I want to know how to approach this question in what direction to think so that i can solve it on my own.
Thank you.

Problem is tagged with dynamic programming

First,  think about each possible configuration of the current state when you add next song

Second,  think about techniques of DP -  compression

well let x[n] be the number of sequences that finish with 1 and y[n] be the number of sequences that finish with 2 of the length n, x[0] = y[0] = 1, x[1] = y[1] = 1, the recurent formula for this is x[n] = y[n - 1] + y[n - 2] + y[n - 3] + .. + y[n - b] and y[n] = x[n - 1] + x[n - 2] + x[n - 3] + .. + x[n - a], basicly for a sequance of n + 1 you must think of the number of ways that the sequance will finish with 1 or with 2

Edited by author 11.08.2017 04:09

I am sorry but I still didn't understand, why x is dependent on y. Won't Y[] include cases having consecutive A times 1 and moreover won't Y[] Include duplicate cases ? I am sorry but I am new to this so that's why I am asking.

well let's approuch one case where your array is finishing with 1 but no more than "a" times in a row, because the 1 array is dependent from array of 2 and array 2 is alwais finishing with 2 it will look like this 12.... that is y[n] = x[n - 1], than 112... that  is y[n] = x[n - 1] + x[n - 2], than 111...112.... which is y[n] = x[n] + x[n - 1] + x[n - 2] + ... + x[n - a] and is the same in the second case