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1. What does this program print? ``

python
tried = 0


def is_balanced(s):
    depth = 0
    for c in s:
        depth += 1 if c == "(" else -1
        if depth < 0:
            return False
    return depth == 0


def all_strings(length, current, result):
    global tried
    if len(current) == length:
        tried += 1
        text = "".join(current)
        if is_balanced(text):
            result.append(text)
        return
    current.append("(")
    all_strings(length, current, result)
    current.pop()
    current.append(")")
    all_strings(length, current, result)
    current.pop()


result = []
all_strings(8, [], result)
print(f"tried={tried} valid={len(result)}")

``

tried=64 valid=5tried=16 valid=14tried=256 valid=42tried=256 valid=14

2. What does this program print? ``

python
def build(n, open_count, close_count, current, result):
    if len(current) == 2 * n:
        result.append("".join(current))
        return
    if open_count < n:
        current.append("(")
        build(n, open_count + 1, close_count, current, result)
        current.pop()
    if close_count < open_count:
        current.append(")")
        build(n, open_count, close_count + 1, current, result)
        current.pop()


zero = []
build(0, 0, 0, [], zero)
print(f"n=0 count={len(zero)} list={zero}")
two = []
build(2, 0, 0, [], two)
print(f"n=2 second={two[1]} first={two[0]}")

``

n=0 count=0 list=[] n=2 second=()() first=(())n=0 count=1 list=[] n=2 second=(()) first=()()n=0 count=1 list=[''] n=2 second=()() first=(())n=0 count=1 list=[''] n=2 second=(()) first=()()

3. The line that checks open_count was changed, and the code below is meant to list the valid strings for n = 1. What does the last line print? ``

python
def build(n, open_count, close_count, current, result):
    if len(current) == 2 * n:
        result.append("".join(current))
        return
    if open_count <= n:
        current.append("(")
        build(n, open_count + 1, close_count, current, result)
        current.pop()
    if close_count < open_count:
        current.append(")")
        build(n, open_count, close_count + 1, current, result)
        current.pop()


result = []
build(1, 0, 0, [], result)
print(result)

``

['()']['((', '()']['()', '()']['((', '))']

4. The is_balanced function below has its early return removed. What does the program print? ``

python
def is_balanced(s):
    depth = 0
    for c in s:
        depth += 1 if c == "(" else -1
    return depth == 0


print(is_balanced(")("))
print(is_balanced("(()())"))
print(is_balanced("())("))

``

False, True, FalseTrue, True, TrueFalse, True, TrueTrue, False, True

5. For n pairs of brackets, which check belongs in the base case that saves a finished string?

len(current) == nopen_count == close_countlen(current) == 2 * nlen(current) == n * n

Parentheses