In the question i'm asked to compute the compression rate in LZ algorithm of a string of the form "abc"*k for 0<k<10
Its not clear to me what kind of answer is expected. There doesn't seem to be a closed expression for this value as a function of k.
The intermediate forms look like this:
k=1:
[a,b,c]
k=2:
[a,b,c,(3,3)]
k=3:
[a,b,c,(3,6)]
k=4:
[a,b,c,(3,6),(3,3)]
k=5:
[a,b,c,(3,6),(3,6)]
k=6:
[a,b,c,(3,6),(6,9)]
k=7:
[a,b,c,(3,6),(6,12)]
k=8:
[a,b,c,(3,6),(9,15)]
k=9:
[a,b,c,(3,6),(9,18)]
Was this what i was supposed to do and then calculate the compression rate for each one? (clearly a posteriori its not so difficult because it doesn' change a lot with k but is there a way to see for example the jump from k=3 to k=4 before calculating?)