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Heap's algoritmas permutacijoms generuoti

Krūvos algoritmas naudojamas generuoti visas N objektų permutacijas. Idėja yra sugeneruoti kiekvieną permutaciją iš ankstesnio permutacijos, pasirinkdami porą elementų, kad būtų galima apsikeisti, netrukdant kitam N-2 elementai. 
Toliau pateikiama visų n nurodytų skaičių permutacijų generavimo iliustracija.
Pavyzdys:  

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

Algoritmas: 



  1. Algoritmas generuoja (n-1)! Pirmųjų N-1 elementų, besiribojančių su paskutiniu elementu kiekvienam iš jų, permutacijos. Tai sugeneruos visas permutacijas, kurios baigiasi paskutiniu elementu.
  2. Jei n yra nelyginis apsikeitimas pirmaThElementas (i yra skaitiklis, pradedamas nuo 0) ir paskutinis elementas ir pakartokite aukščiau pateiktą algoritmą, kol aš nebus mažiau nei n.
  3. Kiekvienoje iteracijoje algoritmas sukurs visas permutacijas, kurios baigiasi dabartiniu paskutiniu elementu.

Įgyvendinimas:   

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#
// 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>

Išvestis
1 2 3 2 1 3 3 1 2 1 3 2 2 3 1 3 2 1 

Laiko sudėtingumas: O (n*n!) Kur n yra duoto masyvo dydis.
Pagalbinė erdvė: O (n) Nr.

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