What is the Change Making problem and how can it be solved using a greedy algorithm?

What is the Change Making problem and how can it be solved using a greedy algorithm?

The Change Making problem is a problem in which we need to find the minimum number of coins or bills needed to make a given amount of money. It can be solved using a greedy algorithm.

The greedy algorithm for the Change Making problem works by selecting the largest denomination coin or bill that is less than or equal to the remaining amount, and subtracting it from the total amount. This process is repeated until the remaining amount becomes zero.

Here is the step-by-step process to solve the Change Making problem using a greedy algorithm:

1. Sort the available denominations of coins or bills in descending order.
2. Initialize a variable to keep track of the total number of coins or bills used.
3. Start with the largest denomination and check if it is less than or equal to the remaining amount.
4. If it is, subtract the denomination from the remaining amount and increment the count of coins or bills used.
5. Repeat steps 3 and 4 until the remaining amount becomes zero.
6. If the remaining amount is not zero, move to the next smaller denomination and repeat steps 3 to 5.
7. Continue this process until the remaining amount becomes zero or all denominations have been checked.

At the end of the algorithm, the total number of coins or bills used will represent the minimum number of coins or bills needed to make the given amount of money.