Course: Data Structures and Aglorithms
whenever recurrence relation is of above form, then check whether
nlogab or f(n) is greater by atleast polynomial function . Whosoever is greater that will be answer.
Course: Data Structures and Aglorithms Question 2 a) Use the substitution method (CLRS section 4.3) to...
Give asymptotic upper and lower bounds for T(n). T(n) is constant for small n. Use either substitution, iteration, or the master method. 1) T(n) = T(n-5) + n 2) T(n) = 2T(n/4) + 16T(n/8) + T(n/8) + 19
(a) Use the recursion tree method to guess tight 5 asymptotic bounds for the recurrence T(n)-4T(n/2)+n. Use substitution method to prove it.
3. Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution and upper and/or lower bounds, when necessary. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as O(n*) or O(nk log2 n) whenever possible. If the algorithm is exponential just give exponential lower bounds c) T(n) T(n-4) cn, T(0) c' d) T(n) 3T(n/3) c, T() c' e) T(n) T(n-1)T(n-4)clog2n, T(0) c' 3. Determine the...
1. [12 marks] For each of the following recurrences, use the “master theorem” and give the solution using big-O notation. Explain your reasoning. If the “master theorem” does not apply to a recurrence, show your reasoning, but you need not give a solution. (a) T(n) = 3T(n/2) + n lg n; (b) T(n) = 9T(3/3) + (n? / 1g n); (c) T(n) = T([n/41) +T([n/4])+ Vn; (d) T(n) = 4T([n/7])+ n.
if n < 8 T(n) 11([n/2]) +T([n/4]) +T([n/8]) +n otherwise Use the substitution method, obtain a Big-Theta bound for T(n). [We expect a rigorous proof. You don't need to explain how you managed to guess the upper and lower bounds.
Problem 1 Use the master method to give tight asymptotic bounds for the following recurrences. a) T(n) = T(2n/3) +1 b) T(n) = 2T("/2) +n4 c) T(n) = T(71/10) +n d) T(n) = 57(n/2) + n2 e) T(n) = 7T(1/2) + 12 f) T(n) = 27(1/4) + Vn g) T(n) = T(n − 2) +n h) T(n) = 27T(n/3) + n° lgn
Please help with this algorithms design problems. Thank you. Use substitution method: 1. Show that the solution of T(n) = T(n-1) +n is O(n) Use master method to find tight asymptotic bounds: 2. T(n) = 2*T(n/4+n 3. T(n) = 2*T(n/4) + n2
Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3 Т(п) 2T (п — 2) + 5 2.2 Solve the following using Master Theorem. 3. recurrenсes T(п) log n n 4T .3 3.1 n 5T 2 n2 log n T(п) 3.2 Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3 Т(п) 2T (п — 2) + 5 2.2 Solve the following using Master Theorem. 3....
For each of the following problems write a recurrence relation describing the running time of each of the following algorithms and determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using substitution and carefully computing lower and upper bounds for the sums. Simplify and express your answer as Θ(n k ) or Θ(n k (log n)) wherever possible. If the algorithm takes exponential time, then just give exponential lower bounds. 5. func5 (A,n) /*...
Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n≤2. Make your bounds as tight as possible, and justify your answer. *Hint : You can use Master method to obtain Θ(.). (a) T(n) = 4T(n/4) + 5n (b) T(n) = 4T(n/5) + 5n (c) T(n) = 5T(n/4) + 4n (d) T(n) = 25T(n/5) + n^2 (e) T(n) = 4T(n/5) + lg n (f) T(n) = 4T(n/5) + lg^5 n...