## Editorial for COCI '06 Contest 4 #4 Zbrka

Remember to use this editorial

**only**when stuck, and**not to copy-paste code from it**. Please be respectful to the problem author and editorialist.**Submitting an official solution before solving the problem yourself is a bannable offence.**This problem is solved using dynamic programming. Let be the number of sequences of length with confusion .

The number of such sequences that start with the number is because the does not affect the confusion of the rest of the sequence and it makes no difference if we use numbers or .

If is the second number, then because whichever element is first, it will form a confused pair with the . It's easy to see that the complete relation is:

The time complexity of a direct implementation of this formula (using dynamic programming) would be , which is too slow.

We need to note that , which leads to a solution. It is also possible to cut down on the memory used by keeping only two rows of the matrix used for calculations at any time.

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