TheAlgorithms · EJG2000 · Oct 8, 2020 · Oct 8, 2020 · Oct 8, 2020 · Oct 8, 2020
diff --git a/backtracking/extendedsudokusolver.py b/backtracking/extendedsudokusolver.py
@@ -0,0 +1,201 @@
+"""
+Given a partially or empty grid, attempts to solve (n^2)*(n^2) sudoku,
+where n is the box size
+Eg:
+sudoku 4*4              sudoku 9*9
+box_size = n = 2        box_size = n = 3
++-------+-------+       +----------+----------+----------+
+| 01 02 | 03 04 |       | 01 02 03 | 04 05 08 | 09 06 07 |
+| 03 04 | 01 02 |       | 04 05 08 | 06 07 09 | 01 02 03 |
++-------+-------+       | 09 06 07 | 01 02 03 | 08 04 05 |
+| 02 01 | 04 03 |       +----------+----------+----------+
+| 04 03 | 02 01 |       | 02 01 09 | 08 03 04 | 05 07 06 |
++-------+-------+       | 03 08 04 | 05 06 07 | 02 01 09 |
+                        | 05 07 06 | 09 01 02 | 03 08 04 |
+                        +----------+----------+----------+
+                        | 08 09 01 | 03 04 06 | 07 05 02 |
+                        | 06 03 02 | 07 08 05 | 04 09 01 |
+                        | 07 04 05 | 02 09 01 | 06 03 08 |
+                        +----------+----------+----------+
+"""
+
+
+class Sudoku:
+    """
+    Class object for sudoku
+    element 0 represents an empty element
+    """
+
+    def __init__(self, box_size: int):
+        """
+        initialize grid and box
+        """
+        self.box_size = box_size
+        self.grid_size = box_size ** 2
+        self.grid = []
+        self.box = dict()
+        for r in range(self.grid_size):
+            self.grid.append([])
+            for c in range(self.grid_size):
+                self.grid[-1].append(0)
+                box_number = self.box_mapper(r, c)
+                if box_number not in self.box:
+                    self.box[box_number] = {0}
+
+    def load_grid(self, arr: list) -> None:
+        """
+        Load the values from arr into the grid
+        """
+        if len(arr) != self.grid_size:
+            raise ValueError("Input grid size do not match")
+
+        for r in range(self.grid_size):
+            if len(arr[r]) != self.grid_size:
+                raise ValueError("Input grid size do not match")
+
+            for c in range(self.grid_size):
+                self.add_element(arr[r][c], r, c)
+
+    def box_mapper(self, row: int, column: int) -> int:
+        """
+        Maps row,column into their respective boxes
+        """
+        return (row // self.box_size) * 10 + (column // self.box_size)
+
+    def possible_values(self, row: int, column: int) -> set:
+        """
+        Gets the possible values at row,column
+        """
+        box_number = self.box_mapper(row, column)
+
+        possible_elements = set(range(1, (self.grid_size) + 1))
+        row_elements = set(self.grid[row])
+        column_elements = set([self.grid[i][column] for i in range(self.grid_size)])
+        box_elements = self.box[box_number]
+
+        return possible_elements - box_elements.union(row_elements, column_elements)
+
+    def next_empty(self, row: int, column: int) -> tuple:
+        """
+        Returns the position of next empty element 0
+        if there exist a empty element
+            returns (True,row,column)
+        else
+            returns (False,-1,-1)
+        """
+        (r, c) = (row, column)
+        while r < self.grid_size:
+            while c < self.grid_size:
+                if self.grid[r][c] == 0:
+                    return (True, r, c)
+                c += 1
+            c = 0
+            r += 1
+        return (False, -1, -1)
+
+    def add_element(self, element: int, row: int, column: int) -> None:
+        """
+        Adds element to grid[row][column]
+        """
+        self.grid[row][column] = element
+        box_number = self.box_mapper(row, column)
+        self.box[box_number].add(element)
+
+    def remove_element(self, row: int, column: int) -> None:
+        """
+        Removes element at grid[row][column]
+        """
+        box_number = self.box_mapper(row, column)
+        element = self.grid[row][column]
+        self.box[box_number].remove(element)
+        self.grid[row][column] = 0
+        self.box[box_number].add(0)
+
+    def solver(self, row: int, column: int) -> bool:
+        """
+        solve the next empty element from row,column
+        if the grid is complete
+            return true
+        else
+            return false
+        """
+        (status, new_row, new_column) = self.next_empty(row, column)
+        if status is False:
+            return True
+
+        for element in self.possible_values(new_row, new_column):
+            self.add_element(element, new_row, new_column)
+            status = self.solver(new_row, new_column)
+            if status is True:
+                return True
+            self.remove_element(new_row, new_column)
+        return False
+
+    def solve(self) -> bool:
+        """
+        Invoke solver and return true if the grid is solved
+        else return False
+        """
+        return self.solver(0, 0)
+
+    def __str__(self):
+        string = ""
+        row_completer = ("+-" + "---" * self.box_size) * self.box_size + "+"
+        box_edge = [
+            x for x in range(self.grid_size) if x % self.box_size == self.box_size - 1
+        ]
+
+        string += row_completer + "\n"
+        for r in range(self.grid_size):
+            string += "| "
+            for c in range(self.grid_size):
+                string += "%02d " % (self.grid[r][c])
+                if c in box_edge:
+                    string += "| "
+            string += "\n"
+            if r in box_edge:
+                string += row_completer + "\n"
+
+        return string
+
+
+if __name__ == "__main__":
+
+    accept_from_user = False
+    if accept_from_user:
+        box_size = int(input("Enter the box size: "))
+        question_grid = []
+        i = 1
+        print("Use zero to represent empty value")
+        while i <= box_size ** 2:
+            row_values = list(map(int, input(f"Enter the row {i} : ")))
+            if len(row_values) != box_size ** 2:
+                print(f"Row length should be {box_size ** 2}")
+                continue
+            question_grid.append(row_values)
+            i += 1
+    else:
+        box_size = 3
+        # a sample question grid
+        question_grid = [
+            [1, 0, 0, 0, 0, 7, 0, 9, 0],
+            [0, 3, 0, 0, 2, 0, 0, 0, 8],
+            [0, 0, 9, 6, 0, 0, 5, 0, 0],
+            [0, 0, 5, 3, 0, 0, 9, 0, 0],
+            [0, 1, 0, 0, 8, 0, 0, 0, 2],
+            [6, 0, 0, 0, 0, 4, 0, 0, 0],
+            [3, 0, 0, 0, 0, 0, 0, 1, 0],
+            [0, 4, 0, 0, 0, 0, 0, 0, 7],
+            [0, 0, 7, 0, 0, 0, 3, 0, 0],
+        ]
+        question = Sudoku(box_size)
+        question.load_grid(question_grid)
+
+    print("The initial question is ", question)
+    print("\nSolving...", end="")
+
+    result = question.solve()
+    if result is True:
+        print("Success. The answer is: ", question)
+    else:
+        print("Failed. Could not find a possible solution")