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Author: muthusk07

backtracking_problems/sudoku_backtracking.cpp

@@ -0,0 +1,126 @@
+#include <bits/stdc++.h> 
+using namespace std; 
+ 
+#define UNASSIGNED 0  
+ 
+#define N 9  
+  
+
+bool FindUnassignedLocation(int grid[N][N],  
+                            int &row, int &col);  
+  
+
+bool isSafe(int grid[N][N], int row, 
+                   int col, int num);  
+  
+
+bool SolveSudoku(int grid[N][N])  
+{  
+    int row, col;  
+  
+    
+    if (!FindUnassignedLocation(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] = UNASSIGNED;  
+        }  
+    }  
+    return false; 
+}  
+  
+
+bool FindUnassignedLocation(int grid[N][N],  
+                            int &row, int &col)  
+{  
+    for (row = 0; row < N; row++)  
+        for (col = 0; col < N; col++)  
+            if (grid[row][col] == UNASSIGNED)  
+                return true;  
+    return false;  
+}  
+  
+
+bool UsedInRow(int grid[N][N], int row, int num)  
+{  
+    for (int col = 0; col < N; col++)  
+        if (grid[row][col] == num)  
+            return true;  
+    return false;  
+}  
+  
+
+bool UsedInCol(int grid[N][N], int col, int num)  
+{  
+    for (int row = 0; row < N; row++)  
+        if (grid[row][col] == num)  
+            return true;  
+    return false;  
+}  
+  
+
+bool UsedInBox(int grid[N][N], 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[N][N], int row,  
+                   int col, int num)  
+{  
+   
+    return !UsedInRow(grid, row, num) &&  
+           !UsedInCol(grid, col, num) &&  
+           !UsedInBox(grid, row - row % 3 ,  
+                      col - col % 3, num) &&  
+            grid[row][col] == UNASSIGNED;  
+}  
+  
+
+void printGrid(int grid[N][N])  
+{  
+    for (int row = 0; row < N; row++)  
+    {  
+    for (int col = 0; col < N; col++)  
+            cout << grid[row][col] << " ";  
+        cout << endl; 
+    }  
+}  
+  
+// Driver Code 
+int main()  
+{  
+    // 0 means unassigned cells  
+    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}};  
+    if (SolveSudoku(grid) == true)  
+        printGrid(grid);  
+    else
+        cout << "No solution exists";  
+  
+    return 0;  
+}