递归递归与迭代（Recursion and iteration）

递归与迭代Recursion and iteration

Recursion and iteration, recursion and iteration

Recursion and iteration

Iteration (iterative) and recursion (recursive) can betransformed mutually. Recursion is often required to beconverted into iteration. Because recursion takes a lot of time.GCD GCD, also known as the common denominator, English GreatestCommon Divider, abbreviated GCD.

N (≥2) natural numbers A1, A2,„the greatest common divisorof an usually has two definitions:

1. the largest of all their common factors;

2. if the natural number m is the common factor of the n naturalnumber, and the arbitrary common factor of the N number is thefactor of M, it is called M is the greatest common factor ofthe N number

A1, A2, „the greatest common factor of an is often referredto as (A1, A2, &hellip, an) in China, and G.C.D. (A1, A2, &hellip,an) is the international universal symbol

Example: the GCD program: (the following procedure is describedin pseudocode) recursive method: procedure (a, b) GCD / a&gtb&gt =0//; if hypothesis; b==0 then return (a) else return (GCD(b a, mod b)) //mod operation mode operation, this type of Italyfor a with the simulation of B / / endifend GCD

Converted to iteration: procedure GCD2 (a, b) while B! =0 dot=b; b= (a mod b) ; a=t; repeat return (a) end GCD2

Another iteration of example:for ((?)) {a[2] =a[0] +a[1] ; a[0]= a[1] ; a[1] = a[2] ; } is repeatedly applying a formulaA discussion:

Looked at such a question, ask, “ program structure design ofthe three basic structure, order, selection, circulation is notnecessary? ” of course, you know, there' s just enough of thesethree, but can you do less? The answer is “ it can be ” thereason is that recursion can take the place of loops, such asthe following function of summing the elements in an array:Float Rsum (float a[], const int n) {if (n<=0) return 0; elsereturn Rsum (a, n – 1) + a[n – 1] ; }

In fact:

Sum for (int = 0; I = 0; I < n i++; sum = a[i]) ;

But the fact is that in any language there is a loop structure,but not any language supports recursion; in a word, recursionis universal, but no recursion is not impossible. However, Isee some people today, no matter what the problem must berecursive, obviously cycle is the first thought of the method,but the brains to find a recursive algorithm.

Often see “ recursive algorithm ” ; “ non recursivealgorithm ” this formulation does not have semantic problems,

and I also use——recursive algorithm. But this is notexplained, recursive algorithm, he is a kind of thought, it isbecause of the guiding ideology of an algorithm is recursive,so it is called recursive algorithm; and arecursive algorithm,when you do not use recursion as the guiding ideology, thusobtained is non recursive algorithm algorithm.——and forthe problem of cyclic energy processing, there is a recursivesolution, in this sense, the cycle algorithm can be called nonrecursive algorithm.

I didn' t mean what else in the US, just want to let you know,can write what kind of algorithm, the key is to look at yourguidance algorithm at. If you start to think of the method ofcirculation, the iteration, you bother to find what Godconsumption recursive algorithm——even found a seeminglysimple “ ” the algorithm is actually inefficient because ofhis waste——you still do this useless what? A typicalscholastic abuse. If you just think of recursion, you want touse the stack to eliminate recursion, and what you do is justdo what the system does,

How much more can you improve your efficiency? Blindsuperstition to eliminate recursion will definitely improveefficiency is groundless——the way you do the work, if notallowed, even worse than the original system practices.From the beginning of the school permutation, the factorial Iknow is like this, n = = 1× 2ׄ„n. If I were to writethe factorial algorithm, I would just think of 1 to n. Again,the Fibonacci sequence, if someone described by naturallanguage, must be the case, the start of the two is 0, 1, each

will be in front of the two and. So let me write and only get

“ save the first two items, and then add to get the result ”iterative solution.——as long as it is now almost as theytalked about recursive stage, called: “ the definition isrecursive, so we write recursive algorithm ” . What I want toask is, where does the recursive abstraction come from? It isdefined from the factorial of a cyclic process abstraction,definition of the Fibonacci sequence is an iterativeabstraction. So, we start from a fact is not recursivedefinition of a recursive, and then we said, “ because theproblem definition is recursive, it is easy towritearecursivealgorithm, then said, ” “we also can be transformed into therecursive algorithm, cyclic iterative algorithm for ” , feelslike 1÷3=0.33„„0. 33„„×, 3=0.99„„then, we spenta great mind to understand 1 = 0.99„„.

There are some people who are bored, talked to the twomentionedrecursive results, none of the students see that the definitionof factorial no doubt, no one for the recursive factorialfunction with admiration of——blind what? So, if you wantto speak to recursion, a compelling example of this example isFeihannuota.

A few questions about iterative recursion for learningreference

1 : iterative method for solving equation problems: functioncountValue () to achieve the following functions: using thesimple iterative method to find the equation: a real root ofCOS (x) -x=0. Xn+1=cos (Xn) iteration steps are as follows: (1)X1 =0; (2) X0=X1, to assign the value of X1 to X0; (3) X1=cos

(X0) , obtained a new X1 ; (4) if the absolute value of X0-X1 isless than 0.000001, step (5) , or step (2) ; (5) the X1 equationcos (X) is a real root -X=0, returned as the value of thefunction

Float countValue (void)

{x1=0.0; do {x0=x1; x1=cos (x0) ; } while (FAB (x0-x1) >=0.000001) return X1; }