Recursively calculate height of left and right subtrees of a node and assign height to the node as max of the heights of two children plus 1. See below pseudo code and program for details.

**Algorithm:**

```
maxDepth()
1. If tree is empty then return 0
2. Else
(a) Get the max depth of left subtree recursively i.e.,
call maxDepth( tree->left-subtree)
(a) Get the max depth of right subtree recursively i.e.,
call maxDepth( tree->right-subtree)
(c) Get the max of max depths of left and right
subtrees and add 1 to it for the current node.
max_depth = max(max dept of left subtree,
max depth of right subtree)
+ 1
(d) Return max_depth
```

**See the below diagram for more clarity about execution of the recursive function maxDepth() for above example tree.**

```
maxDepth('1') = max(maxDepth('2'), maxDepth('3')) + 1
= 2 + 1
/ \
/ \
/ \
/ \
/ \
maxDepth('1') maxDepth('3') = 1
= max(maxDepth('4'), maxDepth('5')) + 1
= 1 + 1 = 2
/ \
/ \
/ \
/ \
/ \
maxDepth('4') = 1 maxDepth('5') = 1
```

**Implementation:**

```
#include<stdio.h>
#include<stdlib.h>
/* A binary tree node has data, pointer to left child
and a pointer to right child */
struct node
{
int data;
struct node* left;
struct node* right;
};
/* Compute the "maxDepth" of a tree -- the number of
nodes along the longest path from the root node
down to the farthest leaf node.*/
int maxDepth(struct node* node)
{
if (node==NULL)
return 0;
else
{
/* compute the depth of each subtree */
int lDepth = maxDepth(node->left);
int rDepth = maxDepth(node->right);
/* use the larger one */
if (lDepth > rDepth)
return(lDepth+1);
else return(rDepth+1);
}
}
/* Helper function that allocates a new node with the
given data and NULL left and right pointers. */
struct node* newNode(int data)
{
struct node* node = (struct node*)
malloc(sizeof(struct node));
node->data = data;
node->left = NULL;
node->right = NULL;
return(node);
}
int main()
{
struct node *root = newNode(1);
root->left = newNode(2);
root->right = newNode(3);
root->left->left = newNode(4);
root->left->right = newNode(5);
printf("Hight of tree is %d", maxDepth(root));
getchar();
return 0;
}
```