N K Ladder using matrix exponentiation

#1

The video says if we use the recurrence relation
f(i)=2f( i-1)+f( i-(k-1) )
then the time complexity for exponentiation method would be O(logN), but should it still not be O(K^3 logN) only since f(i-k-1) is the last term on which ith term is dependent?

#2

firstly correct your recurrences.
second if you use matrix exponentiation then your solution would show time complexity of (k^3logN)

#3

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#4

So even if we use the recurrence relation f(i)=2f( i-1)+f( i-(k+1) ) , the time complexity remains O(k^3logN) only, right?

#5

yess!!!