Merge pull request #1417 from yashmita/SudokuSolver

Sudoku solver

Algorithm/Backtracking/readme.md

@@ -29,4 +29,4 @@ unsolvable.
 
 * Permutation of a string ----> [C++](/Code/C++/permutation_of_a_string.cpp)
 * N Queen Problem ----> [C++](/Code/C++/n_queen_problem.cpp)
-* Sudoku Solver ----> [C++](/Code/C++/sudoku_solver.cpp)
+* Sudoku Solver ----> [C++](/Code/C++/sudoku_solver.cpp) | [Java](/Code/Java/Sudoku_Solver.java)

Code/Java/Sudoku_Solver.java

@@ -0,0 +1,151 @@
+/*
+PROBLEM STATEMENT:
+Given an nxn sized incomplete Sudoku in which 0 represents an empty cell. The task is to print it's solution.  
+*/
+
+import java.util.Scanner;
+class Sudoku_Solver
+{
+	//A function to check whether a number between 1 to n can be placed at the specified cell or not
+	public static boolean CanPlace(int[][] mat, int n, int i, int j, int num)
+	{
+		//check for rows and columns
+		for(int x = 0; x < n; x++)
+		{
+			if(mat[x][j] == num || mat[i][x] == num)
+				return false;
+		}
+
+		//check for the subgrid
+		int root = (int)Math.sqrt(n);
+		int sx = (i/root)*root;	//starting x coordinate of a subgrid
+		int sy = (j/root)*root; //starting y coordinate of a subgrid
+		for(int x = sx; x < sx+root; x++)
+		{
+			for(int y = sy; y < sy+root; y++)
+			{
+				if(mat[x][y] == num)
+					return false;
+			}
+		}
+
+		//else if it is possible to place num at mat[i][j], return true
+		return true;
+	}
+
+	//A function to solve the Sudoku, once solved it prints the solution and returns true, otherwise false
+	public static boolean SudokuSolver(int[][] mat, int n, int i, int j)
+	{
+		//base case
+		if(i == n)
+		{
+			//print solution
+			for (i = 0; i < n; i++)
+			{
+				for (j = 0; j < n; j++)
+				{
+					System.out.print(mat[i][j]);
+					System.out.print(" ");
+				}
+				System.out.print("\n");
+			}
+			return true;
+		}
+
+		//if a row ends, recursive call to next row
+		if(j == n)
+			return SudokuSolver(mat, n, i+1, 0);
+
+		//if the cell is pre-filled, recursive call to the next cell
+		if(mat[i][j] != 0)
+			return SudokuSolver(mat, n, i, j+1);
+
+		//Loop to fill any one of the number from 1 to n in a cell
+		for(int num = 1; num <= n; num++)
+		{
+			//A function call to check whether it is possible to place num in the given cell or not
+			if(CanPlace(mat, n, i, j, num))
+			{
+				mat[i][j] = num;
+				//recursive call for the next cell
+				boolean solvenext = SudokuSolver(mat, n, i, j+1);
+				if(solvenext)
+					return true;
+			}
+		}
+
+		//if none of the number can be placed then, backtrack
+		mat[i][j] = 0;
+		return false;
+	}
+
+	// Driver Code
+	public static void main(String[] args)
+	{
+		//Size input from user
+		System.out.print("Enter size of the Sudoku: ");
+		Scanner sc = new Scanner(System.in);
+		int n = sc.nextInt();
+		System.out.println("Enter elements of Sudoku: ");    
+		int mat[][] = new int[n][n];
+
+		//Elements input from user
+		for(int i = 0; i < n; i++)
+		{            
+			for(int j = 0; j < n; j++)
+			{
+				mat[i][j] = sc.nextInt();
+			}
+		}
+
+		//function call to solve sudoku
+		if(!SudokuSolver(mat, n, 0, 0))
+			System.out.print("No Solution!");		
+	}
+}
+
+/*
+TEST CASES:
+1.
+Input:
+Enter size of the Sudoku: 9
+Enter elements of Sudoku:
+3 0 6 5 0 8 4 0 0
+5 2 0 0 0 0 0 0 0 
+0 8 7 0 0 0 0 3 1 
+0 0 3 0 1 0 0 8 0 
+9 0 0 8 6 3 0 0 5 
+0 5 0 0 9 0 6 0 0 
+1 3 0 0 0 0 2 5 0
+0 0 0 0 0 0 0 7 4 
+0 0 5 2 0 6 3 0 0
+Output: 
+3 1 6 5 7 8 4 9 2 
+5 2 9 1 3 4 7 6 8 
+4 8 7 6 2 9 5 3 1 
+2 6 3 4 1 5 9 8 7 
+9 7 4 8 6 3 1 2 5 
+8 5 1 7 9 2 6 4 3 
+1 3 8 9 4 7 2 5 6 
+6 9 2 3 5 1 8 7 4 
+7 4 5 2 8 6 3 1 9 
+
+2.
+Input:
+Enter size of the Sudoku: 9
+Enter elements of Sudoku:
+3 0 6 5 0 8 4 0 0
+5 2 0 0 0 0 0 0 0 
+0 8 7 0 0 0 0 3 1 
+0 0 3 0 1 0 4 8 0 
+9 0 0 8 6 3 0 0 5 
+0 5 0 0 9 0 6 0 0 
+1 3 0 0 0 0 2 5 0
+0 0 0 0 0 0 0 7 4 
+0 0 5 2 0 6 3 0 0
+Output:
+No Solution!
+
+TIME COMPLEXITY:  O(9^(n*n)), as there will be 9 options from 1 to 9 to fill in an empty cell.
+SPACE COMPLEXITY: O(n*n), where n denotes the size of Sudoku grid
+*/