Question

In: Computer Science

Solve the following recurrence relations: (find an asymptotic upper bound O(?) for each one) a. T(n)...

Solve the following recurrence relations: (find an asymptotic upper bound O(?) for each one)

a. T(n) = T(2n/3)+T(n/3) + n^2

b. T(n) = √nT(√n) + n

c. T(n) = T(n-1)+T(n/2) + n

The base case is that constant size problems can be solved in constant time (O(1)). You can use the induction, substitution or recursion tree method

Solutions

Expert Solution


Related Solutions

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n) =...
Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n) = 2T(n/3) + 2n. Use the substitution method to verify your answer
Use a recursive tree method to compute a tight asymptotic upper bound for recurrence function T(n)=...
Use a recursive tree method to compute a tight asymptotic upper bound for recurrence function T(n)= 2T(n/5)+3n . then use substitution method to verify your answer.
Use a recursion tree to determine a good asymptotic upper bound on the recurrence ?(?) =...
Use a recursion tree to determine a good asymptotic upper bound on the recurrence ?(?) = 3?(?/3) + ?. Use the substitution method to verify your answer.
Prove the upper and lower bound of T(n) = T(n/3) + T(2n/3) + O(n)
Prove the upper and lower bound of T(n) = T(n/3) + T(2n/3) + O(n)
6. Solve the following recurrence relations t(n) = t(n-1) + 3 for n>1 t(1) = 0...
6. Solve the following recurrence relations t(n) = t(n-1) + 3 for n>1 t(1) = 0 t(n) = t(n-1) + n   for n>1 t(1) = 1 t(n) = 3t(n/2) + n    for n>1, n is a power of 2 t(1) = ½ t(n) = 6t(n-1) – 9t(n-2)   for n>1 t(0) = 0 t(1) = 1
1. Using domain and range transformations, solve the following recurrence relations: a) T(1) = 1, T(n)...
1. Using domain and range transformations, solve the following recurrence relations: a) T(1) = 1, T(n) = 2T(n/2) + 6n - 1 b) T(1) = 1, T(n) = 3T(n/2) + n^2 - n
Solve the following recurrence relations. a. x(n) = x(n − 1) + 3 for n >...
Solve the following recurrence relations. a. x(n) = x(n − 1) + 3 for n > 1, x(1) = 0 b. x(n) = 5x(n − 1) for n > 1, x(1) = 6 c. x(n) = x(n/5) + 1 for n > 1, x(1) = 1 (solve for n = 5k )
Give asymptotic upper and lower bounds for T(n). Assume that T(n) is constant for n <=...
Give asymptotic upper and lower bounds for T(n). Assume that T(n) is constant for n <= 2. Make your bounds as tight as possible, and justify your answers. T(n) = T(n-2) + n^2
Give upper and lower bounds for T(n) in the following recurrence: T(n) = 3T(n/4) + n
Give upper and lower bounds for T(n) in the following recurrence: T(n) = 3T(n/4) + n
- Solve the following recurrence relation : T(n) = T(αn) + T((1 − α)n) + n
- Solve the following recurrence relation : T(n) = T(αn) + T((1 − α)n) + n
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT