Min distance between two given nodes of a Binary Tree.cpp

/*
Min distance between two given nodes of a Binary Tree
=====================================================

Given a binary tree and two node values your task is to find the minimum distance between them.

Example 1:
Input:
        1
      /  \
     2    3
a = 2, b = 3
Output: 2
Explanation: The tree formed is:
       1
     /   \ 
    2     3
We need the distance between 2 and 3.
Being at node 2, we need to take two
steps ahead in order to reach node 3.
The path followed will be:
2 -> 1 -> 3. Hence, the result is 2. 
Your Task:
You don't need to read input or print anything. Your task is to complete the function findDist() which takes the root node of the Tree and the two node values a and b as input parameters and returns the minimum distance between the nodes represented by the two given node values.

Expected Time Complexity: O(N).
Expected Auxiliary Space: O(Height of the Tree).

Constraints:
1 <= Number of nodes <= 104
1 <= Data of a node <= 105

Note:The Input/Ouput format and Example given are used for system's internal purpose, and should be used by a user for Expected Output only. As it is a function problem, hence a user should not read any input from stdin/console. The task is to complete the function specified, and not to write the full code.
*/

/* A binary tree node
struct Node
{
    int data;
    Node* left, * right;
}; */

Node *lca(Node *root, int n1, int n2)
{
  if (!root)
    return NULL;
  if (root->data == n1 || root->data == n2)
    return root;

  auto left = lca(root->left, n1, n2);
  auto right = lca(root->right, n1, n2);

  if (left && right)
    return root;

  if (left)
    return left;
  return right;
}

int path(Node *root, int a)
{
  if (!root)
    return 1000000;
  if (root->data == a)
    return 0;

  return 1 + min(path(root->left, a), path(root->right, a));
}

/* Should return minimum distance between a and b
   in a tree with given root*/
int findDist(Node *root, int a, int b)
{
  Node *common = lca(root, a, b);
  return path(common, a) + path(common, b);
}