ALGORITME DE HEAP PER GENERAR PERMUTACIONS

Algoritme de Heap s'utilitza per generar totes les permutacions dels n objectes. La idea és generar cada permutació a partir de la permutació anterior escollint un parell d’elements per intercanviar -se sense molestar l’altre N-2 elements.
A continuació, es mostra la il·lustració de generar totes les permutacions de n números donats.
Exemple:

  Input:   1 2 3   Output:   1 2 3 2 1 3 3 1 2 1 3 2 2 3 1 3 2 1

Algoritme:

L’algoritme genera (N-1)! permutacions dels primers elements N-1 que es troben al costat de l'últim element a cadascun d'aquests. Això generarà totes les permutacions que s’acaben amb l’últim element.
Si n és estrany intercanvi el primer i el darrer element i si n és fins i tot, canvia el i^thElement (I és el comptador a partir de 0) i l'últim element i repeteix l'algoritme anterior fins que I sigui inferior a N.
En cada iteració, l'algoritme produirà totes les permutacions que acaben amb l'últim element actual.

Implementació:

C++

// C++ program to print all permutations using // Heap's algorithm #include    using namespace std; // Prints the array void printArr(int a[] int n) {  for (int i = 0; i < n; i++)  cout << a[i] << ' ';  printf('n'); } // Generating permutation using Heap Algorithm void heapPermutation(int a[] int size int n) {  // if size becomes 1 then prints the obtained  // permutation  if (size == 1) {  printArr(a n);  return;  }  for (int i = 0; i < size; i++) {  heapPermutation(a size - 1 n);  // if size is odd swap 0th i.e (first) and   // (size-1)th i.e (last) element  if (size % 2 == 1)  swap(a[0] a[size - 1]);  // If size is even swap ith and   // (size-1)th i.e (last) element  else  swap(a[i] a[size - 1]);  } } // Driver code int main() {  int a[] = { 1 2 3 };  int n = sizeof a / sizeof a[0];  heapPermutation(a n n);  return 0; }

Java

// Java program to print all permutations using // Heap's algorithm import java.io.*; class HeapAlgo {  // Prints the array  void printArr(int a[] int n)  {  for (int i = 0; i < n; i++)  System.out.print(a[i] + ' ');  System.out.println();  }  // Generating permutation using Heap Algorithm  void heapPermutation(int a[] int size int n)  {  // if size becomes 1 then prints the obtained  // permutation  if (size == 1)  printArr(a n);  for (int i = 0; i < size; i++) {  heapPermutation(a size - 1 n);  // if size is odd swap 0th i.e (first) and  // (size-1)th i.e (last) element  if (size % 2 == 1) {  int temp = a[0];  a[0] = a[size - 1];  a[size - 1] = temp;  }  // If size is even swap ith   // and (size-1)th i.e last element  else {  int temp = a[i];  a[i] = a[size - 1];  a[size - 1] = temp;  }  }  }  // Driver code  public static void main(String args[])  {  HeapAlgo obj = new HeapAlgo();  int a[] = { 1 2 3 };  obj.heapPermutation(a a.length a.length);  } } // This code has been contributed by Amit Khandelwal.

Python3

# Python program to print all permutations using # Heap's algorithm # Generating permutation using Heap Algorithm def heapPermutation(a size): # if size becomes 1 then prints the obtained # permutation if size == 1: print(a) return for i in range(size): heapPermutation(a size-1) # if size is odd swap 0th i.e (first) # and (size-1)th i.e (last) element # else If size is even swap ith # and (size-1)th i.e (last) element if size & 1: a[0] a[size-1] = a[size-1] a[0] else: a[i] a[size-1] = a[size-1] a[i] # Driver code a = [1 2 3] n = len(a) heapPermutation(a n) # This code is contributed by ankush_953 # This code was cleaned up to by more pythonic by glubs9

// C# program to print all permutations using // Heap's algorithm using System; public class GFG {  // Prints the array  static void printArr(int[] a int n)  {  for (int i = 0; i < n; i++)  Console.Write(a[i] + ' ');  Console.WriteLine();  }  // Generating permutation using Heap Algorithm  static void heapPermutation(int[] a int size int n)  {  // if size becomes 1 then prints the obtained  // permutation  if (size == 1)  printArr(a n);  for (int i = 0; i < size; i++) {  heapPermutation(a size - 1 n);  // if size is odd swap 0th i.e (first) and  // (size-1)th i.e (last) element  if (size % 2 == 1) {  int temp = a[0];  a[0] = a[size - 1];  a[size - 1] = temp;  }  // If size is even swap ith and  // (size-1)th i.e (last) element  else {  int temp = a[i];  a[i] = a[size - 1];  a[size - 1] = temp;  }  }  }  // Driver code  public static void Main()  {  int[] a = { 1 2 3 };  heapPermutation(a a.Length a.Length);  } } /* This Java code is contributed by 29AjayKumar*/

JavaScript

<script> // JavaScript program to print all permutations using // Heap's algorithm // Prints the array function printArr(an) {  document.write(a.join(' ')+'  
');   } // Generating permutation using Heap Algorithm function heapPermutation(asizen) {  // if size becomes 1 then prints the obtained  // permutation  if (size == 1)  printArr(a n);    for (let i = 0; i < size; i++) {  heapPermutation(a size - 1 n);    // if size is odd swap 0th i.e (first) and  // (size-1)th i.e (last) element  if (size % 2 == 1) {  let temp = a[0];  a[0] = a[size - 1];  a[size - 1] = temp;  }    // If size is even swap ith  // and (size-1)th i.e last element  else {  let temp = a[i];  a[i] = a[size - 1];  a[size - 1] = temp;  }  } } // Driver code let a=[1 2 3]; heapPermutation(a a.length a.length); // This code is contributed by rag2127 </script>

Producció

1 2 3 2 1 3 3 1 2 1 3 2 2 3 1 3 2 1

Complexitat del temps: O (n*n!) On n és la mida de la matriu donada.
Espai auxiliar: O (n) per a un espai de pila recursiu de la mida N.

Referències:
1. 'https://en.wikipedia.org/wiki/heap%27s_algorithm#cite_note-3

TechCodeview

Algoritme de Heap per generar permutacions