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Algoritem hitre izbire

Quickselect je izbirni algoritem za iskanje k-tega najmanjšega elementa na neurejenem seznamu. Povezan je z hitro razvrščanje algoritem za razvrščanje.
Primeri:

Input: arr[] = {7, 10, 4, 3, 20, 15} k = 3 Output: 7 Input: arr[] = {7, 10, 4, 3, 20, 15} k = 4 Output: 10>

Algoritem je podoben QuickSortu. Razlika je v tem, da se namesto ponavljanja za obe strani (po iskanju vrtišča) ponavlja samo za del, ki vsebuje k-ti najmanjši element. Logika je preprosta, če je indeks particioniranega elementa večji od k, se ponovimo za levi del. Če je indeks enak k, smo našli k-ti najmanjši element in se vrnemo. Če je indeks manjši od k, se ponovimo za desni del. To zmanjša pričakovano kompleksnost z O(n log n) na O(n), z najslabšim primerom O(n^2).

function quickSelect(list, left, right, k) if left = right return list[left] Select a pivotIndex between left and right pivotIndex := partition(list, left, right, pivotIndex) if k = pivotIndex return list[k] else if k  C++14       // CPP program for implementation of QuickSelect  #include  using namespace std;    // Standard partition process of QuickSort().  // It considers the last element as pivot  // and moves all smaller element to left of  // it and greater elements to right  int partition(int arr[], int l, int r)  {   int x = arr[r], i = l;   for (int j = l; j <= r - 1; j++) {   if (arr[j] <= x) {   swap(arr[i], arr[j]);   i++;   }   }   swap(arr[i], arr[r]);   return i;  }    // This function returns k'th smallest  // element in arr[l..r] using QuickSort  // based method. ASSUMPTION: ALL ELEMENTS  // IN ARR[] ARE DISTINCT  int kthSmallest(int arr[], int l, int r, int k)  {   // If k is smaller than number of   // elements in array   if (k>0 && k<= r - l + 1) {     // Partition the array around last   // element and get position of pivot   // element in sorted array   int index = partition(arr, l, r);     // If position is same as k   if (index - l == k - 1)   return arr[index];     // If position is more, recur   // for left subarray   if (index - l>k - 1) vrni kthNajmanjši (arr, l, indeks - 1, k);     // Drugače se ponovi za desno podmatriko vrni kthSmallest(arr, index + 1, r, k - index + l - 1);   } // Če je k več kot število // elementov v matriki return INT_MAX;  } // Program gonilnika za testiranje zgornjih metod int main() { int arr[] = { 10, 4, 5, 8, 6, 11, 26 };   int n = sizeof(arr) / sizeof(arr[0]);   int k = 3;   cout<< 'K-th smallest element is '  << kthSmallest(arr, 0, n - 1, k);   return 0;  }   Java       // Java program of Quick Select  import java.util.Arrays;    class GFG {     // partition function similar to quick sort   // Considers last element as pivot and adds   // elements with less value to the left and   // high value to the right and also changes   // the pivot position to its respective position   // in the final array.   public static int partition(int[] arr, int low,   int high)   {   int pivot = arr[high], pivotloc = low;   for (int i = low; i <= high; i++) {   // inserting elements of less value   // to the left of the pivot location   if (arr[i]   int temp = arr[i];   arr[i] = arr[pivotloc];   arr[pivotloc] = temp;   pivotloc++;   }   }     // swapping pivot to the final pivot location   int temp = arr[high];   arr[high] = arr[pivotloc];   arr[pivotloc] = temp;     return pivotloc;   }     // finds the kth position (of the sorted array)   // in a given unsorted array i.e this function   // can be used to find both kth largest and   // kth smallest element in the array.   // ASSUMPTION: all elements in arr[] are distinct   public static int kthSmallest(int[] arr, int low,   int high, int k)   {   // find the partition   int partition = partition(arr, low, high);     // if partition value is equal to the kth position,   // return value at k.   if (partition == k - 1)   return arr[partition];     // if partition value is less than kth position,   // search right side of the array.   else if (partition 1)   return kthSmallest(arr, partition + 1, high, k);     // if partition value is more than kth position,   // search left side of the array.   else  return kthSmallest(arr, low, partition - 1, k);   }     // Driver Code   public static void main(String[] args)   {   int[] array = new int[] { 10, 4, 5, 8, 6, 11, 26 };   int[] arraycopy   = new int[] { 10, 4, 5, 8, 6, 11, 26 };     int kPosition = 3;   int length = array.length;     if (kPosition>dolžina) { System.out.println('Indeks zunaj meja');   } else { // najdi k-to najmanjšo vrednost System.out.println( 'K-ti najmanjši element v nizu : ' + kthSmallest(arraycopy, 0, length - 1, kPosition));   } } } // To kodo je prispevala Saiteja Pamulapati Python3 # Python3 program Quick Select # Standardni proces particije QuickSort().  # Zadnji element obravnava kot vrtišče # in premakne vse manjše elemente levo od # njega in večje elemente na desno def partition(arr, l, r): x = arr[r] i = l za j v obsegu(l, r): če arr[j]<= x:   arr[i], arr[j] = arr[j], arr[i]   i += 1    arr[i], arr[r] = arr[r], arr[i]   return i    # finds the kth position (of the sorted array)  # in a given unsorted array i.e this function  # can be used to find both kth largest and  # kth smallest element in the array.  # ASSUMPTION: all elements in arr[] are distinct  def kthSmallest(arr, l, r, k):     # if k is smaller than number of   # elements in array   if (k>0 in k<= r - l + 1):     # Partition the array around last   # element and get position of pivot   # element in sorted array   index = partition(arr, l, r)     # if position is same as k   if (index - l == k - 1):   return arr[index]     # If position is more, recur   # for left subarray   if (index - l>k - 1): vrni kthNajmanjši(arr, l, indeks - 1, k) # Drugače se ponovi za desno podmatriko vrni kthNajmanjši(arr, indeks + 1, r, k - indeks + l - 1) print('Indeks izven bound') # Koda gonilnika arr = [ 10, 4, 5, 8, 6, 11, 26 ] n = len(arr) k = 3 print('K-ti najmanjši element je ', end = ' ') print(kthSmallest(arr, 0, n - 1, k)) # To kodo je prispeval Muskan Kalra.   C# // program C# za hitro izbiro s sistemom;    class GFG { // funkcija razdeljevanja, podobna hitremu razvrščanju // Zadnji element obravnava kot vrtišče in doda // elemente z manjšo vrednostjo na levo in // visoko vrednostjo na desno ter prav tako spremeni // položaj vrtišča v njegov ustrezni položaj / / v matriki samo za branje.   statične int particije (int []arr,int nizko, int visoko) { int pivot = arr[visoko], pivotloc = nizko, temp;   za (int i = nizko; i<= high; i++)   {   // inserting elements of less value   // to the left of the pivot location   if(arr[i]   {   temp = arr[i];   arr[i] = arr[pivotloc];   arr[pivotloc] = temp;   pivotloc++;   }   }     // swapping pivot to the readonly pivot location   temp = arr[high];   arr[high] = arr[pivotloc];   arr[pivotloc] = temp;     return pivotloc;   }     // finds the kth position (of the sorted array)   // in a given unsorted array i.e this function   // can be used to find both kth largest and   // kth smallest element in the array.   // ASSUMPTION: all elements in []arr are distinct   static int kthSmallest(int[] arr, int low,   int high, int k)   {   // find the partition   int partition = partitions(arr,low,high);     // if partition value is equal to the kth position,   // return value at k.   if(partition == k)   return arr[partition];     // if partition value is less than kth position,   // search right side of the array.   else if(partition   return kthSmallest(arr, partition + 1, high, k );     // if partition value is more than kth position,   // search left side of the array.   else  return kthSmallest(arr, low, partition - 1, k );   }     // Driver Code   public static void Main(String[] args)   {   int[] array = {10, 4, 5, 8, 6, 11, 26};   int[] arraycopy = {10, 4, 5, 8, 6, 11, 26};     int kPosition = 3;   int length = array.Length;     if(kPosition>dolžina) { Console.WriteLine('Indeks izven meja');   } else { // najdi k-to najmanjšo vrednost Console.WriteLine('K-ti najmanjši element v nizu : ' + kthSmallest(arraycopy, 0, length - 1, kPosition - 1));   } } } // To kodo je prispeval 29AjayKumar Javascript // Javascript program Quick Select // particijska funkcija, podobna hitremu razvrščanju // Zadnji element obravnava kot vrtilni in doda // elemente z manjšo vrednostjo na levi strani in // visoko vrednostjo v desno in prav tako spremeni // položaj vrtenja v njegov ustrezni položaj // v končnem nizu.  funkcija _particija(arr, nizka, visoka) { let pivot = arr[visoka], pivotloc = nizka;   za (naj i = nizko; i<= high; i++)   {     // inserting elements of less value   // to the left of the pivot location   if (arr[i]   {   let temp = arr[i];   arr[i] = arr[pivotloc];   arr[pivotloc] = temp;   pivotloc++;   }   }     // swapping pivot to the final pivot location   let temp = arr[high];   arr[high] = arr[pivotloc];   arr[pivotloc] = temp;     return pivotloc;  }    // finds the kth position (of the sorted array)   // in a given unsorted array i.e this function   // can be used to find both kth largest and   // kth smallest element in the array.   // ASSUMPTION: all elements in arr[] are distinct  function kthSmallest(arr, low, high, k)  {     // find the partition   let partition = _partition(arr, low, high);     // if partition value is equal to the kth position,   // return value at k.   if (partition == k - 1)   return arr[partition];     // if partition value is less than kth position,   // search right side of the array.   else if (partition   return kthSmallest(arr, partition + 1, high, k);     // if partition value is more than kth position,   // search left side of the array.   else  return kthSmallest(arr, low, partition - 1, k);  }    // Driver Code  let array = [ 10, 4, 5, 8, 6, 11, 26];  let arraycopy = [10, 4, 5, 8, 6, 11, 26 ];  let kPosition = 3;  let length = array.length;    if (kPosition>dolžina) {document.write('Indeks izven meja ');  } else { // poišči kth najmanjšo vrednost document.write( 'K-th najmanjši element v nizu : ' + kthSmallest(arraycopy, 0, length - 1, kPosition)+' ');  } // To kodo je prispeval rag2127 Izhod: K-ti najmanjši element je 6. Pomembne točke: Tako kot hitro razvrščanje je v praksi hiter, vendar ima slabo zmogljivost v najslabšem primeru. Uporablja se v. Postopek particije je enak kot QuickSort, razlikuje se le rekurzivna koda. Obstaja algoritem, ki najde k-ti najmanjši element v O(n) v najslabšem primeru, vendar QuickSelect v povprečju deluje bolje.    Sorodna funkcija C++: std::nth_element v C++>