What Is Height of a Tree in Data Structure With Example?

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Heather Bennett

What Is Height of a Tree in Data Structure With Example?

In data structures, a tree is a hierarchical structure that consists of nodes connected by edges. Each node can have zero or more child nodes, and there is always one node called the root.

The height of a tree refers to the maximum number of edges between the root and any leaf node in the tree. In other words, it represents the length of the longest path from the root to a leaf.

Example:

Let’s consider an example to understand the concept of tree height better. Suppose we have a binary tree as shown below:

        A
       / \
      B   C
         / \
        D   E
       /
      F
  • Step 1: Start with the root node ‘A’.
  • Step 2: Move to its child nodes ‘B’ and ‘C’.
  • Step 3: For each child node, repeat steps 2 and 3 until we reach the leaf nodes.

Now, let’s calculate the height of this tree using these steps:

  • Starting at node ‘A’:
    • Moving to node ‘B’: There are no further child nodes.
    • Moving to node ‘C’: We have one child node (‘D’).
      • Moving to node ‘D’: We have one child node (‘F’).
        • Moving to node ‘F’: There are no further child nodes.
    • Moving to node ‘E’: There are no further child nodes.
  • Calculating the height:

The longest path from the root node ‘A’ to any leaf node is A – C – D – F. Hence, the height of this tree is 3.

In conclusion, the height of a tree in data structure refers to the maximum number of edges between the root and any leaf node. It helps us understand the overall structure and complexity of a tree-based data structure.

By following a step-by-step approach, as shown in the example above, we can determine the height of any given tree.

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