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Minimum number of nodes in an AVL Tree with given height using C++.
Problem statement
Given the height of an AVL tree, the task is to find the minimum number of nodes the tree can have.
If height = 0 then AVL tree can have one 1 node If height = 5 then AVL tree can have minimum 20 nodes
Algorithm
In an AVL tree, we have to maintain the height balance property, i.e. a difference in the height of the left and the right subtrees cannot be more than -1, 0 or 1 for each node. Using this property, we can create below recurrence relation −
1. If height = 0 then return 1 2. If height = 1 then return 2 3. If height > 1 then return (1 + getMinAVLNodes(h – 1) + getMinAVLNodes(h – 2))
Example
#include <iostream>
using namespace std;
int getMinAVLNodes(int h){
if (h < 0) {
return 0;
}
if (h == 0 || h == 1) {
return h + 1;
}
return 1 + getMinAVLNodes(h - 1) + getMinAVLNodes(h -2);
}
int main(){
int h = 5;
cout << "Minimum nodes for " << h << " height = " << getMinAVLNodes(h) << endl;
return 0;
}Output
When you compile and execute the above program. It generates the following output −
Minimum nodes for 5 height = 20
Updated on: 31-Oct-2019
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