5 100 90 80 98 40 30 21 80
23 We are obtaining three bamboos of lengths $100, 90, 80$ from five bamboos $98, 40, 30, 21, 80$. We already have a bamboo of length $80$, and we can obtain bamboos of lengths $100, 90$ by using the magics as follows at the total cost of $23$ MP, which is optimal. 1. Use Extension Magic twice on the bamboo of length $98$ to obtain a bamboo of length $100$. (MP consumed: $2$) 2. Use Composition Magic on the bamboos of lengths $40, 30$ to obtain a bamboo of length $70$. (MP consumed: $10$) 3. Use Shortening Magic once on the bamboo of length $21$ to obtain a bamboo of length $20$. (MP consumed: $1$) 4. Use Composition Magic on the bamboo of length $70$ obtained in step 2 and the bamboo of length $20$ obtained in step 3 to obtain a bamboo of length $90$. (MP consumed: $10$)
8 100 90 80 100 100 90 90 90 80 80 80
0 If we already have all bamboos of the desired lengths, the amount of MP needed is $0$. As seen here, we do not necessarily need to use all the bamboos.
8 1000 800 100 300 333 400 444 500 555 600 666
243
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