Sword finger offer 14- I. cut rope

I'll give you a length of n The rope of , Please cut the rope to the whole length m paragraph （m、n Are integers. ,n>1 also m>1）, The length of each rope is recorded as k[0],k[1]...k[m-1] . Excuse me, k[0]*k[1]*...*k[m-1] What's the maximum possible product ？ for example , When the length of the rope is 8 when , We cut it into lengths of 2、3、3 Three paragraphs of , The maximum product we get here is 18.

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Ideas ： According to mathematical derivation 3 Is the factor that can achieve the maximum product

n by 1 and 2 The result is 1 1|1*1

n by 3 The result is 2 |1*2

Using a loop On the condition that n》4 So the only thing left 3 2 1  The result is that each cycle is multiplied by 3 n Subtract... From each cycle 3