完全二叉树和完全二叉树的区别

一种 二叉树是一种数据结构，每个节点最多只能有两个后代，分别命名为“左”和“右”孩子。

A Binary Tree

二叉树有不同的类型，但在这里我们将讨论完全二叉树和完全二叉树的区别。

完整的二叉树：

完全二叉树是所有节点都有 0 或 2 个后代的二叉树。换句话说，完全二叉树是一种二叉树，其中除叶节点外的所有节点都有两个后代。

A Full Binary Tree

Let, i be the number of internal nodes
 n be the  total number of nodes
l be number of leaves
λ be number of levels

Then,

The number of leaves is (i + 1).
The total number of nodes is (2i + 1).
The number of internal nodes is (n – 1) / 2.
The number of leaves is (n + 1) / 2.
The total number of nodes is (2l – 1).
The number of internal nodes is (l – 1).
The number of leaves is at most (2^λ – 1).

完整的二叉树：

当二叉树的所有层都被完全填满时，除了最后一层，它可以包含 1 或 2 个子节点并从左开始填充，就称它是完全二叉树。

A Complete Binary Tree

There are 2 points that you can recognize from here,  

1. The leftmost side of the leaf node must always be filled first.
2. It isn’t necessary for the last leaf node to have a right sibling.

检查以下示例以更好地理解完整和完整的二叉树。

Example 1:

Neither complete nor full

• Node C has just one child therefore, it is not a Complete binary tree. 
• Node C also has a right child but no left child, therefore it is also not a Complete binary tree. 

Hence, the binary tree shown above is neither complete nor full binary tree.

Example 2:

Full but not complete

• All of the nodes have either 0 or 2 offspring, therefore, it is a Full binary tree. 
• It is not a Complete binary tree because node B has no children whereas node C has children, and according to a complete binary tree, nodes should be filled from the left side.

Hence, the binary tree shown above is a Full binary tree and it is not a Complete binary tree.

Example 3:

Complete but not full

• It is a complete binary tree as all the nodes are left filled.
• Node B has just one child, therefore, it is not a full binary tree.

Hence, the binary tree shown above is a Complete binary tree and it is not a Full binary tree.

Example 4:

Complete and full

• It is a Complete binary tree because all the nodes are left filled.
• All of the nodes have either 0 or 2 offspring, therefore, it is a full binary tree.

Hence, the binary tree shown above is both a complete and a full binary tree.

S. No.	Complete Binary Tree	Full Binary Tree
1.	In a complete binary tree, a node in the last level can have only one child.	In a full binary tree, a node cannot have just one child.
2.	In a complete binary tree, the node should be filled from the left to right.	There is no order of filling nodes in a full binary tree.
3.	Complete binary trees are mainly used in heap-based data structures.	Full binary tree has no application as such but is also called a proper binary tree.