nesting.py

"""
A string S consisting of N characters is called properly nested if:

S is empty;
S has the form "(U)" where U is a properly nested string;
S has the form "VW" where V and W are properly nested strings.
For example, string "(()(())())" is properly nested but string "())" isn't.

Write a function:

def solution(S)

that, given a string S consisting of N characters, returns 1 if string S is
properly nested and 0 otherwise.

For example, given S = "(()(())())", the function should return 1 and given
S = "())", the function should return 0, as explained above.

Assume that:

N is an integer within the range [0..1,000,000];
string S consists only of the characters "(" and/or ")".
Complexity:

expected worst-case time complexity is O(N);
expected worst-case space complexity is O(1) (not counting the storage required
for input arguments).
"""

def solution(S):
    num_open = 0

    for bracket in S:
        if bracket == '(':
            num_open += 1
        else:
            num_open -= 1

        if num_open < 0:
            return 0

    return 1 if num_open == 0 else 0