Quin és el factorial d'un nombre?
- El factorial d'un nombre enter no negatiu és la multiplicació de tots els nombres enters positius menors o iguals a n. Per exemple, el factorial de 6 és 6*5*4*3*2*1, que és 720.
- Un factorial es representa amb un nombre i un ! marca al final. S'utilitza àmpliament en permutacions i combinacions per calcular el total de resultats possibles. Un matemàtic francès Christian Kramp va utilitzar primer l'exclamació.
Creem un programa factorial utilitzant funcions recursives. Fins que el valor no sigui igual a zero, la funció recursiva s'anomenarà a si mateixa. El factorial es pot calcular mitjançant la fórmula recursiva següent.
n! = n * (n – 1)!
n! = 1 si n = 0 o n = 1
A continuació es mostra la implementació:
C++
// C++ program to find> // factorial of given number> #include> using> namespace> std;> > // Function to find factorial> // of given number> unsigned>int> factorial(unsigned>int> n)> > >if> (n == 0> > // Driver code> int> main()> {> >int> num = 5;> >cout <<>'Factorial of '> ><< num <<>' is '> << factorial(num) << endl;> >return> 0;> }> // This code is contributed by Shivi_Aggarwal> |
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vaja en java
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C
// C program to find factorial of given number> #include> > // function to find factorial of given number> unsigned>int> factorial(unsigned>int> n)> {> >if> (n == 0)> >return> 1;> >return> n * factorial(n - 1);> }> > int> main()> {> >int> num = 5;> >printf>(>'Factorial of %d is %d'>, num, factorial(num));> >return> 0;> }> |
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Java
// Java program to find factorial of given number> class> Test {> >// method to find factorial of given number> >static> int> factorial(>int> n)> >{> >if> (n ==>0>)> >return> 1>;> > >return> n * factorial(n ->1>);> >}> > >// Driver method> >public> static> void> main(String[] args)> >{> >int> num =>5>;> >System.out.println(>'Factorial of '> + num> >+>' is '> + factorial(>5>));> >}> }> |
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Python 3
# Python 3 program to find> # factorial of given number> > # Function to find factorial of given number> def> factorial(n):> > >if> n>=>=> 0>:> >return> 1> > >return> n>*> factorial(n>->1>)> > # Driver Code> num>=> 5>;> print>(>'Factorial of'>, num,>'is'>,> factorial(num))> > # This code is contributed by Smitha Dinesh Semwal> |
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C#
// C# program to find factorial> // of given number> using> System;> > class> Test {> >// method to find factorial> >// of given number> >static> int> factorial(>int> n)> >{> >if> (n == 0)> >return> 1;> > >return> n * factorial(n - 1);> >}> > >// Driver method> >public> static> void> Main()> >{> >int> num = 5;> >Console.WriteLine(>'Factorial of '> >+ num +>' is '> + factorial(5));> >}> }> > // This code is contributed by vt_m> |
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PHP
// PHP program to find factorial // of given number // function to find factorial // of given number function factorial($n) { if ($n == 0) return 1; return $n * factorial($n - 1); } // Driver Code $num = 5; echo 'Factorial of ', $num, ' is ', factorial($num); // This code is contributed by m_kit ?>> |
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Javascript
> // Javascript to find factorial> // of given number> > // function to find factorial> // of given number> function> factorial(n) {> >if> (n == 0)>return> 1;> >return> n * factorial(n - 1);> }> > // Driver Code> let num = 5;> document.write(>'Factorial of '> + num +>' is '> + factorial(num));> > // This code is contributed by Saurabh Jaiswal> > > |
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>Sortida
Factorial of 5 is 120>
Complexitat temporal: O(n)
Espai auxiliar: O(n)
Solució iterativa per trobar el factorial d'un nombre:
El factorial també es pot calcular iterativament, ja que la recursió pot ser costosa per a grans nombres. Aquí hem mostrat l'enfocament iteratiu utilitzant bucles for i while.
Enfocament 1: Utilitzant el bucle For
Seguiu els passos per resoldre el problema:
- Utilitzant un bucle for, escriurem un programa per trobar el factorial d'un nombre.
- Al programa s'utilitzarà una variable entera amb un valor d'1.
- Amb cada iteració, el valor augmentarà en 1 fins que sigui igual al valor introduït per l'usuari.
- El factorial del nombre introduït per l'usuari serà el valor final de la variable fet.
A continuació es mostra la implementació de l'enfocament anterior:
C++
// C++ program for factorial of a number> #include> using> namespace> std;> > // function to find factorial of given number> unsigned>int> factorial(unsigned>int> n)> {> >int> res = 1, i;> >for> (i = 2; i <= n; i++)> >res *= i;> >return> res;> }> > // Driver code> int> main()> {> >int> num = 5;> >cout <<>'Factorial of '> ><< num <<>' is '> ><< factorial(num) << endl;> >return> 0;> }> > // This code is contributed by Shivi_Aggarwal> |
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C
#include> > // function to find factorial of given number> unsigned>int> factorial(unsigned>int> n)> {> >int> res = 1, i;> >for> (i = 2; i <= n; i++)> >res *= i;> >return> res;> }> > int> main()> {> >int> num = 5;> >printf>(> >'Factorial of %d is %d'>, num, factorial(num));> >return> 0;> }> |
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Java
peus contra peus
// Java program to find factorial of given number> class> Test {> > >// Method to find factorial of the given number> >static> int> factorial(>int> n)> >{> >int> res =>1>, i;> >for> (i =>2>; i <= n; i++)> >res *= i;> >return> res;> >}> > >// Driver method> >public> static> void> main(String[] args)> >{> >int> num =>5>;> >System.out.println(> >'Factorial of '> + num> >+>' is '> + factorial(>5>));> >}> }> |
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Python 3
# Python 3 program to find> # factorial of given number> > # Function to find factorial of given number> def> factorial(n):> > >res>=> 1> > >for> i>in> range>(>2>, n>+>1>):> >res>*>=> i> >return> res> > # Driver Code> num>=> 5>;> print>(>'Factorial of'>, num,>'is'>,> factorial(num))> > # This code is contributed by Smitha Dinesh Semwal> |
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ssis
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C#
// C# program to find> // factorial of given number> using> System;> > class> Test {> >// Method to find factorial> >// of given number> >static> int> factorial(>int> n)> >{> >int> res = 1, i;> > >for> (i = 2; i <= n; i++)> >res *= i;> >return> res;> >}> > >// Driver method> >public> static> void> Main()> >{> >int> num = 5;> >Console.WriteLine(> >'Factorial of '> + num> >+>' is '> + factorial(5));> >}> }> > // This code is contributed by vt_m> |
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PHP
// function to find factorial // of given number function factorial( $n) { $res = 1; $i; for ($i = 2; $i <= $n; $i++) $res *= $i; return $res; } // Driver Code $num = 5; echo 'Factorial of ', $num, ' is ', factorial($num); // This code is contributed // by anuj_67. ?>> |
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Javascript
> // JavaScript program to find factorial of given number> > >// Method to find factorial of the given number> >function> factorial(n)> >{> >var> res = 1, i;> >for> (i = 2; i <= n; i++)> >res *= i;> >return> res;> >}> > >// Driver method> > >var> num = 5;> >document.write(>'Factorial of '> + num +>' is '> + factorial(5));> > > // This code is contributed by shivanisinghss2110.> > > |
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>Sortida
Factorial of 5 is 120>
Complexitat temporal: O(n)
Espai auxiliar: O(1)
Enfocament 2: Aquest exemple utilitza un bucle while per implementar l'algorisme i trobar el programa factorial.
C
// C program for factorial of a number> #include> > // function to find factorial of given number> unsigned>int> factorial(unsigned>int> n)> {> >if>(n == 0)> >return> 1;> >int> i = n, fact = 1;> >while> (n / i != n) {> >fact = fact * i;> >i--;> >}> >return> fact;> }> > int> main()> {> >int> num = 5;> >printf>(>'Factorial of %d is %d'>, num, factorial(num));> >return> 0;> }> |
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C++
// C++ program for factorial of a number> #include> using> namespace> std;> > // function to find factorial of given> // number using while loop> unsigned>int> factorial(unsigned>int> n)> {> >if>(n == 0)> >return> 1;> >int> i = n, fact = 1;> >while> (n / i != n) {> >fact = fact * i;> >i--;> >}> >return> fact;> }> > // Driver code> int> main()> {> >int> num = 5;> >cout <<>'Factorial of '> ><< num <<>' is '> ><< factorial(num) << endl;> >return> 0;> }> // This code is contributed by Shivi_Aggarwal> |
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Java
// Java program to find factorial of given number> > class> Test {> > >// Method to find factorial of the given number> >static> int> factorial(>int> n)> >{> >if>(n ==>0>)> >return> 1>;> >int> i = n, fact =>1>;> >while> (n / i != n) {> >fact = fact * i;> >i--;> >}> >return> fact;> >}> > >// Driver method> >public> static> void> main(String[] args)> >{> >int> num =>5>;> >System.out.println(> >'Factorial of '> + num> >+>' is '> + factorial(>5>));> >}> }> |
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Python 3
# Python 3 program to find> # factorial of given number> > # Function to find factorial of given number> def> factorial(n):> >if>(n>=>=> 0>):> >return> 1> >i>=> n> >fact>=> 1> > >while>(n>/> i !>=> n):> >fact>=> fact>*> i> >i>->=> 1> > >return> fact> > # Driver Code> num>=> 5>;> print>(>'Factorial of'>, num,>'is'>,> factorial(num))> > # This code is contributed by Smitha Dinesh Semwal> |
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C#
// C# program to find> // factorial of given number> using> System;> > class> Test {> >// Method to find factorial> >// of given number> >static> int> factorial(>int> n)> >{> >if>(n == 0)> >return> 1;> >int> i = n, fact = 1;> >while> (n / i != n) {> >fact = fact * i;> >i--;> >}> >return> fact;> >}> > >// Driver method> >public> static> void> Main()> >{> >int> num = 5;> >Console.WriteLine(> >'Factorial of '> + num> >+>' is '> + factorial(5));> >}> }> |
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Javascript
java conté una subcadena
> >// JavaScript Program to implement> >// the above approach> >// function to find factorial of given> >// number using while loop> >function> factorial(n) {> >if> (n == 0)> >return> 1;> >let i = n, fact = 1;> >while> (Math.floor(n / i) != n) {> >fact = fact * i;> >i--;> >}> >return> fact;> >}> > >// Driver code> >let num = 5;> >document.write(>'Factorial of '> >+ num +>' is '> >+ factorial(num) +>' '>);> > // This code is contributed by Potta Lokesh> > >> |
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>Sortida
Factorial of 5 is 120>
Complexitat temporal: O(N)
Espai auxiliar: O(1)
Enfocament 3: A operador ternari es pot considerar com una abreviatura d'una declaració if...else. Es proporcionen les condicions, juntament amb les declaracions que s'executaran en funció d'elles. Aquí teniu el programa per al factorial amb un operador ternari.
C++
// C++ program to find factorial of given number> #include> using> namespace> std;> > int> factorial(>int> n)> > >// single line to find factorial> >return> (n == 1> > // Driver Code> int> main()> {> >int> num = 5;> >cout <<>'Factorial of '> << num <<>' is '><< factorial(num);> >return> 0;> }> > // This code is contributed by shivanisinghss2110> |
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C
// C++ program to find factorial of given number> #include> > int> factorial(>int> n)> n == 0) ? 1 : n * factorial(n - 1);> > > // Driver Code> int> main()> {> >int> num = 5;> >printf>(>'Factorial of %d is %d'>, num, factorial(num));> >return> 0;> }> > // This code is contributed by Rithika palaniswamy.> |
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Java
// Java program to find factorial> // of given number> class> Factorial {> > >int> factorial(>int> n)> > n ==>0>) ?>1> : n * factorial(n ->1>);> >> > >// Driver Code> >public> static> void> main(String args[])> >{> >Factorial obj =>new> Factorial();> >int> num =>5>;> >System.out.println(> >'Factorial of '> + num> >+>' is '> + obj.factorial(num));> >}> }> > // This code is contributed by Anshika Goyal.> |
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Python 3
# Python 3 program to find> # factorial of given number> > def> factorial(n):> > ># single line to find factorial> >return> 1> if> (n>=>=> 1> or> n>=>=> 0>)>else> n>*> factorial(n>-> 1>)> > > # Driver Code> num>=> 5> print> (>'Factorial of'>, num,>'is'>,> >factorial(num))> > # This code is contributed> # by Smitha Dinesh Semwal.> |
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C#
// C# program to find factorial> // of the given number> using> System;> > class> Factorial {> > >int> factorial(>int> n)> >> > >// Driver Code> >public> static> void> Main()> >{> >Factorial obj =>new> Factorial();> >int> num = 5;> > >Console.WriteLine(> >'Factorial of '> + num> >+>' is '> + obj.factorial(num));> >}> }> > // This code is contributed by vt_m.> |
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PHP
// PHP program to find factorial // of given number function factorial( $n) $n == 0) ? 1: $n * factorial($n - 1); // Driver Code $num = 5; echo 'Factorial of ', $num, ' is ', factorial($num); // This code is contributed by anuj_67. ?>> |
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Javascript
> > // JavaScript program to find factorial of given number> function> factorial(n)> > > // Driver Code> > >var> num = 5;> >document.write(>'Factorial of '> +num +>' is '> + factorial(num));> > // This code is contributed by shivanisinghss2110.> > > |
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>Sortida
làtex de mida de text
Factorial of 5 is 120>
Complexitat temporal: O(n)
Espai auxiliar: O(n)
Problemes en l'escriptura del codi factorial
Quan el valor de n canvia augmenta en 1, el valor del factorial augmenta en n. Per tant, la variable que emmagatzema el valor del factorial hauria de tenir una mida gran. A continuació es mostra el valor de n el factorial del qual es pot emmagatzemar en la mida corresponent.
1. nombre enter –> n<=12
2. llarg llarg int –> n<=19
A partir de les dades anteriors, podem veure que es pot calcular un valor molt petit de n a causa del creixement més ràpid de la funció factorial. Tanmateix, podem trobar el valor mod del factorial de valors més grans prenent mod a cada pas.
La solució anterior provoca un desbordament per a grans nombres. Consulteu el factorial de nombre gran per a una solució que funcioni per a nombres grans.
Si us plau, escriviu comentaris si trobeu algun error al codi/algoritme anterior o trobeu altres maneres de resoldre el mateix problema.