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)

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We have put all the question in the above images.

Some formula are use like sum of A.P.(arithmetic progression) in question d.

venereology answered 2 years ago

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 recurrence equation. T(n) = 3T (n/3) + Cn T(1) = C

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 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 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 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 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

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

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