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Summary of binary tree recursive routines
2022-07-05 23:07:00 【Bright morning light】
The time complexity of all previous binary tree recursion routines is O ( N ) O(N) O(N), among N N N Is the number of nodes in a binary tree , And they are all optimal solutions .
A node gets information from left and right children , Then integrate into this node , At this time, the left and right children are no longer needed , The parent node of this node also repeats this process , The whole process is equivalent to After the sequence traversal , Do dynamic planning on the tree , So it's called tree dp.
This routine includes two levels :
Thought reminder
How to achieve the goal :X How to achieve the goal of a binary tree with root node ?
Means of implementation : Ask for information from the left and right trees , List the possibilities , This possibility must be based on the information from the left and right trees ( Constant time can be obtained ), The processed information of the same magnitude is also constant time .
Design information body , Analyze possibilities , The common classification is “ And target X of ” and “ And target X irrelevant ”.Templates
① DesignInfo
Information body ;
②process
function :process
Function must returnInfo
; When empty , If the value is bad, it will return null , Set it if it is good ;
③ By default, the left tree information is obtained first , Then get the right tree information ;
④ After analyzing the possibility , hold X All the necessary information is processed , This is highly templated .
This routine can solve most binary tree problems, especially tree type dp problem , The essence is to use Recursively traversing a binary tree The convenience of .
The whole process is summarized as follows :
1) Suppose X Node as root , Suppose you can ask X Left tree and X The right tree wants any information
2) Under the assumptions of the previous step , Discuss with X Is the tree of the root node , Got the answer possibility ( above all )
3) After listing all the possibilities , Determine what kind of information you need from the left tree and the right tree
4) Find the complete set of left tree information and right tree information , Is the information that any subtree needs to return S
5) Recursive functions return S, Every sub tree asks so
6) Write code , In the code, consider how to integrate the information of the left tree and the information of the right tree into the information of the whole tree
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