Added Backtracking Algorithm for solving Soduku

c++/Sudoku_Solver.cpp

@@ -0,0 +1,116 @@
+   // Solving sudoku using Backtracking
+
+#include <bits/stdc++.h>
+using namespace std;
+
+bool Any_Unassigned_Location(int grid[9][9], int& row, int& col)
+{
+    for (row = 0; row < 9; row++)
+        for (col = 0; col < 9; col++)
+            if (grid[row][col] == 0)
+                return true;
+    return false;
+}
+
+bool if_UsedInRow(int grid[9][9], int row, int num)
+{
+    for (int col = 0; col < 9; col++)
+        if (grid[row][col] == num)
+            return true;
+    return false;
+}
+
+bool if_UsedInCol(int grid[9][9], int col, int num)
+{
+    for (int row = 0; row < 9; row++)
+        if (grid[row][col] == num)
+            return true;
+    return false;
+}
+
+bool if_UsedInBox(int grid[9][9], int boxStartRow, int boxStartCol, int num)
+{
+    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;
+}
+
+bool isSafe(int grid[9][9], int row, int col, int num)
+{
+    return !if_UsedInRow(grid, row, num)
+           && !if_UsedInCol(grid, col, num)
+           && !if_UsedInBox(grid, row - row % 3,
+                         col - col % 3, num)
+           && grid[row][col] == 0;
+}
+
+bool SolveSudoku(int grid[9][9])
+{
+    int row, col;
+
+    if (!Any_Unassigned_Location(grid, row, col))
+        return true;
+
+    for (int num = 1; num <= 9; num++)
+    {
+        if (isSafe(grid, row, col, num))
+        {     
+            grid[row][col] = num;
+            if (SolveSudoku(grid))
+                return true;
+            grid[row][col] = 0;
+        }
+    }
+
+    return false;
+}
+
+int main()
+{
+    /*sample input-
+
+    0 0 0 2 6 0 7 0 1
+    6 8 0 0 7 0 0 9 0
+    1 9 0 0 0 4 5 0 0
+    8 2 0 1 0 0 0 4 0
+    0 0 4 6 0 2 9 0 0
+    0 5 0 0 0 3 0 2 8
+    0 0 9 3 0 0 0 7 4
+    0 4 0 0 5 0 0 3 6
+    7 0 3 0 1 8 0 0 0
+
+    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 
+
+    */
+
+    int grid[9][9];
+    for(int i = 0; i<9; i++){
+        for(int j =0; j<9; j++){
+            cin>>grid[i][j];
+            }
+    }
+
+    if (SolveSudoku(grid) == true){
+
+        for (int row = 0; row < 9; row++)
+        {
+            for (int col = 0; col < 9; col++)
+                cout << grid[row][col] << " ";
+            cout << endl;
+        }
+    }
+    else
+        cout << "No solution exists for the given sudoku";
+
+    return 0;
+}