Added Sudoku Problem using Backtracking in cpp

Algorithms/Sudoku Problem using Backtracking in cpp

@@ -0,0 +1,89 @@
+#include <iostream>
+using namespace std;
+
+int grid[N][N] = {
+   {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}
+};
+
+bool isPresentInCol(int col, int num) { //check whether num is present in col or not
+   for (int row = 0; row < N; row++)
+      if (grid[row][col] == num)
+         return true;
+   return false;
+}
+
+bool isPresentInRow(int row, int num) { //check whether num is present in row or not
+   for (int col = 0; col < N; col++)
+      if (grid[row][col] == num)
+         return true;
+   return false;
+}
+
+bool isPresentInBox(int boxStartRow, int boxStartCol, int num) {
+//check whether num is present in 3x3 box or not
+   for (int row = 0; row < 3; row++)
+      for (int col = 0; col < 3; col++)
+         if (grid[row+boxStartRow][col+boxStartCol] == num)
+            return true;
+   return false;
+}
+
+void sudokuGrid() { //print the sudoku grid after solve
+   for (int row = 0; row < N; row++){
+      for (int col = 0; col < N; col++){
+         if(col == 3 || col == 6)
+            cout << " | ";
+         cout << grid[row][col] <<" ";
+      }
+      if(row == 2 || row == 5){
+         cout << endl;
+         for(int i = 0; i<N; i++)
+            cout << "---";
+      }
+      cout << endl;
+   }
+}
+
+bool findEmptyPlace(int &row, int &col) { //get empty location and update row and column
+   for (row = 0; row < N; row++)
+      for (col = 0; col < N; col++)
+         if (grid[row][col] == 0) //marked with 0 is empty
+            return true;
+   return false;
+}
+
+bool isValidPlace(int row, int col, int num) {
+   //when item not found in col, row and current 3x3 box
+   return !isPresentInRow(row, num) && !isPresentInCol(col, num) && !isPresentInBox(row - row%3 ,
+col - col%3, num);
+}
+
+bool solveSudoku() {
+   int row, col;
+   if (!findEmptyPlace(row, col))
+      return true; //when all places are filled
+   for (int num = 1; num <= 9; num++){ //valid numbers are 1 - 9
+      if (isValidPlace(row, col, num)){ //check validation, if yes, put the number in the grid
+         grid[row][col] = num;
+         if (solveSudoku()) //recursively go for other rooms in the grid
+            return true;
+         grid[row][col] = 0; //turn to unassigned space when conditions are not satisfied
+      }
+   }
+   return false;
+}
+
+int main() {
+   if (solveSudoku() == true)
+      sudokuGrid();
+   else
+      cout << "No solution exists";
+}