain satisfaction problem (CSP), and we implement and analyze the performance of the three algorithms of CSP:
- Backtracking
- Backtracking with forward checking
- Backtracking with arc consistency
The KenKen board is represented by a square n-by-n grid of cells. The grid may contain between 1 and n boxes (cages) represented by a heavily outlined perimeter. Each cage will contain in superscript: the target digit value for the cage followed by a mathematical operator.
Each valid solution must follow the below rules:
- The only numbers you may write are 1 to N for a NxN size puzzle.
- A number cannot be reapeated within the same row.
- A number cannot be reapeated within the same solumn.
- In a one-cell cage, just write the target number in that cell.
- Each "cage" (region bounded by a heavy border) contains a "target number" and an arithmetic operation. You must fill that cage with numbers that produce the target number, using only the specified arithmetic operation. Numbers may be repeated within a cage, if necessary, as long as they do not repeat within a single row or column.
The below table represents the time performance of each algorithm, to solve different size puzzles each 100 times.
| Size | BT | BT+FC | BT+AC |
|---|---|---|---|
| 3x3 | 0.113s | 0.129s | 0.147s |
| 5x5 | 5.456s | 2.808s | 4.832s |
- This is the front window in which the user specifies the board size as a single number and the algorithm used to solve the board.
- This is an example of 4x4 board generated using backtracking with arc consistency
- Warnings to guide the user if they haven't filled all input fields or enterd wrong value
