Suppose a complete binary tree has 1000 nodes, then this complete binary tree has () leaf nodes and () nodes with degree 2.

1. Problem

Suppose a complete binary tree has 1000 nodes, then this complete binary tree has (500) leaf nodes, and there are (500) a>) nodes with degree 2. 499

Analysis:
1. Leaf node: a node with degree 0.
2. Let n0 represent the node with degree 0, and n2 represent the node with degree 2 .
3. According to the properties of the binary tree, n0 = n2 +1.

Therefore, we only need to find n0 to find the number of nodes of n2. The implementation of the idea is as follows:

2. Implementation of ideas

• The first step is to find the number of n0.
  A complete binary tree with 1000 nodes has 10 levels ($2^9$ - 1 < 1000 < $2^{10}$-1), of which the first 9 levels of are full binary trees with a total of 512-1=511 nodes.

  Therefore, there are 1000-511=489, indicating thatthere are 489 nodes in the 10th layer, and the nodes in the 10th layer are all Leaf nodes (nodes with degree 0).

  And 489/2 = 244...1, it means that there are 244+1 (245) nodes with child nodes in the 9th level, and according to the full binary tree, there are $2^8$ = 256 nodes, then the number of nodes (leaf nodes) with degree 0 in the ninth layer is 256-245 = 11.

  n0 = the number of leaf nodes in the 9th layer + the number of leaf nodes in the 10th layer = 489+11 = 500, that is, the number of leaf nodes is 500.

• The second step is to find n0 = n2 +1 and solve for the number of n2.
  From the number of leaf nodes obtained in the first step, the number of nodes with degree 2 in the binary tree can be obtained:
  n2=n0-1=500-1 =499
  That is: there are 499 nodes with degree 2.

Problem recording time: 2023.11.5

Code_Lissel (CSDN) (A Coder who likes ancient poetry and programming)
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