Hvad er fakultetet for et tal?
- Faktoriel af et ikke-negativt heltal er multiplikationen af alle positive heltal mindre end eller lig med n. For eksempel er fakultet på 6 6*5*4*3*2*1, hvilket er 720.
- En faktor er repræsenteret ved et tal og et ! mærke til sidst. Det er meget brugt i permutationer og kombinationer til at beregne de samlede mulige udfald. En fransk matematiker Christian Kramp brugte først udråbet.
Lad os oprette et faktorielt program ved hjælp af rekursive funktioner. Indtil værdien ikke er lig med nul, vil den rekursive funktion kalde sig selv. Faktoriel kan beregnes ved hjælp af følgende rekursive formel.
n! = n * (n – 1)!
n! = 1 hvis n = 0 eller n = 1
Nedenfor er implementeringen:
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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flette sorter i 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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Python3
# 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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eksempler på python-programmer
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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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>Produktion
Factorial of 5 is 120>
Tidskompleksitet: På)
Hjælpeplads: På)
Iterativ løsning til at finde fakultet af et tal:
Faktoriel kan også beregnes iterativt, da rekursion kan være dyrt for store tal. Her har vi vist den iterative tilgang ved at bruge både for og while loops.
Fremgangsmåde 1: Brug af For loop
Følg trinene for at løse problemet:
- Ved hjælp af en for-løkke vil vi skrive et program til at finde et tals fakultet.
- En heltalsvariabel med værdien 1 vil blive brugt i programmet.
- Med hver iteration vil værdien stige med 1, indtil den er lig med den værdi, som brugeren har indtastet.
- Faktoren for det tal, som brugeren har indtastet, vil være den endelige værdi i faktavariablen.
Nedenfor er implementeringen af ovenstående tilgang:
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
// 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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Python3
# 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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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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>Produktion
Factorial of 5 is 120>
Tidskompleksitet: På)
Hjælpeplads: O(1)
Fremgangsmåde 2: Dette eksempel bruger en while-løkke til at implementere algoritmen og finde det faktorielle program.
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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Python3
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# 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
> >// 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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>Produktion
Factorial of 5 is 120>
Tidskompleksitet: PÅ)
Hjælpeplads: O(1)
Fremgangsmåde 3: EN ternær operatør kan opfattes som en stenografi for en if…else-sætning. Betingelserne er angivet sammen med erklæringer, der skal udføres baseret på dem. Her er programmet til faktoriel brug af en ternær operator.
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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Python3
# 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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>Produktion
pandas loc
Factorial of 5 is 120>
Tidskompleksitet: På)
Hjælpeplads: På)
Problemer med at skrive kode af factorial
Når værdien af n ændringer stiger med 1, stiger værdien af faktoren med n. Så den variabel, der lagrer værdien af faktorial, bør have en stor størrelse. Følgende er værdien af n, hvis factorial kan lagres i den respektive størrelse.
1. heltal –> n<=12
2. lang lang int –> n<=19
Ud fra ovenstående data kan vi se, at en meget lille værdi af n kan beregnes på grund af den hurtigere vækst af faktorfunktionen. Vi kan dog finde mod-værdien af factorial af større værdier ved at tage mod ved hvert trin.
Ovenstående løsning forårsager overløb for store tal. Se venligst factorial af stort tal for en løsning, der fungerer for store tal.
Skriv venligst kommentarer, hvis du finder en fejl i ovenstående kode/algoritme, eller find andre måder at løse det samme problem på.