(Game: Sudoku) Revise Programming Exercise 22.21 to display...

(Game: Sudoku) Revise Programming Exercise 22.21 to display all solutions for the Sudoku game, as shown in Figure 22.17a. When you click the Solve button, the program stores all solutions in an ArrayList. Each element in the list is a two-dimensional 9-by-9 grid. If the program has multiple solutions, the Next button appears as shown in Figure 22.17b. You can click the Next button to display the next solution and also a label to show the solution count. When the Clear button is clicked, the cells are cleared and the Next button is hidden as shown in Figure $22.17 \mathrm{c}$. FIGURE CANT COPY Ficure 22.17 The program can display multiple Sudoku solutions.

(Game: Sudoku) Revise Programming Exercise 22.21 to display all solutions for the Sudoku game, as shown in Figure 22.17a. When you click the Solve button, the program stores all solutions in an ArrayList. Each element in the list is a two-dimensional 9-by-9 grid. If the program has multiple solutions, the Next button appears as shown in Figure 22.17b. You can click the Next button to display the next solution and also a label to show the solution count. When the Clear button is clicked, the cells are cleared and the Next button is hidden as shown in Figure $22.17 \mathrm{c}$.
FIGURE CANT COPY
Ficure 22.17 The program can display multiple Sudoku solutions.

Key Concepts

Backtracking Search

Backtracking is a recursive algorithmic strategy for exploring all possible solutions in a problem. In the context of Sudoku, it systematically fills empty cells with valid numbers while backtracking upon encountering a conflict. This method is key to efficiently generating all possible valid board configurations.

Recursive Algorithms

Recursion is used to break down the large Sudoku puzzle problem into smaller subproblems by repeatedly making choices and exploring the consequences. Recursive calls allow the solution to progress cell by cell, invoking backtracking as necessary to explore every branch of possibility.

Data Structures: ArrayList and Two-Dimensional Arrays

Two-dimensional arrays are fundamental for representing the 9-by-9 Sudoku grid, providing a clear, structured way to manage the puzzle data. An ArrayList is used to store multiple such grids, each representing a valid solution, which allows dynamic resizing as solutions are added during the computation process.

Event-Driven Programming and GUI Interaction

Event-driven programming is essential in interactive applications like Sudoku solvers. GUI components such as buttons (Solve, Next, and Clear) and labels facilitate user interaction. They trigger events that control the flow of the program, from initiating the solution search to navigating through multiple results.

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