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yrelhan4
 one year ago
A student can do the things bellow:
a. Do his homework in 2 days
b. Write a poem in 2 days
c. Go on a trip for 2 days
d. Study for exams for 1 day
e. Play pc games for 1 day
A schedule of n days can be completed by any combination of the activities above. For example 3 possible schedules for 7 days are:
homework, poem, homework, play
poem, study, play, homework, study
trip, trip, trip, study
Find a recursive function T(n) that represents the number of all possible schedules for n days.
I just need a start. Any ideas will be greatly appreciated.
yrelhan4
 one year ago
A student can do the things bellow: a. Do his homework in 2 days b. Write a poem in 2 days c. Go on a trip for 2 days d. Study for exams for 1 day e. Play pc games for 1 day A schedule of n days can be completed by any combination of the activities above. For example 3 possible schedules for 7 days are: homework, poem, homework, play poem, study, play, homework, study trip, trip, trip, study Find a recursive function T(n) that represents the number of all possible schedules for n days. I just need a start. Any ideas will be greatly appreciated.

This Question is Closed

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.12Basically you want to find the number of nonnegative integer solutions to below equation \[n=2a+2b+2c+d+e\]

yrelhan4
 one year ago
Best ResponseYou've already chosen the best response.1So, T(n)=3T(n2)+2T(n1)?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.12may i know how you got that

yrelhan4
 one year ago
Best ResponseYou've already chosen the best response.1Well to be honest, i don't exactly know how. I have been searching for examples over the net and this is how they write a recursive function. For example, i read this question where there are n steps, and a person can either take 1 step at a time, or 2 steps at a time. We had to tell the number of ways to take n steps. and as you said, the equation that time would be a+2b=n.. and the recursive fucntion they wrote was t(n)=t(n1)+t(n2).. so yeah I don't exactly know how. I have been taking this for granted. I'd be very happy if could tell me more about it.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.12check this http://math.stackexchange.com/questions/614356/difficultrecursionproblem

yrelhan4
 one year ago
Best ResponseYou've already chosen the best response.1I checked that out before posting it here. Don't really understand it completely.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.12suppose \(n=1\), how many ways can you schedule \(1\) day ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.12you can either `study` or `play`, so only \(2\) ways, yes ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.12that means \[T(1)=2\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.12next let \(n=2\) and work the number of ways \(2\) days can be scheduled

yrelhan4
 one year ago
Best ResponseYou've already chosen the best response.1I get it now. Thank you very much... also, suppose i don't want the duplicates.. like, i treat "poem, study, play, homework, study" and "study, poem, play, homework, study" the same... how do I draft an algo for that? @ganeshie8

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no idea how you can even solve this its more of an opinion than a math question.
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