Find Minimum and Maximum in Binary Tree in Python

In this problem, we are given a binary tree. Our task is to find the minimum and maximum nodes in the given binary tree.

Let us see an example to understand the problem:

Input:

Output:

 (1, 7) 

The minimum node value of the tree is 1, and the maximum node value of the tree is 7.

Approach - 1

In the binary search tree, the maximum node is the node present in the rightmost node of the tree. We can reach this node by expanding the right sub-tree of the current node. We will traverse the right pointer until we reach the rightmost node of the tree. However, in the binary tree, we have to compare every node to find the tree's maximum and minimum node values. To solve the problem, we will traverse every node of the tree and return the maximum value of the three nodes: the first is the node value, the second is the node of the left subtree, and the third is the node of the right subtree.

Below is the Python code to implement this idea.

Code

Output:

 The maximum element of the tree 10 

Time Complexity: We have visited each node once; therefore, the worst-case time complexity of this program is O(N).

Auxiliary Space: The space complexity of this program is O(N) to store the recursive stack.

To find the minimum element of the binary tree, we must find the minimum node value out of the three nodes. Below is the Python code to find the minimum value.

Code

Output:

 The minimum element of the tree is 0