Return Cash-Register Change in Named Denominations

Problem Statement

Design a function that computes the exact change to return to a customer given the purchase price and the cash tendered. Both values are provided as decimal strings.

To avoid floating-point precision issues, all monetary calculations must be performed using integer arithmetic (e.g., converting dollars and cents into total cents).

Use the following standard currency denominations:

Rules

1. If cash_given < price, return "ERROR".
2. If cash_given == price, return "ZERO".
3. Otherwise, determine the minimum number of bills and coins needed using a greedy approach (taking the largest possible denomination first until the remaining balance is zero). Return a comma-separated string of the names of all dispensed items sorted in alphabetical order. If a denomination is used multiple times, it must appear in the output as many times as it was dispensed.

Function Signature

def calculate_change(price: str, cash_given: str) -> str:
    pass

Input and Output

• Input: Two strings, price and cash_given, each formatted as a non-negative decimal with up to two decimal places (e.g., "15.94", "20", "0.5").
• Output: A single string containing "ERROR", "ZERO", or a comma-separated, alphabetically sorted list of denomination names.

Constraints

• 0.00 <= price, cash_given <= 10000.00
• Inputs contain only digits and at most one decimal point.

Examples

Example 1

calculate_change("15.94", "16.00")
# Output: "NICKEL,PENNY"

Explanation: Change is 6 cents. Greedy selection yields 1 NICKEL (5¢) and 1 PENNY (1¢). Sorted alphabetically: "NICKEL,PENNY".

Example 2

calculate_change("1.02", "1.24")
# Output: "DIME,DIME,PENNY,PENNY"

Explanation: Change is 22 cents. Greedy selection yields 2 DIME (10¢ each) and 2 PENNY (1¢ each). Sorted alphabetically: "DIME,DIME,PENNY,PENNY".

Example 3

calculate_change("50.00", "40.00")
# Output: "ERROR"

Explanation: The customer provided less money than the purchase price.