Added Sudoku Solver backtracking algorithm with test cases

Author: khalidx3

src/main/java/com/thealgorithms/backtracking/SudokuSolver.java

@@ -0,0 +1,85 @@
+package main.java.com.thealgorithms.backtracking;
+
+public class SudokuSolver {
+      public static boolean sudokuSolver(int sudoku[][], int row, int col) {
+            // base case
+            if (row == 9) {
+                  return true;
+            }
+            // recursion
+            int nextRow = row, nextCol = col + 1;
+            if (col + 1 == 9) {
+                  nextRow = row + 1;
+                  nextCol = 0;
+            }
+            if (sudoku[row][col] != 0) {
+                  return sudokuSolver(sudoku, nextRow, nextCol);
+            }
+            for (int digit = 1; digit <= 9; digit++) {
+                  if (isSafe(sudoku, row, col, digit)) {
+                        sudoku[row][col] = digit;
+
+                        if (sudokuSolver(sudoku, nextRow, nextCol)) {
+                              return true;
+                        }
+                        sudoku[row][col] = 0;
+                  }
+            }
+
+            return false;
+      }
+
+      public static boolean isSafe(int sudoku[][], int row, int col, int digit) {
+            // col
+            for (int i = 0; i <= 8; i++) {
+                  if (sudoku[i][col] == digit) {
+                        return false;
+                  }
+            }
+            // row
+            for (int j = 0; j <= 8; j++) {
+                  if (sudoku[row][j] == digit) {
+                        return false;
+                  }
+            }
+            // grid
+            int sr = (row / 3) * 3;
+            int sc = (col / 3) * 3;
+            for (int i = sr; i < sr + 3; i++) {
+                  for (int j = sc; i < sr + 3; i++) {
+                        if (sudoku[i][j] == digit) {
+                              return false;
+                        }
+                  }
+            }
+            return true;
+      }
+
+      public static void print(int sudoku[][]) {
+            for (int i = 0; i < 9; i++) {
+                  for (int j = 0; j < 9; j++) {
+                        System.out.print(sudoku[i][j] + " ");
+                  }
+                  System.out.println();
+            }
+      }
+
+      public static void main(String[] args) {
+            int 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 } };
+            if (sudokuSolver(sudoku, 0, 0)) {
+
+                  print(sudoku);
+            } else {
+                  System.out.println("not valid");
+            }
+      }
+
+}