The identification of common sub-expression and replaement of run time computatuopns by compiler time computations is
Answers
Answer:
Constant folding is the process of recognizing and evaluating constant expressions at compile time rather than computing them at runtime. Terms in constant expressions are typically simple literals they may also be variables whose values are assigned at compile time.
Answer:
Minimum number of nodes in an AVL Tree with given height
Given the height of an AVL tree ‘h’, the task is to find the minimum number of nodes the tree can have.
Examples :
Input : H = 0
Output : N = 1
Only '1' node is possible if the height
of the tree is '0' which is the root node.
Input : H = 3
Output : N = 7
Recommended: Please try your approach on {IDE} first, before moving on to the solution.
Recursive Approach : In an AVL tree, we have to maintain the height balance property, i.e. difference in the height of the left and the right subtrees can not be other than -1, 0 or 1 for each node.
We will try to create a recurrence relation to find minimum number of nodes for a given height, n(h).
For height = 0, we can only have a single node in an AVL tree, i.e. n(0) = 1
For height = 1, we can have a minimum of two nodes in an AVL tree, i.e. n(1) = 2
Now for any height ‘h’, root will have two subtrees (left and right). Out of which one has to be of height h-1 and other of h-2. [root node excluded]
So, n(h) = 1 + n(h-1) + n(h-2) is the required recurrence relation for h>=2 [1 is added for the root node]