# Root to leaf path with maximum distinct nodes

Given a Binary Tree, find count of distinct nodes in a root to leaf path with maximum distinct nodes.
Examples:

```Input :   1
/
2      3
/     /
4   5  6   3

8   9
Output : 4
The root to leaf path with maximum distinct
nodes is 1-3-6-8.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A simple solution is to explore all root to leaf paths. In every root to leaf path, count distinct nodes and finally return the maximum count.

An efficient solution is to use hashing. We recursively traverse the tree and maintain count of distinct nodes on path from root to current node. We recur for left and right subtrees and finally return maximum of two values.

Below is implementation of above idea

## C++

 `// C++ program to find count of distinct nodes ` `// on a path with maximum distinct nodes. ` `#include ` `using` `namespace` `std; ` ` `  `// A node of binary tree ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node *left, *right; ` `}; ` ` `  `// A utility function to create a new Binary ` `// Tree node ` `Node* newNode(``int` `data) ` `{ ` `    ``Node* temp = ``new` `Node; ` `    ``temp->data = data; ` `    ``temp->left = temp->right = NULL; ` `    ``return` `temp; ` `} ` ` `  `int` `largestUinquePathUtil(Node* node, unordered_map<``int``, ``int``> m) ` `{ ` `    ``if` `(!node) ` `        ``return` `m.size(); ` ` `  `    ``// put this node into hash ` `    ``m[node->data]++; ` ` `  `    ``int` `max_path = max(largestUinquePathUtil(node->left, m), ` `                       ``largestUinquePathUtil(node->right, m)); ` ` `  `    ``// remove current node from path "hash" ` `    ``m[node->data]--; ` ` `  `    ``// if we reached a condition where all duplicate value ` `    ``// of current node is deleted ` `    ``if` `(m[node->data] == 0) ` `        ``m.erase(node->data); ` ` `  `    ``return` `max_path; ` `} ` ` `  `// A utility function to find long unique value path ` `int` `largestUinquePath(Node* node) ` `{ ` `    ``if` `(!node) ` `        ``return` `0; ` ` `  `    ``// hash that store all node value ` `    ``unordered_map<``int``, ``int``> hash; ` ` `  `    ``// return max length unique value path ` `    ``return` `largestUinquePathUtil(node, hash); ` `} ` ` `  `// Driver program to test above functions ` `int` `main() ` `{ ` `    ``// Create binary tree shown in above figure ` `    ``Node* root = newNode(1); ` `    ``root->left = newNode(2); ` `    ``root->right = newNode(3); ` `    ``root->left->left = newNode(4); ` `    ``root->left->right = newNode(5); ` `    ``root->right->left = newNode(6); ` `    ``root->right->right = newNode(7); ` `    ``root->right->left->right = newNode(8); ` `    ``root->right->right->right = newNode(9); ` ` `  `    ``cout << largestUinquePath(root) << endl; ` ` `  `    ``return` `0; ` `} `

## Python3

# Python3 program to find count of
# distinct nodes on a path with
# maximum distinct nodes.

# A utility class to create a
# new Binary Tree node
class newNode:
def __init__(self, data):
self.data = data
self.left = self.right = None

def largestUinquePathUtil(node, m):
if (not node):
return len(m)

# put this node into hash
if node.data in m:
m[node.data] += 1
else:
m[node.data] = 1

max_path = max(largestUinquePathUtil(node.left, m),
largestUinquePathUtil(node.right, m))

# remove current node from path “hash”
m[node.data] -= 1

# if we reached a condition
# where all duplicate value
# of current node is deleted
if (m[node.data] == 0):
del m[node.data]

return max_path

# A utility function to find
# long unique value path
def largestUinquePath(node):
if (not node):
return 0

# hash that store all node value
Hash = {}

# return max length unique value path
return largestUinquePathUtil(node, Hash)

# Driver Code
if __name__ == ‘__main__’:

# Create binary tree shown
# in above figure
root = newNode(1)
root.left = newNode(2)
root.right = newNode(3)
root.left.left = newNode(4)
root.left.right = newNode(5)
root.right.left = newNode(6)
root.right.right = newNode(7)
root.right.left.right = newNode(8)
root.right.right.right = newNode(9)

print(largestUinquePath(root))

# This code is contributed by PranchalK

```4
```

Time Complexity :O(n)

## tags:

Hash Tree cpp-unordered_map Hash Tree