Question

In: Advanced Math

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

Solutions

Expert Solution


Related Solutions

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
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 )
Using the backward substitution method, solve the following recurrence relations: a.T(n)= T(n−1)+3forn>1 ,T(1)=0 b.T(n)=3T(n−1) forn>1 ,T(1)=7...
Using the backward substitution method, solve the following recurrence relations: a.T(n)= T(n−1)+3forn>1 ,T(1)=0 b.T(n)=3T(n−1) forn>1 ,T(1)=7 c.T(n)= T(n−1)+n for n>0 ,T(0)=0 d.T(n)= T(n/2)+n for n>1 ,T(1)=1(solve for n=2k) e.T(n)= T(n/3)+1forn>1 ,T(1)=1(solve for n=3k)
- 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
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
Solve the recurrence equations by Substitution a) T(n) = 4T (n/2) + n, T (1) =...
Solve the recurrence equations by Substitution a) T(n) = 4T (n/2) + n, T (1) = 1 b) T(n) = 4T (n/2) + n2 , T (1) = 1 c) T(n) = 4T (n/2) + n3 , T (1) = 1
Solve the recurrence equation. T(n) = 3T (n/3) + Cn T(1) = C
Solve the recurrence equation. T(n) = 3T (n/3) + Cn T(1) = C
Solve the given non-homogeneous recurrence relations: an = an-1 + 6an-2 + f(n) a) an =...
Solve the given non-homogeneous recurrence relations: an = an-1 + 6an-2 + f(n) a) an = an-1 + 6an-2 - 2n+1 with a0 = -4, a1= 5 b) an = an-1 + 6an-2 + 5 x 3n with a0 = 2, a1 = 5 c) an = an-1 + 6an-2 - 36n with a0 = 10, a1= 40
Use recursion tree to solve the recurrence: T(n) = T(n/15) + T(n/10) + 2T(n/6) + n^(1/2)
Use recursion tree to solve the recurrence: T(n) = T(n/15) + T(n/10) + 2T(n/6) + n^(1/2)
What is the recurrence relation for T(n) = (n-1)T(n-1) + n?
What is the recurrence relation for T(n) = (n-1)T(n-1) + n?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT