**π‘ Problem Formulation:** Imagine you’re running a lemonade stand where each lemonade costs $5. Customers pay with either $5, $10, or $20 bills. You must provide change with the least number of bills. The challenge is to write a Python function that determines if you can provide all customers with correct change. For example, if the input is a list of bills like `[5, 5, 5, 10, 20]`

, the output should be `True`

, as you can provide change for all customers.

## Method 1: Iterative Count Tracking

This method involves iterating through the list of bills and tracking the count of $5 and $10 bills to determine if change can be provided for future customers. It ensures that the larger bills are given as change only if sufficient smaller bills are not available.

Here’s an example:

def lemonadeChange(bills): fives = tens = 0 for bill in bills: if bill == 5: fives += 1 elif bill == 10: if fives == 0: return False fives -= 1 tens += 1 else: if tens > 0 and fives > 0: tens -= 1 fives -= 1 elif fives >= 3: fives -= 3 else: return False return True print(lemonadeChange([5, 5, 5, 10, 20]))

Output:

True

This snippet defines the function `lemonadeChange`

, which takes a list of integers representing the bills provided by customers. It returns `True`

if change can be provided for all, otherwise `False`

. The function uses two counters, `fives`

and `tens`

, to keep track of available change, ensuring that a $10 bill is used only if a $5 bill is not available.

## Method 2: Greedy Algorithm with Early Exit

The Greedy Algorithm approach makes the optimal local choice at each stage with the hope of finding the global optimum. In the case of lemonade change, this method greedily uses the highest bill possible for giving change and exits early if change cannot be provided.

Here’s an example:

def lemonadeChangeGreedy(bills): five, ten = 0, 0 for bill in bills: if bill == 5: five += 1 elif bill == 10: if not five: return False five, ten = five - 1, ten + 1 else: if ten and five: ten, five = ten - 1, five - 1 elif five >= 3: five -= 3 else: return False return True print(lemonadeChangeGreedy([5, 10, 5, 10, 20]))

Output:

True

The function `lemonadeChangeGreedy`

follows a greedy algorithm approach, attempting to use larger bills before smaller ones when making change. Similar to method 1, we keep track of $5 and $10 bills using variables `five`

and `ten`

. The function is efficient since it makes an early exit when change can’t be provided, avoiding unnecessary computation.

## Method 3: Dictionary-Based Counting

This strategy uses a dictionary to keep track of the bill counts. Change is given out by checking the dictionary and updating the bill counts accordingly. This method provides a clear structure for maintaining the state of our cash register.

Here’s an example:

def lemonadeChangeDict(bills): register = {'5': 0, '10': 0} for bill in bills: if bill == 5: register['5'] += 1 elif bill == 10: if register['5'] == 0: return False register['5'] -= 1 register['10'] += 1 else: if register['10'] > 0 and register['5'] > 0: register['10'] -= 1 register['5'] -= 1 elif register['5'] >= 3: register['5'] -= 3 else: return False return True print(lemonadeChangeDict([5, 5, 10, 10, 20]))

Output:

True

The `lemonadeChangeDict`

function utilizes a Python dictionary to keep track of the count of $5 and $10 bills. By updating the dictionary values, we are effectively mimicking a cash register which makes it simple to understand the logic for providing change or determining if it is possible at all.

## Method 4: Using Default Dictionary for Cleaner Code

This version refines Method 3 by using Python’s `collections.defaultdict`

to automatically handle missing keys. This method provides cleaner and more concise code by abstracting the initialization of bill counts.

Here’s an example:

from collections import defaultdict def lemonadeChangeDefaultDict(bills): register = defaultdict(int) for bill in bills: if bill == 5: register[5] += 1 elif bill == 10: if register[5] == 0: return False register[5] -= 1 register[10] += 1 else: if register[10] > 0 and register[5] > 0: register[10] -= 1 register[5] -= 1 elif register[5] >= 3: register[5] -= 3 else: return False return True print(lemonadeChangeDefaultDict([5, 5, 10, 5, 20]))

Output:

True

Here, `lemonadeChangeDefaultDict`

employs a `defaultdict`

to simplify the bill counting process. Upon trying to access a nonexistent key, `defaultdict`

automatically creates the key with a default value of zero. This results in cleaner code by eliminating the need to check if a key exists before updating the count.

## Bonus One-Liner Method 5: Inline Dictionary Update

While less readable, this approach achieves the same result as Method 4 but with a one-liner using Python’s tuple unpacking and inline dictionary updating within a list comprehension, mainly for fun and as a code challenge.

Here’s an example:

def lemonadeChangeOneLiner(bills): register = defaultdict(int) return all([(register[bill] += 1) or ( bill == 10 and (register[5] -= 1)) or (bill == 20 and ( (register[10] -= 1, register[5] -= 1) if register[10] and register[5] else (register[5] -= 3))) for bill in bills if bill != 5 or not (register[5] < 0 or register[10] < 0)]) print(lemonadeChangeOneLiner([5, 5, 10, 10, 20]))

Output:

True

This curious one-liner, `lemonadeChangeOneLiner`

, attempts to condense the logic into a single, albeit complex, list comprehension. It achieves the same result as previous methods but sacrifices readability for brevity. This method should be used with caution as it may be difficult for others to understand.

## Summary/Discussion

**Method 1: Iterative Count Tracking.**Straightforward and efficient. Easy to understand. Its simplicity may lead to less flexibility in more complicated scenarios.**Method 2: Greedy Algorithm with Early Exit.**Optimal and efficient. Makes early decisions to exit, saving time. Can be less intuitive due to greedy nature.**Method 3: Dictionary-Based Counting.**Offers clear state management of the cash register. Slightly more complex than simple counters. More readable than utilizing plain counters.**Method 4: Using Default Dictionary for Cleaner Code.**Cleanest code among the dictionary methods. Abstracts away initialization. Relies on importing`defaultdict`

which may not be immediately clear to beginners.**Method 5: Inline Dictionary Update One-Liner.**A fun exercise in Python’s capabilities. Highly compact. Not recommended for production due to poor readability and maintainability.