8.6. Function Recurrence

• Aby zrozumieć rekurencję – musisz najpierw zrozumieć rekursję.

• Aby zrozumieć rekursję - musisz najpierw zrozumieć rekurencję.

8.6.1. Rationale

• Also known as recursion

• Python isn't a functional language

• CPython implementation doesn't optimize tail recursion

• Tail recursion is not a particularly efficient technique in Python

• Unbridled recursion causes stack overflows!

• Rewriting the algorithm iteratively, is generally a better idea

8.6.2. Example

def factorial(n: int) -> int:
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)

factorial(5)                                    # = 120
    return 5 * factorial(4)                     # 5 * 24 = 120
        return 4 * factorial(3)                 # 4 * 6 = 24
            return 3 * factorial(2)             # 3 * 2 = 6
                return 2 * factorial(1)         # 2 * 1 = 2
                    return 1 * factorial(0)     # 1 * 1 = 1
                        return 1                # 1

8.6.3. Recursion Depth Limit

• Default recursion depth limit is 1000

• Warning: Anaconda sets default recursion depth limit to 2000

import sys

sys.setrecursionlimit(3000)

8.6.4. Assignments

8.6.4.1. Balanced Brackets

• Complexity level: medium

• Lines of code to write: 10 lines

• Estimated time of completion: 15 min

• Solution: solution/function_recurrence_brackets.py

English

1. Create function which checks if brackets are balanced

2. Brackets are balanced, when each opening bracket has closing pair

3. Use recursion

4. Types of brackets:

   • round: ( i )

   • square: [ i ]

   • curly { i }

   • angle < i >

Polish

1. Stwórz funkcję, która sprawdzi czy nawiasy są zbalansowane

2. Nawiasy są zbalansowane, gdy każdy otwierany nawias ma zamykającą parę

3. Użyj rekurencji

4. Typy nawiasów:

   • okrągłe: ( i )

   • kwadratowe: [ i ]

   • klamrowe { i }

   • trójkątne < i >

def is_bracket_balanced(text: str) -> bool:
    """
    >>> is_bracket_balanced('{}')
    True
    >>> is_bracket_balanced('()')
    True
    >>> is_bracket_balanced('[]')
    True
    >>> is_bracket_balanced('<>')
    True
    >>> is_bracket_balanced('')
    True
    >>> is_bracket_balanced('(')
    False
    >>> is_bracket_balanced('}')
    False
    >>> is_bracket_balanced('(]')
    False
    >>> is_bracket_balanced('([)')
    False
    >>> is_bracket_balanced('[()')
    False
    >>> is_bracket_balanced('{()[]}')
    True
    >>> is_bracket_balanced('() [] () ([]()[])')
    True
    >>> is_bracket_balanced("( (] ([)]")
    False
    """
    pass