Suppose you are given an amount 'amount' and a set of coin denominations. The goal is to find the minimum number of coins needed to make up that amount.

Let's say we have the following denominations: $1,5,10,25($denominations of coins $-$$$1,$$$5,$ $$10,$$$25)$ and we want to make a change for $$30.$

The minimum number of coins required to make a change for $$30$ using denominations $1,5,10,25$ is $2$ coins.

The maximum number of coins required to make a change for $$30$ using denominations $1,5,10,25$ is $30$ coins.

You need to design an algorithm and find out the running time of the designed algorithm. The algorithm should include algorithm name, input, output and steps for solving the problem.

Explain your answer clearly in a professional style.