Queens: 3 solutions

src/complexity.md

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+<your_inline_code>
+
+Для первого, переборного решения:
+1. Цикл из функции is_valid_place "for first_place in range(n):" имеет сложность $O(N)$
+2. В функции queen_placement "permutations" занимает O(N!)
+3. В добавок далее строится массив queens со сложностью O(N)
+
+    Итого: $O(N \cdot N! \cdot N)$ ~ $O(N^2 \cdot N!)$
+
+Для второго, рекурсивного решения:
+1. В функции trees_from_rows вызывется цикл перебора всех колонок N раз => $O(N)$
+2. Рекурсивный вызов со сменой строки занимает $O(N - 1)$ (первую строку уже посчитали)
+
+    Итого: $O(N \cdot (N - 1))$
+
+Для третьего, чуть более оптимального решения со словарем:
+    I. Если N <= 15, то сложность программы - $O(c)$
+    II. Если N >= 15, то сложность как и у второй программы - $O(N \cdot (N - 1))$

src/dictionary_queens.py

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+variations = []
+
+
+def queens_placement(side):
+    def trees_from_rows(row, columns, main_diagonal, collateral_diagonal):
+        if row == side:
+            return 1
+
+        count = 0
+
+        for column in range(side):
+            main = row - column
+            collateral = row + column
+
+            if (
+                column not in columns
+                and (main) not in main_diagonal
+                and (collateral) not in collateral_diagonal
+            ):
+                columns.add(column)
+                main_diagonal.add(main)
+                collateral_diagonal.add(collateral)
+
+                count += trees_from_rows(
+                    row + 1, columns, main_diagonal, collateral_diagonal
+                )
+
+                columns.remove(column)
+                main_diagonal.remove(main)
+                collateral_diagonal.remove(collateral)
+
+        return count
+
+    return trees_from_rows(0, set(), set(), set())
+
+
+for i in range(15):
+    variations.append(queens_placement(i))
+    print(variations)

src/queens_on_the_table_1.py

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+import itertools
+
+user_side = int(input("Write the lenght of the side of the field: "))
+
+
+def is_valid_place(positions):
+    for first_place in range(user_side):
+        for second_place in range(first_place + 1, user_side):
+            row1, column1 = positions[first_place]
+            row2, column2 = positions[second_place]
+            if abs(row1 - row2) == abs(column1 - column2):
+                return False
+    return True
+
+
+def queen_placement(side):
+    count = 0
+    for rows in itertools.permutations(range(side)):
+        queens = [(row, column) for row, column in enumerate(rows)]
+        if is_valid_place(queens):
+            count += 1
+    return count
+
+
+print("Count of right placing: ", queen_placement(user_side))

src/queens_on_the_table_2.py

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+def queens_placement(side):
+    columns = set()
+    main_diagonal = set()
+    collateral_diagonal = set()
+
+    def trees_from_rows(row):
+        if row == side:
+            return 1
+
+        count = 0
+
+        for column in range(side):
+            main = row - column
+            collateral = row + column
+
+            if (
+                column not in columns
+                and (main) not in main_diagonal
+                and (collateral) not in collateral_diagonal
+            ):
+                columns.add(column)
+                main_diagonal.add(main)
+                collateral_diagonal.add(collateral)
+
+                count += trees_from_rows(row + 1)
+
+                columns.remove(column)
+                main_diagonal.remove(main)
+                collateral_diagonal.remove(collateral)
+
+        return count
+
+    return trees_from_rows(0)
+
+
+user_side = int(input("Write the value of the side of the field: "))
+
+print("Count of right placing: ", queens_placement(user_side))

src/queens_on_the_table_3.py

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+dictionary = [
+    0,
+    1,
+    0,
+    0,
+    2,
+    10,
+    4,
+    40,
+    92,
+    352,
+    724,
+    2680,
+    14200,
+    73712,
+    365596,
+    2279184,
+]
+from queens_on_the_table_2 import queens_placement
+
+
+def queens_placement(side):
+    return trees_from_rows(0)
+
+
+user_side = int(input("Write the value of the side of the field: "))
+
+if user_side <= len(dictionary):
+    print("Count of right placing: ", dictionary[user_side])
+else:
+    user_answer = input(
+        "Your number is large, and the calculation may take a VERY long time. Are you willing to wait? Y/N"
+    )
+
+    if user_answer in "Yy":
+        queens_placement(user_side)
+    else:
+        print("Enter a smaller side value please")