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Challenge: Number of Ways to Represent N Dollars

Explore how to count the number of distinct ways to represent a target amount using provided currency bills. Learn to avoid overcounting by developing a recursive solution and then optimize it with dynamic programming approaches like top-down or bottom-up methods.

Problem statement

Given a list of currency bills, you are required to count the number of ways in which you can represent a certain amount. For example, if you have only two kinds of bills, $10 and $20, and you want to represent $30, there are only two ways:

  • 3 bills of
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