Add the following recursive method to your binary tree's node class:
size_t Node::count_leaves()
{
if (!left && !right) return 1; // this node is a leaf
size_t count = 0;
if (left) count += left-count_leaves(); // count leaves on left
if (right) count += right-leaves(); // count leaves on right;
return count; // return total leaves.
}
To count the leaves of the entire tree, call the method on the root node of the tree. To count the leaves of a subtree, call the method on the root node of the subtree.
In a binary tree with a maximum depth of ( H ), the number of leaf nodes can vary depending on the structure of the tree. However, if the tree is a complete binary tree, the maximum number of leaf nodes occurs at depth ( H ), which is ( 2^H ). For a full binary tree, the minimum number of leaf nodes at depth ( H ) is ( 1 ), occurring when all nodes except the last level are filled. Thus, the number of leaf nodes can range from ( 1 ) to ( 2^H ).
For a full binary tree of height 3 there are 4 leaf nodes. E.g., 1 root, 2 children and 4 grandchildren.
The number of nodes in any subtree is the number of nodes in its left subtree, plus the number of nodes in its right subtree, plus one, so you can use a recursive algorithm and start at the root.unsigned intbinarytree_count_recursive(const node *root){unsigned int count = 0;if (root != NULL) {count = 1 + binarytree_count_recursive(root->left)+ binarytree_count_recursive(root->right);}return count;}
A binary tree of n elements has n-1 edgesA binary tree of height h has at least h and at most 2h - 1 elementsThe height of a binary tree with n elements is at most n and at least ?log2 (n+1)?
It will be come a terminal node. Normally we call terminal nodes leaf nodes because a leaf has no branches other than its parent.
int countleaves(struct node* root){ if(root!=null) { countleaves(root->left); if(root->left==NULL&&root->right==NULL) { count++; } countleaves(root->right); } }
In a binary tree with a maximum depth of ( H ), the number of leaf nodes can vary depending on the structure of the tree. However, if the tree is a complete binary tree, the maximum number of leaf nodes occurs at depth ( H ), which is ( 2^H ). For a full binary tree, the minimum number of leaf nodes at depth ( H ) is ( 1 ), occurring when all nodes except the last level are filled. Thus, the number of leaf nodes can range from ( 1 ) to ( 2^H ).
The height of a complete binary tree is in terms of log(n) where n is the number of nodes in the tree. The height of a complete binary tree is the maximum number of edges from the root to a leaf, and in a complete binary tree, the number of leaf nodes is equal to the number of internal nodes plus 1. Since the number of leaf nodes in a complete binary tree is equal to 2^h where h is the height of the tree, we can use log2 to find the height of a complete binary tree in terms of the number of nodes.
The height of a binary search tree is the maximum number of edges from the root node to a leaf node. It represents the longest path from the root to a leaf in the tree.
Ne=N2+1Here Ne=no. of leaf nodesN2= no. of nodes of degree 2
Complete Binary tree: -All leaf nodes are found at the tree depth level -All nodes(non-leaf) have two children Strictly Binary tree: -Nodes can have 0 or 2 children
Complete Binary tree: All leaf nodes are found at the tree depth level and All non-leaf nodes have two children. Extended Binary tree: Nodes can have either 0 or 2 children.
IF EVERY NON-LEAF NODE IN A BINARY TREE HAS HAS NONEMPTY LEFT AND RIGHT SUBTREES, THE TREE IS TERMED AS A STRICTLY BINARY TREE. SUCH A TREE WITH n LEAVES ALWAYS CONTAINS 2n-1 NODES.
Here's what you do... take a graph paper.. the 1mm x 1mm graduated. trace the leaf on the graph paper. remove the leaf. then count the whole squares occupied by the leaf. write down the number. count the half 3/4th filled squares and write the number down. count the number of half filled squares and divide the number by two and write it down. leave out 1/4th filled squares. add the numbers you have written down. the number you get is the surface area of one side of leaf. doubling it will give you the surface area of the entire leaf in sq cm
For a full binary tree of height 3 there are 4 leaf nodes. E.g., 1 root, 2 children and 4 grandchildren.
A strictly binary tree is a tree in which every node other than the leaf nodes has exactly two children. OR in the Graph Theory perspective a tree having it's root vertex with degree 2 and all other non-leaf vertex of degree 3 and leaf vertex of degree 1, is called as the strictly binary tree. it is also called as the 2-tree or full binary tree.
The number of nodes in any subtree is the number of nodes in its left subtree, plus the number of nodes in its right subtree, plus one, so you can use a recursive algorithm and start at the root.unsigned intbinarytree_count_recursive(const node *root){unsigned int count = 0;if (root != NULL) {count = 1 + binarytree_count_recursive(root->left)+ binarytree_count_recursive(root->right);}return count;}