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 |

int heightOfBinaryTree(BinaryTree node) { if (node == null) { return -1; } else { return 1 + Math.max(heightOfBinaryTree(node.left), heightOfBinaryTree(node.right)); } }

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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Data Structure Programming Help