Find the best big O bound you can on T(n) if it satisfies the recurrence T(n)...
Find the best big O bound you can on T(n) if it satisfies the recurrence T(n) ≤ T(n/4) + T(n/2) + n, with T(n) = 1 if n < 4.
Homework Answers
Recursion tree would looklike this-
First two levels are shown.
All subsequent levels will have the same pattern: dividin node of m into two pieces, of size m/2 and m/4.
Total contribution from second layer = n/2+n/4 = 3n/4.
For third layer we can say that it will be 3/4 if 3n/4.
...and so on.
So total contribution to T(n) would be
=n+(3/4)n+(3/4)2n+(3/4)3n+ ...
geometric series, Thus
T(n)<=n/(1-3/4)=4n
So, upper bound can be given as O(n).
feel free to ask any doubt.
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Find the best big O bound you can on T(n) if it
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From the code below with Binary Search Tree recurrence T(n)=? use the recursion method and substitution method to solve the recurrence. Find the tightest bound g(n) for T(n) you can for which T(n)= O(...
From the code below with Binary Search Tree recurrence T(n)=?
use the recursion method and substitution method to solve the
recurrence. Find the tightest bound g(n) for T(n) you can for which
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method.
void insert(int data) {
struct node *tempNode = (struct node*) malloc(sizeof(struct node));
struct node *current;
struct node *parent;
tempNode->data = data;
tempNode->leftChild = NULL;
tempNode->rightChild = NULL;
//if tree is empty
if(root == NULL) {
root = tempNode;...
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Dont use master theorm and find tight Big-O bound for the
following recurrence:
If n = 0 2* S(17n/10]) ifn >0 S(n) =
If n = 0 2* S(17n/10]) ifn >0 S(n) =
Use the iteration technique to find a Big-Oh bound for the recurrence relation belov Note you may find the following mathematical result helpful: 2log3n = nlog32 {i=0(2/3)= 3 T(n) = 2T(n/3) + cn
4. Suppose T (n) satisfies the recurrence equations T(n) = 2 * T( n/2 ) + 6 * n, n 2 We want to prove that T (n)-o(n * log(n)) T(1) = 3 (log (n) is log2 (n) here and throughout ). a. compute values in this table for T (n) and n*log (n) (see problem #7) T(n) | C | n * log(n) 2 4 6 b. based on the values in (a) find suitable "order constants" C and...
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Prove that the solution of the recurrence T(n) = T(n/2) +6(logk n) with T(1-6(1), for any integer k 2 0, is T(n) = Θ(logk+1 n) (Hint: the upper bound T(n) = O(logk+1 n) is easy;...
From the code below with Binary Search Tree recurrence T(n)=?
use the recursion method and substitution method to solve the
recurrence. Find the tightest bound g(n) for T(n) you can for which
T(n)= O(g(n)). Explain your answer and use recursion tree
method.
void insert(int data) {
struct node *tempNode = (struct node*) malloc(sizeof(struct node));
struct node *current;
struct node *parent;
tempNode->data = data;
tempNode->leftChild = NULL;
tempNode->rightChild = NULL;
//if tree is empty
if(root == NULL) {
root = tempNode;...
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