Ok, lets calc value dp[i] — maximum number of peaces we can cut rope with length i.

How to calc it?

Let's look to last peace. It can have length a, b or c. If we know length of last peace we can reduse problem to probl with smaller i.

For example, it length of last peace is a answer equal to dp[i-a]+1.

But we can choose any of three types of peaces so we need to take best.

And we get a formula:

dp[i]=max(dp[i-a],dp[i-b],dp[i-c])+1