in order to understand recursion must first understand recursion

in order to understand recursion must first understand recursion

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lot of repeated computation, resulting in waste. In contrast, the iterative memory requirements are much less, because the iteration is the result of each step of the operation to participate in the next operation, does not produce too many duplicate calculations, so the calculation is very fast, but the iterative mode of thinking is not easy to figure out, need to replace the intermediate number. and the tail recursion, I think it is a new algorithm

Although I have read a few articles, I have summarized them.
First, call yourself
Second, the order is large to small.
Third: When the variable is 1, the recursive if (temp = 1) return 1 is introduced; that is, the exit must be set; otherwise, the loop will continue.
Fourth:
When a function calls itself, it allocates memory for the new local variables and parameters in the stack, and the function code re-runs with these variables and parameters.

layer is returned, this layer of local variables will be popped from the stack, destroyed. Therefore, we should never use the return of local variables when designing recursive programs to get the changes caused by the next layer of operations to local variables, because they are not returned. See diagram below for details.(2) Return in line 15, this code is necessary, cannot default program does not conform to the recursive condition, will return itself. If you do not write this sentence here,

Image (including dynamic graph) is an efficient way of transmitting information, which can enhance the response intensity of imagery, memory and thinking. The so-called picture wins thousands of words, that is the truth.
Today, we have compiled 10 sheets of GIFs to help you understand the specific operation of the concepts of cyclic, recursive, and binary retrieval. Code instances are written in the Python language.
First, the circulation
GIF 1: T

General recursive formInt fun (int n) {Mathematical model:
N = 0 0
N! = 0 f (n)
General Form of tail recursionInt fun (int sum, int n) {
Comparison of Two recursive forms:
Recursion: f (n). The return value is used by the caller.
Tail recursion: f (m, n). The return value is not used by the caller.
In-depth comparison of the two types of recursion:
Due

--- Binary Tree recursion (non-recursion) Implement first-order, middle-order, and post-order traversal (with code), --- Binary Tree
Today, I said that I did not touch the code, but I still couldn't resist it. I learned how to learn data structures and algorithms. Let's talk

*New= (num*)malloc(sizeof(NUM));//2nd step, create pointer new, for storing new data $ if(New==NULL) the { theprintf"failed to allocate memory \ n"); the return; the } - New->num = num;//School Number in New->next = NULL;//last point to null the theP->next =New;//3rd step, p points to new About } the the voidPrint (NUM *head)//sequential printing, non-recursive the { +NUM *p = head;//Create a pointer for moving - intCount =0;//counter the Bayi while(P->nex

Binary Tree pre-order middle-order post-order traversal (of course not recursive !), Binary Tree Recursion
The three traversal methods of Binary Trees have always been an interview question. It is the simplest way to test a person's understanding of recursion to write three

clause from left to right, andthrough backtracking is recovered from the error selection. These procedural aspects have an important impact on how your queries actually work. We've seen some examples in their declarative and procedural mismatches (remember P:-P?). ), Next, wewill continue to see that it is easy to define a program that is logically the same, but very different in implementation, in Prolog. Let us consider the following scenario.Please recall our definition of "younger generatio

(Programming training) Let's look back again. The data structure is the pre-order, middle-order, and post-order traversal (recursion) of the binary tree, and then let's look back at the binary tree.
I recently reviewed the data structure and took a look at the code I wrote in my freshman year. After reading the code, I

; int Val; BOOL Isnode; Stack_element (node *_node, int _val, bool _isnode): Node (_node), Val (_val), Isnode (_isnode) {}};vectorThird, post-sequential traversalAnalysis:1. The element that is considered to be pressed into the stack is the value of the node or node, as in the middle sequence traversal.2, the only difference is the traversal order, so the middle sequence traversal of the code (20~22 line) slightly changed.struct node{ int

We usually use recursion to implement infinitus classification. We all know that recursion is very inefficient. The following describes an improved forward-order traversal tree algorithm, which does not apply to recursion to implement infinitus classification, it is more efficient to achieve tree-level structure with l

Php uses the pre-order traversal tree to implement non-recursive Infinitus classification and recursion. Php uses the forward-order traversal tree to implement an infinite-pole classification without recursion. recursive examples in this article show that php uses the forward-order

Php uses the pre-order traversal tree to implement non-recursive infinitus classification and Recursion
This example describes how php uses a forward-order traversal tree to implement infinitely polar classification without recursion. Share it with you for your reference. The details are as follows:
We usually use

Public classtest{Intermediate VariablesPrivateString res = "0";Method Public intFuncinti) { if(i>0){ inttemp = i%10; Res= res+string.valueof (temp); Func (i/10); } returninteger.valueof (RES); } Public Static voidMain (string[] args) {Test T=NewTest (); intA = T.func (987); System.out.println (The inverse number is: "+a); }}This function is done using recursive thinking.The main idea is to get the last one by dividing by 10, using re

internallyCharacteristics:There must be a definite end condition, no end condition will result in exceeding the maximum number of recursive layers (English) error, maximum 999 levelsEvery step deeper, the problem should be less than it was last time.Inefficient, function is called by the stack, may cause stack OverflowIn Python, division by default can be the result of a decimal, and if you want to take an integer, truncate (//) with an int (1/2). ）Recursive Plus breakpoint debuggingFunction-Ty

The data structure is recursive. After a deep understanding, write a three-Order Non-recursive version.
//测试数据：abd##eg##h##c#f###include
[Data structure] a binary tree is traversed in ascending order before non-recursion.

Python is encapsulated into a dictionarydefFun_test6 (a,**Kvavgs):Print(a)Print(Kvavgs) Fun_test6 ("a", x="b", y="C", z="D")#Multiple return Valuesdeffun_test7 ():return0,"a",("b","C"),["D","e","e"],{"F","g"},{"name":"Zhang"," Age": 20}res=fun_test7 ()#This returns the returned result into a tuplePrint(RES)#recursive functions that function themselves to call themselves#recursive functions must have a few three special: 1. There are definite end conditions, 2 each entering a deeper layer, the p

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