Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 10.4, Problem 2E
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Draw the recursion tree to compute Fibonacci number for n=6.
Draw the recursion tree:
function(A[1.n])
{
if n = 1 then return;
for i:= 1 to n/2:
A[) := A[i]+i;
function (A[1.n/2);
Find the closed form of recurrence with substitution, iteration method or recursion tree method.
Chapter 10 Solutions
Introduction to Algorithms
Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3E
Ch. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10 - Prob. 1PCh. 10 - Prob. 2PCh. 10 - Prob. 3P
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- Given a binary tree, let an H-node be defined as a non-leaf node in the tree whose value is greater than or equal to its children nodes (1 or 2 children). Write a function called countHNodes(TreeNode* p), that returns the number of H-nodes in a binary tree (pointed by p). Use recursion in the function.arrow_forwardGiven below is a recursive function fib for computing the nth fibonacci number. Draw the recursive tree for computing fib(4) def fib(n): if n <= 1: return 1 else: return fib(n - 1) + fib(n - 2)arrow_forwardRecursion Trees Use the recursion tree method to determine the asymptotic upper bound of T(n). T(n) satisfies the recurrence T(n) = 2T(n-1) + n, and T(0)=0.arrow_forward
- Find the minimum node of a BST. Use either recursive or non-recursive approach.arrow_forwardUsing the recursion tree method find the upper and lower bounds for the following recurrence (if they are the same, find the tight bound). T (n) = T (n/2) + 2T (n/3) + n.arrow_forwardGiven a binary tree, let an H-node be defined as a non-leaf node in the tree whose value is greater than or equal to its children nodes (1 or 2 children). Write a function, countHNodes(), that returns the number of H-nodes in a binary tree (pointed by p) using recursion.arrow_forward
- Write pseudocode for one of the classic traversal algorithms (preorder, inorder, and postorder) for binary trees. Assuming that your algorithm is recursive, find the number of recursive calls made.arrow_forwardDesign a recursive linear-time algorithm that tests whether a binary tree satisfies the search tree order property at every node. Use c++arrow_forwardWrite a binary search tree method that takes two keys, low and high, and prints all elements X that are in the range specified by low and high. Your program should run in O(K + log N) average time, where K is the number of keys printed. Thus, if K is small, you should be examining only a small part of the tree. Use a hidden recursive method and do not use an in-order iterator. Bound the running time of your algorithmarrow_forward
- Create a recursion tree like for T(n)=3T(n/2)+2n^2, with T(1)=2, for n=8 . Like is done in the figure that calculates the total number of comparisons.arrow_forwardA binomial tree is a special type of rooted tree, defined recursively as follows: Basis Step: The Oth binomial tree, Bo, is a single vertex. Recursive Step: For k > 1, the kth binomial tree, B, consists of two copies of B-1 and an additional edge making the root of one copy the child of the root of the other. a) Draw B2 b) Find a (non-recursive) formula for the number of vertices in B, and prove your formula correct. c) Prove that there are C(k, l) vertices at level l of Be (You may find Pascal's identity useful: C(n + 1, k) = C(n, k – 1) + C(n, k))arrow_forwardCreate a binary linked tree, and traverse the tree by using the recursive function. The structure of the tree is as follow: //PICTURE// You should input the nodes in pre-order sequence. If a child of a node is NULL, input a space. Write the function of create binary tree, pre-order to print the nodes, in-order to print the nodes and post-order to print the nodes. Also Count the height of the tree. PLEASE USE C LANGUAGEarrow_forward
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