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I'm having a little trouble with creating a function to find the average depth of a binary search tree. The definition of average depth of a tree is the sum of the depth of all nodes divided by the total number of nodes. The definition of the depth of a node is the distance from the root of the tree to the node. Can anyone help me?

So an example would be if you had a BST of:

   /   \
  3     8
 / \     \
2   4     9

Then the average depth is 1.571 because from 6 to 3 has depth of 1 and 6 to 2 has depth of 2. Do that for the rest of the nodes and sum them up then divide by the total number of nodes and that is the average depth. So it's (1 + 1 + 2 + 2 + 2 + 3)/7. Can anyone help me?
Posted 23-Apr-11 14:24pm
Updated 23-Apr-11 14:44pm
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Solution 1

The problem is not finding the depth, the problem is to do it just once. Here is the way to do it: do not create a function for finding a depth of the current node. Instead, include the depth of a current node as a parameter of the recursive function.

void AccumulateNodeInfo(
    node * parent, uint parentDepth,
    uint & accumulatedDepth, uint & nodeCount);

Initialize accumulatedDepth and nodeCount to 0 and call this function with the root node. The function should call the current node's children with parentDepth + 1, add parentDepth to accumulatedDepth and increment the nodeCount. After this function traverses all the tree, accumulatedDepth will be equal to sum of the depths and nodeCount equal to the node count.

algrn912005 24-Apr-11 16:53pm
Thank you, that worked beautifully.
SAKryukov 24-Apr-11 21:14pm
Great. You're welcome.
Thanks for accepting this solution.
Good luck,
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Solution 2

For every thing i do with trees i use walk functions.
Example for a walk function:
class INode
  INode*  _child;
  INode*  _next;
class IWalk
public: // IWalk
  virtual HRESULT Enter(INode* pNode) = 0;
  virtual HRESULT Leave(INode* pNode) = 0;

void Walk(INode* pNode,IWalk* pWalk)
  if(pNode && pWalk)
      for(INode* p=pNode->_child;p;p=p->_next) Walk(p,pWalk);

// implementation
class iWalk : public IWalk
public: // IWalk
  virtual HRESULT Enter(INode* pNode){ ++_node_count; _node_level_sum += _level; ++_level; return S_OK; }
  virtual HRESULT Leave(INode* pNode){ --_level; return S_OK; }
  iWalk(){ _node_count = _node_level_sum = _level = 0; }
  unsigned int  _node_count;
  unsigned int  _node_level_sum;
  unsigned int  _level;
double Calc()
  iWalk  w;
  return 0<w._node_count?(double)w._node_level_sum/(double)w._node_count:0;

Good luck.
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Solution 3

You have to find average depth at once .I use this formula->
This you can find from the formula as we can find maximum no.of nodes by //n=(2^d)-1
Where d is depth of the tree.

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