Thursday, 30 May 2013

Binary Tree - height and size

What is height and what is size of Binary Tree?
The size of a tree is the size of the root. The size of a node is the number of descendants it has including itself. Therefore, the tree size is the number of all tree nodes.
The height (or depth) of a tree is the length of the path from the root to the deepest node in the tree. A (rooted) tree with only one node (the root) has a depth of zero. Conventionally, an empty tree (tree with no nodes, if such are allowed) has depth and height −1.
In the picture below you see a binary tree with height 3 and size 9.
Binary Tree - size and height
Binary Tree
Here are two functions calculating the size and the height of a binary tree. The first function is recursive and returns the height:
int heightOfBinaryTree(BinaryTree node) {
    if (node == null) {
        return -1;
    } else {
        return 1 + Math.max(heightOfBinaryTree(node.left),

The size solution is recursive, too:
int binaryTreeSize(BinaryTree node) {
    if (node == null) {
        return 0;
    return (binaryTreeSize(node.left) + binaryTreeSize(node.right) + 1);

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