Question

I am looking at big code base in C++. There is line mentioned as below

int capacity( ) const
{
    return ( 1 << theTrees.size( ) ) - 1;
}

Here theTrees is

vector<int> theTrees

What is statement 1 << theTrees.size( ) likely trying to achieve? Assume we have tree size of 25 elements.

Answer 1

A left shift by n is basically multiplying by 2 to the nth power. Whenever you have 1 << n you’re just calculating the nth power of 2. E.g.:

1 << 0 = 1
1 << 1 = 2
1 << 2 = 4
1 << 3 = 8

Etc.

I suspect theTrees.size() returns not the number of elements in the tree but the height of the tree (number of levels), because that’s the only way this makes sense. Given a full binary tree, the number of nodes is 2^N – 1, where N is the height of the tree. E.g., a tree with three levels (n = 3) can hold 2^3 – 1 = 7 nodes. Check it: The first level has one, the second has two and the third has four. 1 + 2 + 4 = 7.