Basic knowledge of binary tree, BFC, DFS

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Computer science
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Copyright notice ： This paper is about CSDN Blogger 「 Pu Shangqing sky 」 The original article of

Knowledge point

Binary tree

• If specified The number of node layers of the root is 1, Then the... Of a non empty binary tree i There is a maximum of 2 Of i-1 Power （i > 0） Nodes
• If the root node depth of the binary tree is specified as 1, Then the depth is K Two fork tree Maximum number of nodes 2 Of k Power -1
• For any binary tree , If the number of leaf nodes is n0, Degree is 2 The number of non leaf nodes is n2, be n0=n2+1
• have n The depth of a complete binary tree of nodes k be equal to log With 2 Bottom n+1, Rounding up
• Subscript relation
  If the parent node is known parent The subscript
  Left the child ：leftChild = 2parent+1
  The right child ：rightChild = 2parent +2
  If the child is known child node
  parent = （child-1）/2

Binary tree traversal

DFS： Depth-first traversal - Stack

The former sequence traversal ：

traversal order : recursive
Put the root node in front
1. First , Handle The root node
2. next , Complete traversal of the root The left subtree
3. Last , Complete traversal of the root Right subtree

① We are from Root node Start ,
namely ： A{ } { }
② Because we are traversing first The left subtree
therefore , A { B{}{} } { }
A { B{ D{}{} }{} } { }

A { B{ D{}{undefinedG} }{} } { }
③ Last traversal Right subtree ：

A { B{ D{}{undefinedG} }{} } { C{}{} }

A { B{ D{}{undefinedG} }{} } { C{undefinedE}{} }

A { B{ D{}{undefinedG} }{} } { C{undefinedE}{ F{}{} } }

A { B{ D{}{undefinedG} }{} } { C{undefinedE}{ F{undefinedH}{} } }

So we get the result of our first order traversal ：
A B D G C E F H

In the sequence traversal

• traversal order ：（ recursive ）
  1. First traverse the whole tree The left subtree
  2. Intermediate treatment The root node
  3. Then traverse the whole tree Right subtree
  
  Let's go through The left subtree , The traversal method is In the sequence traversal

{ {}B{} } A { }

{ { {}D{} }B{} } A { }

{ { {}D{undefinedG} }B{} } A { }

Let's go over Right subtree , The traversal method is still In the sequence traversal

{ { {}D{undefinedG} }B{} } A { {}C{} }

{ { {}D{undefinedG} }B{} } A { {E}C{} }

{ { {}D{undefinedG} }B{} } A { {undefinedE}C{ {}F{} } }

{ { {}D{undefinedG} }B{} } A { {undefinedE}C{ {H}F{} } }

So we get our In the sequence traversal The result ：
D G B A E C H F

After the sequence traversal

• traversal order （ recursive ）
  1. First traversal The left subtree
  2. Re traversal Right subtree
  3. Finally deal with The root node
  
  Let's go through The left subtree , The traversal method is After the sequence traversal ：

{ {}{}B } { }A

{ { {}{}D }{}B } { }A

{ { {}{undefinedG}D }{}B } { }A

Let's go over Right subtree , The traversal method is still After the sequence traversal

{ { {}{undefinedG}D }{}B } { }A

{ { {}{undefinedG}D }{}B } { {}{}C }A

{ { {}{undefinedG}D }{}B } { {undefinedE}{}C }A

{ { {}{undefinedG}D }{}B } { {undefinedE}{ {}{}F }C }A

{ { {}{undefinedG}D }{}B } { {undefinedE}{ {undefinedH}F}{}C }A

So we get our After the sequence traversal The result ：
G D B E H F C A

BFC： Breadth first traversal

Sequence traversal （ queue ）

purpose ： Determine whether it is a complete binary tree

• From top to bottom , Traverse the binary tree from left to right
• 

Code order

1. Start-up phase ： Put the root node in the queue

2. Turn on the cycle , Until the queue is empty （isEmpty）

• Take the first node from the queue
• Sequence traversal passes through this node （ Print ）
• Put the left of the node / Put the right child node into the queue
  

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