Use the substitution method to prove the solutions for the following recurrences: Recurrence Solution 1 T(n)...

Use the substitution method to prove the solutions for the following recurrences:

	Recurrence	Solution
1	T(n) = T(n-1) + n	O(n²)
2	T(n) = T(n/2) + 1	O(lgn)
3	T(n) = T(n/2) + n	ϴ(nlgn)
4	T(n) = 3T(n/2) + n	O(n^lg(3)).
5	T(n) = 2T(n/2) + n²	O(n²)
6	T(n) = 4T(n/2 + 2) + n	O(n²)
7	T(n) = 2T(n – 1) + 1	O(2ⁿ)
8	T(n) = T(n – 1) + T(n/2) + n	O(2ⁿ)
9	T(n) = 4T(n/2) + cn.	ϴ(n²)

Expert Solution

venereology answered 6 months ago

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

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)

Use the recursion tree method to determine the asymptoticupper bound of T(n).T(n) satisfies the recurrence T(n)=2T(n-1)+...

Use the recursion tree method to determine the asymptoticupper bound of T(n).T(n) satisfies the recurrence T(n)=2T(n-1)+ c, where c is a positive constant, andT(0)=0.

- Solve the following recurrence relation : T(n) = T(αn) + T((1 − α)n) + n

What is the recurrence relation for T(n) = (n-1)T(n-1) + 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

Use recursion tree to solve the recurrence: T(n) = T(n/15) + T(n/10) + 2T(n/6) + n^(1/2)

Solve the following recurrences by assuming T(n) is constant for sufficiently small values of n and...

Solve the following recurrences by assuming T(n) is constant for sufficiently small values of n and find time complexity ?(?) = ?(? − 1) + ? (?/2) + ? ?(?) = 4? (?/3) + ???(?) ?(?)=?(?−2)+ 1/ lg(?)

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.

Characterize each of the following recurrence equations using the master method (assuming that T(n) = c...

Characterize each of the following recurrence equations using the master method (assuming that T(n) = c for n ≤ d, for constants c > 0 and d ≥ 1). a. T(n) = 2T(n/2) + √n b. T(n) = 8T(n/2) + n2 c. T(n) = 16T(n/2) + n4 d. T(n) = 7T(n/3) + n e. T(n) = 9T(n/3) + n3.1

Question