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The solution to this problem is a good example of an efficient and tight Dynamic Programming algorithm. For those of you who are struggling with it, here's a tip. The number of ways you can make change for n using only the first m coins can be calculated using:

(1) the number of ways you can make change for n using only the first m-1 coins.

(2) the number of ways you can make change for n-C[m] using the first m coins (where C is the array of coins).

This data allows you to build the recurrence relation.

## The Coin Change Problem

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The solution to this problem is a good example of an efficient and tight Dynamic Programming algorithm. For those of you who are struggling with it, here's a tip. The number of ways you can make change for

nusing only the firstmcoins can be calculated using:(1) the number of ways you can make change for

nusing only the firstm-1coins.(2) the number of ways you can make change for

n-C[m]using the firstmcoins (whereCis the array of coins).This data allows you to build the recurrence relation.