A complete binary tree has a total number of nodes, how many leaf nodes does the binary tree have? H

Satisfactory Answer: Telescope Level 8 2010-03-22 Complete Binary Tree.

For example, there are 7 nodes in a 3-layer complete binary tree, and the total number of nodes is (2 to the 3rd power) minus 1; Leaf nodes.

If the number is 2 (3 minus 1 power), it is 4. If it is an n-layer complete binary tree, the total number of nodes is (2 to the nth power) minus 1; The number of leaf nodes is 2 (n minus 1 power); Yes, it's very simple. Do you understand this time?

Follow-up question: If there are 700 nodes in a complete binary tree, how many leaf nodes are there?

The so-called complete binary tree cannot have 700 nodes, the nth layer of a complete binary tree will be 2 n-1 power nodes, and the upper layer is n-2 power nodes, so the total number of nodes should be 2n power minus 1,700 is not such a number, so there will not be 700 nodes. If it is two layers, it should be 4 1 3 nodes, three layers, 8 1 7 nodes four layers, 16 1 15 nodes five layers, 32 1 31 nodes six layers, 64 1 63 nodes seven layers, 128 1 127 nodes eight layers, 256 1 255 nodes nine layers, 512 1 511 nodes ten layers, 1024 1 1023 nodes... As a result, there will be no full binary tree of 700 nodes.

Follow-up: But I did it!

Are you sure it's a complete binary tree?

Is there a word for "completely"?

Follow-up: There is indeed a question in the question, and the answer is 350

That's exactly half of the summary points!

That's easy to remember.

The answer on the ground floor is correct, but the interpretation is seriously problematic. "In a complete binary number, there is no node with a degree of 1. This statement is wrong.

Full Binary Tree Definition:

If the height of the binary tree is h, divide by the first.

Layer H, other layers.

1～h-1)

The number of nodes has reached the maximum number.

The H layer is continuously missing a number of nodes from right to left, which is a complete binary tree.

Algorithm for complete binary tree leaf nodes:

If a binary tree with a depth k with n nodes corresponds one-to-one to a node numbered 1 n in a full binary tree with a depth k, the binary tree is called a complete binary tree.

It can be deduced according to the formula, assuming that n0 is the total number of nodes with degrees of 0 (i.e., the number of leaf nodes), n1 is the total number of nodes with degrees of 1, and n2 is the total number of nodes with degrees of 2, and from the properties of the binary tree, it can be seen that n0 n2 1, then n=

n0 n1 n2 (where n is the total number of nodes in a complete binary tree), and n2 is eliminated by the above formula: n=

2n0+n1 1, since there are only two possible 0 or 1 for the number of nodes with a degree of 1 in a complete binary tree, n0 (n 1) 2 or n0 n 2 are combined into a single formula: n0 (n 1) 2

The number of leaf nodes can be calculated based on the total number of nodes in a complete binary tree.

Therefore the number of leaf nodes is (699+1) 2=350

The number of leaf nodes is 2 (n minus 1 power);

If the depth of the binary tree is k, the number of nodes in all layers (1 k-1) will reach the maximum number except for the k-layer back.

All the nodes in the k-layer are continuously concentrated on the far left, which is a complete binary tree.

If the nodes of a full binary tree are numbered, the agreed numbering starts from the root node, from top to bottom, and from left to right. then a binary tree with n nodes of depth k if and only if each of its nodes corresponds one-to-one with nodes numbered from 1 to n in a full binary tree of depth k.

The depth is n, the number of nodes is (2 n)-1, and the leaf nodes are 2 (n-1), and 2 n represents the nth power of 2.

It's okay to find a branch and count it. Naturally, it will count!

The calculation formula is as follows: n0 = n2+1, n0 is the number of leaf nodes, and n2 is the number of nodes with degree 2.

In a data structure, a tree is a nonlinear data structure that consists of nodes and edges, each of which can have zero or more child nodes. A leaf node of a tree is a node that does not have a child node, which can also be called a terminal node or a leaf node.

There are usually two ways to calculate the number of leaf nodes:

Recursive: Iterate through the entire tree starting from the root node, for each node, add one to the counter if it has no children, otherwise recursively iterate through each of its children.

Non-recursive: Use a data structure such as a stack or queue to traverse the entire tree, and for each node, if it has no children, then add one to the counter, otherwise its children are queued or stacked, and continue to traverse.

It should be noted that when calculating the leaf nodes of the tree, the hail code needs to exclude the case of empty trees, that is, there are no nodes in the tree.

It can be deduced according to the formula, assuming that n0 is the total number of nodes with a degree of 0 (i.e., the number of leaf nodes), n1 is the total number of nodes with a degree of 1, and n2 is the total number of nodes with a degree of 2, and it can be seen from the nature of the binary tree: n0=n2+1, then n= n0+n1+n2 (where n is the total number of nodes of the complete binary tree), and by eliminating n2 from the above formula, n= 2n0+n1-1, since there are only two possible 0 or 1 nodes with a degree of 1 in a complete binary tree, n0=(n+1) is obtained 2 or n0=n 2, the number of leaf nodes can be calculated from the total number of nodes in a complete binary tree.

There could be 8, 9 or 10.

According to the binary tree property, n0 = n2 +1, that is, the number of nodes with degrees of 2 is the number of nodes with degrees of 0 and the number of nodes with degrees of 0 - 1, that is, 70-1 = 69

Therefore, the total number of nodes in this binary tree is n0 + n1 + n2 = 70 + 80 + 69 = 219.