Little Sugar (Trees : relations)

A complete binary tree has odd number of nodes .

Number of leaves + number of internal nodes ( both even) +
1 = number of nodes in a tree

The number of internal nodes + 1 = number of leaves

number of internal nodes = number of leaves - 1

n = number of nodes

n = number of leaves + number of internal nodes

n +1 = 2 * number of leaves

number of leaves = (n+1)/2

The number of total nodes upto height h :

= pow(2,h+1) - 1

The number of nodes for any binary tree at height (h) :

= ceil(n / pow(2,h+1))

Little Sugar (Trees : relations)

A complete binary tree has odd number of nodes .

Number of leaves + number of internal nodes ( both even) +
1 = number of nodes in a tree

The number of internal nodes + 1 = number of leaves

number of internal nodes = number of leaves - 1

n = number of nodes

n = number of leaves + number of internal nodes

n +1 = 2 * number of leaves

number of leaves = (n+1)/2

type conversions : C++

Implicit type conversions in C++ can be quite problematic . To take care of type conversion issues , C++ provides us with a simple mechanism .

use the explicit keyword .

so for a class like Array

class Array{

public:
explicit Array(int size){
...
}

};

so by using the explicit keyword in this manner , you tell the compiler to use the constructor only
when explicit object construction is taking place.

another way around the explicit keyword is :

class Array{
public:
class ArraySize{
public:
ArraySize(int size)
this->size = size;
}

private:
int size;
};

Array(ArraySize size){
...
}
};

So by using the nested public ArraySize class in this manner , you 'll see that even if the compiler makes implicit type conversions for cases like

Array a(10);

the integer 10 is correctly transformed to ArraySize and the constructor having ArraySize as a parameter is called .

The beauty of this last technique is that it works in many cases , cause the compiler is allowed to make 1 implicit type conversion but now two.