Consider the following recurrence relation: if n 0 H(n) 1 if n 1or n = 2 H(n 1) if n > 2 H(n 2) H(n - 3) _ (a) Compu...
Need answers for 1-5 Consider the following recurrence relation: H(n) = {0 if n lessthanorequalto 0 1 if n = 1 or n = 2 H(n - 1) + H (n - 2)-H(n - 3) if n > 2. (a) Compute H(n) for n = 1, 2, ...., 10. (b) Using the pattern from part (a), guess what H(100) is. 2. Consider the recurrence relation defined in Example 3.3 (FROM TEXT BOOK, also discussed in class and shown in slides)...
3. Consider the recurrence relation an = 80n/2 + n², where n=2", for some integer k. a) Give a big-O estimate for an. b) What is the recurrence relation for the sequence bk obtained from an by doing the substitution n= n=2k ?
6. Consider the recurrence relation T(n) = 2T(n-1) + 5 for integers n 1 and T(O) = 0. Find a closed-form solution Using induction, prove your solution correct for all integers n 20.
Write a recurrence relation describing the worst case running time of each of the following algorithms, and determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution by using substitution or a recursion tree. You may NOT use the Master Theorem. Simplify your answers, expressing them in a form such as O(nk) or (nklog n) whenever possible. If the algorithm takes exponential time, then just give an exponential lower bound using the 2 notation. function...
Write a recurrence relation describing the worst-case running time of each of the following algorithms and determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution by using substitution or a recursion tree. You may NOT use the Master Theorem. 上午1:46 3月21日周四 令52%. " 5. endfor 6. return (r); function func4(A, n) *Aarray of n integers */ 1. if n s 20 then return (A[n]); 4. while (i < n/2) do 7. endwhile 8. x...
Solve the recurrence relation S(1) = 0, S(n) = 2S(n/2) + n using the formula c^(n-1) * S(1) + sum(c^(n-i) * g(i)) from i=2 to n.
1. Let f(n)2 = f(n +1) be a recurrence relation. Given f(0) = 2, solve. 2. Let be a recurrence relation. Given f(0) = 1, f(1) = 1 and n 1, solve.
a) Find a recurrence relation for an - number of n digit quarternary sequences (using digts from (0, 1,2, 3]) with at least one 1 and the first 1 occurring before the first O.( It is possible that there is no 0 in the sequence). Hint: Consider the cases: the sequence starts with a 1 or with a 2 or with a 3. Note that it cannot start with a O. Explain all steps a) Find a recurrence relation for...
8. Solve the recurrence relation together with the initial conditions an--an_ 1 +an-2 + an-3 for n 23,a0-0, al = 1,a2-6.
Algorithm Question: Problem 3. Solve the recurrence relation T(n) = 2T(n/2) + lg n, T(1) 0.