What are the traversal methods used for the number of leaf nodes and the depth of the binary tree?

The concept of data structures such as stacks, queues, binary trees, and graphs is proposed in order to save and manage data more effectively and conveniently, and to provide an interface to access any of these elements.

This interface to access all the constituent elements of a data structure is called the traversal method of that data structure.

It follows that the purpose of the traversal method is to access the data domain.

When calculating the number of leaf nodes, it doesn't matter what a node is a leaf node, what the data domain object is, focus on the pointer field, you take a look**, when calculating the leaf node, you never need to access the data domain, I guess you are confusing the concept of traversal and recursion, calculating the number and depth of leaf nodes in the binary tree does not use any traversal method, your ** just uses the recursive method to calculate, it has nothing to do with traversal, binary tree due to its special structure, The recursive algorithm must be the preferred algorithm for manipulating binary trees, and trying to understand more about the divide and conquer algorithm will be very beneficial to you in the future.

The number of leaf nodes is traversed by breadth, and the depth is traversed by depth.

A full binary tree means that all nodes in each layer have two sub-accommodating nodes except for the last layer; That is, in a full binary tree, the number of nodes on each layer reaches the maximum value, then there are 2k-1 nodes in the k-th layer of the full binary tree, and there are 2m-1 nodes in the full binary tree with a monthly depth of m. A full binary tree with a depth of 7 has a leaf node count of 27-1=26=64.

If the root level is 1, then a full binary tree with a depth of 7 has leaves all in the 7th layer, and there are 2 (7-1) = 64.

In a full binary tree with depth k, the number of leaf nodes is 2 (k-1), so in a full binary tree with a depth of 7 and a level of 7, there are a total of 2 (7-1)=64 leaf nodes.

On the k-th level of a full binary tree there are: 2 to the kth power minus 1 node (the maximum level of the tree is called the depth of the tree, and the node without posteriors is called the leaf node.) A full binary tree with a depth of 7 has 127 leaf nodes.

You can understand it this way:

Nodes: Refers to the points in the binary tree, which are the ones in the figure below;

Degree: Refers to how many child nodes there are under the parent node, give two examples and you will understand. For junction 1, he has two children below, so the degree of junction 1 is trembling chakra 2; For junction 4, he doesn't have any children below, so the degree of junction 4 is 0;

Placing it in traversal is a little cumbersome, but to grasp the following points on it (no matter what big or small the tree is):

Forerunner: The root node is the first to visit, then the left and right children are visited;

Sequence: The root node is visited last, and the left and right children are interviewed first;

Middle order: The second visit to the root node, the left child is visited first, and the right child is visited last.

The following picture is an example: I will write the answer to you, and you will study it yourself

Pre-sequence: 0134256

Later Lease Sequence: 3415620

Intermediate sequence: 3140526

Traverse the nodes along the depth of the tree, searching the branches of the tree as deep as possible. If the current node is on all edges, it goes back to the start node of the edge where the current node is located. This is repeated until all reachable nodes of the source node are discovered.

This data structure helps us solve the DFS algorithm quickly. Because the stack isLIFIGso we can put it firstThe right subtree is stacked, and the left subtree is stacked, so that the left subtree is at the top of the stack, which ensures that the left subtree is traversed first and then the right subtree.

When we are pressing, we must make sure that the left and right subtrees of the node are empty, if not, we need to stack the right subtree first, and then the left subtree. Wait until the left and right subtrees are stacked before the nodes are stacked.

Solution

Starting at the root node, traverse the tree's nodes along the width of the tree until all nodes have been traversed.

Because it is traversed layer by layer, we consider introducing itQueuesA binary tree is given, and its node value is returnedFrom the bottom uphierarchical order traversal.

Workaround: Similar to the above implementation, except that the container needs to be flipped over at the end.

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.

The total number of nodes in a complete binary tree at the n level is 2 to the nth power minus 1, that is, 2 n -1 Your complete binary tree has 700 nodes Through 2 n-1<=700, you can calculate the number of layers with full nodes, and the remaining layer is the number of leaf nodes.

The maximum number of nodes in the first 9 layers is 2 9-1=511.

So the number of leaf nodes included is 700 - 511 = 189 <>

In a complete binary tree, there are one or equal number of leaf nodes than non-leaf nodes. The number of nodes in this problem is 699, so the leaf nodes are (699+1) 2=350.

The binary tree is that each node has a maximum of two children, the full binary tree has two children in each node except for the last layer, and the complete binary tree is the last layer of the full binary tree that is continuously missing n points from right to left, n can be 0, it is obvious that the leaf node is equal to the non-leaf node, so the leaf |The sub-nodes are:

n0+n1+n2=700

n0=n2+1

Here, because it's a full binary tree, and the total number of nodes is 700, which is exactly an even number, so n1=1 can solve the equation.

Of course, if it's 701, then n1=0 will do.

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 degree 0 (i.e., the number of leaf nodes), n1 is the total number of nodes with degree 1, and n2 is the total number of nodes with degree 2, it can be seen from the properties 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) 2 or n0 n is obtained 2. Merge into one formula:

n0 (n 1) 2 , the number of leaf nodes can be calculated from the total number of nodes in a complete binary tree.

Number of leaves = number of leaf nodes = 700 2 = 350 (700 nodes in this algorithm include leaf nodes).

The number of copies of leaf nodes is 64

The popular theory of leaf nodes is that there are no children in the binary tree nodes, and du is the last layer of the binary tree, which is called the leaf dao child node. 2 (7-1)=2 6=64 Formula: In a full binary tree with depth n, the number of leaf nodes is:

2 (n-1), i.e. 2 to the n-1 power Insert the formula, n=7, to calculate: 64.

The leaf node is the part of the binary tree node that has no children, that is, the last node in the binary tree is called the leaf node. 2^(7-1)=2^6=64

You're going to have to read more copies of the book.

You can push this out by yourself, this is the multiplier relationship, 1 root node has two child nodes, and these two child nodes each have 2 child nodes, which is 4, and so on. A full binary tree with a depth of 7 should be 2 to the 6th power of leaf nodes (a binary tree with only one root has a depth of 1), i.e. 64 leaf nodes.

There are 7 layers, and the number of nodes with degrees of 0, 1, and 2 is n0, n1, and n2 respectively

Then n0+n1+n2=7=1+n1+n2*2, then n0=n2+1, and n0=1, then n2=0, n1=6, the binary tree is a vertical column, so there are 7 layers in total.

The binary tree is 7 layers deep. If there is only one leaf node, it is obvious that the tree is linear.

Layer 7, it must start from the root node, and each node can only have a maximum of 1 child node.