CareerCup

maximum number of leaf nodes would be 2^10.

I think the maximum number of leaf nodes should be 2^9

2^10 - 1

number of nodes will not odd for sure except for root level which has 1 node. Number of nodes depends upon whether u consider root as level 1 or level 0. If root is level 0 then level at depth 10 will have 2^10 nodes otherwise 2^9

A balanced binary tree is where the depth of all the leaves differs by at most 1. Balanced trees have a predictable depth (how many nodes are traversed from the root to a leaf, root counting as node 0 and subsequent as 1, 2, ..., depth). This depth is equal to the integer part of log2(n) where n is the number of nodes on the balanced tree. Example 1: balanced tree with 1 node, log2(1) = 0 (depth = 0). Example 2: balanced tree with 3 nodes, log2(3) = 1.59 (depth=1). Example 3: balanced tree with 5 nodes, log2(5) = 2.32 (depth of tree is 2 nodes).

so log2(number of nodes)= depth
so number of Nodes = 2 power 10

i copied from wiki
http://en.wikipedia.org/wiki/Binary_tree

void FindNodeInDepth(node* root, int currentLayer, int targetLayer, int& count)
{
if (currentLayer == targetLayer)
{
++count;
}
else
{
if (root->left)
FindNodeInDepth(root->left, currentLayer+1, targetLayer, count);
if (root->right)
FindNodeInDepth(root->right, currentLayer+1, targetLayer, count);
}
}