rename Backtracking -> backtracking (#654)

backtracking/sudoku_solve.cpp

@@ -0,0 +1,117 @@
+#include <iostream>
+using namespace std;
+///N=9;
+int n = 9;
+
+bool isPossible(int mat[][9], int i, int j, int no)
+{
+    ///Row or col nahin hona chahiye
+    for (int x = 0; x < n; x++)
+    {
+        if (mat[x][j] == no || mat[i][x] == no)
+        {
+            return false;
+        }
+    }
+
+    /// Subgrid mein nahi hona chahiye
+    int sx = (i / 3) * 3;
+    int sy = (j / 3) * 3;
+
+    for (int x = sx; x < sx + 3; x++)
+    {
+        for (int y = sy; y < sy + 3; y++)
+        {
+            if (mat[x][y] == no)
+            {
+                return false;
+            }
+        }
+    }
+
+    return true;
+}
+void printMat(int mat[][9])
+{
+
+    for (int i = 0; i < n; i++)
+    {
+        for (int j = 0; j < n; j++)
+        {
+            cout << mat[i][j] << " ";
+            if ((j + 1) % 3 == 0)
+            {
+                cout << '\t';
+            }
+        }
+        if ((i + 1) % 3 == 0)
+        {
+            cout << endl;
+        }
+        cout << endl;
+    }
+}
+
+bool solveSudoku(int mat[][9], int i, int j)
+{
+    ///Base Case
+    if (i == 9)
+    {
+        ///Solve kr chuke hain for 9 rows already
+        printMat(mat);
+        return true;
+    }
+
+    ///Crossed the last  Cell in the row
+    if (j == 9)
+    {
+        return solveSudoku(mat, i + 1, 0);
+    }
+
+    ///Blue Cell - Skip
+    if (mat[i][j] != 0)
+    {
+        return solveSudoku(mat, i, j + 1);
+    }
+    ///White Cell
+    ///Try to place every possible no
+    for (int no = 1; no <= 9; no++)
+    {
+        if (isPossible(mat, i, j, no))
+        {
+            ///Place the no - assuming solution aa jayega
+            mat[i][j] = no;
+            bool aageKiSolveHui = solveSudoku(mat, i, j + 1);
+            if (aageKiSolveHui)
+            {
+                return true;
+            }
+            ///Nahin solve hui
+            ///loop will place the next no.
+        }
+    }
+    ///Sare no try kr liey, kisi se bhi solve nahi hui
+    mat[i][j] = 0;
+    return false;
+}
+
+int main()
+{
+
+    int mat[9][9] =
+        {{5, 3, 0, 0, 7, 0, 0, 0, 0},
+         {6, 0, 0, 1, 9, 5, 0, 0, 0},
+         {0, 9, 8, 0, 0, 0, 0, 6, 0},
+         {8, 0, 0, 0, 6, 0, 0, 0, 3},
+         {4, 0, 0, 8, 0, 3, 0, 0, 1},
+         {7, 0, 0, 0, 2, 0, 0, 0, 6},
+         {0, 6, 0, 0, 0, 0, 2, 8, 0},
+         {0, 0, 0, 4, 1, 9, 0, 0, 5},
+         {0, 0, 0, 0, 8, 0, 0, 7, 9}};
+
+    printMat(mat);
+    cout << "Solution " << endl;
+    solveSudoku(mat, 0, 0);
+
+    return 0;
+}