# find depth of binary search tree

We can find the depth of the binary search tree in three different recursive ways
– using instance variables to record current depth and total depth at every level
– without using instance variables in top-bottom approach
– without using instance variables in bottom-up approach

Full source code can be downloaded here
Approach #1: using instance variables to record current depth and total depth at every level

```	int currentDepth, depth;
public int depth(BinaryNode n) {
if (n != null) {
currentDepth++;

// record total depth if current depth is greater than total depth
if (currentDepth > depth) {
depth = currentDepth;
}

// recursively traverse entire tree
depth(n.left);
depth(n.right);

// decrement as we traverse up the binary tree
currentDepth--;
}
return depth;
}
```

Pros: Easier to implement and understand
Cons: Usage of instance variables. Ideally any recursive call should not make use of instance variables and by doing so it moves close towards linear programming.

Approach #2: without using instance variables in top-bottom approach

```	public int depth3(BinaryNode node, int d){
int leftDepth = d, rightDepth = d;

if(node.left != null){
leftDepth = depth3(node.left, d+1);
}
if(node.right != null){
rightDepth = depth3(node.right, d+1);
}

return leftDepth > rightDepth ? leftDepth : rightDepth;
}

```

Approach #3: without using instance variables in bottom-up approach

```	public int depth2(BinaryNode node){
if(node == null)
return 0;
int left = depth2(node.left);
int right = depth2(node.right);

int x = left > right ? left+1 : right+1;
return x;
}
```

Approach #2 and #3 are actually recursive way of finding the depth. In #2 we only depend on the return type of the method because back-tracking helps us to keep track of the tree depth. In #3, since we are incrementing the depth in top-bottom fashion, we need additional parameter to the method to track the depth.

My 2 cents for best approach is #2.

Full source code can be downloaded here

Output:

```Maximum depth of the Binary Tree is using instance variables: 3
Maximum depth of the Binary Tree is without using instance variables in bottom-up approach: 3
Maximum depth of the Binary Tree is without using instance variables in top-bottom approach: 3
|	|-------28
|-------25
|	|-------22
20
|	|-------18
|-------15
|	|-------12

```
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### 3 Responses to find depth of binary search tree

1. 242196se says:

One question: in the piece of code “using instance variables to record current depth and total depth at every level”, shouldn’t be the decrementation just before the call to depth(n.right)?

depth(n.left);

currentDepth–;
depth(n.right);

2. ivor says:

determineDepth( TreeNode *ptr, int *totPtr, int *currPtr ) const

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