算法题：快速选择算法

2021年4月21日18:47:40 发表评论 1,125 次浏览

本文概述

快速选择是一种选择算法, 用于在无序列表中找到第k个最小的元素。它与快速排序排序算法。

例子：

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

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

该算法类似于QuickSort。不同之处在于, 它只对包含第k个最小元素的部分重复出现, 而不是在两侧都重复出现。逻辑很简单, 如果分区元素的索引大于k, 则针对左部分递归。如果index与k相同, 则找到第k个最小元素, 然后返回。如果索引小于k, 则返回正确的部分。这将预期的复杂度从O(n log n)降低到O(n), 最坏的情况是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 <pivotIndex
      right := pivotIndex - 1
   else
      left := pivotIndex + 1

C ++

//CPP program for implementation of QuickSelect
#include <bits/stdc++.h>
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) 
             return kthSmallest(arr, l, index - 1, k);
  
         //Else recur for right subarray
         return kthSmallest(arr, index + 1, r, k - index + l - 1);
     }
  
     //If k is more than number of 
     //elements in array
     return INT_MAX;
}
  
//Driver program to test above methods
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] <pivot)
             {
                 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)
             return arr[partition];    
              
         //if partition value is less than kth position, //search right side of the array.
         else if (partition <k )
             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> length)
         {
             System.out.println( "Index out of bound" );
         }
         else
         {
             //find kth smallest value
             System.out.println( "K-th smallest element in array : " + 
                                 kthSmallest(arraycopy, 0 , length - 1 , kPosition - 1 )); 
         } 
     }
}
  
//This code is contributed by Saiteja Pamulapati

Python3

# Python3 program of Quick Select
  
# 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
def partition(arr, l, r):
      
     x = arr[r]
     i = l
     for j in range (l, r):
          
         if 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 and 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 ):
             return kthSmallest(arr, l, index - 1 , k)
  
         # Else recur for right subarray 
         return kthSmallest(arr, index + 1 , r, k - index + l - 1 )
     return INT_MAX
  
# Driver Code
arr = [ 10 , 4 , 5 , 8 , 6 , 11 , 26 ]
n = len (arr)
k = 3
print ( "K-th smallest element is " , end = "")
print (kthSmallest(arr, 0 , n - 1 , k))
  
# This code is contributed by Muskan Kalra.

C#

//C# program of Quick Select
using System;
  
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 readonly array.
     static int partitions( int []arr, int low, int high)
     {
         int pivot = arr[high], pivotloc = low, temp;
         for ( int i = low; i <= high; i++)
         {
             //inserting elements of less value 
             //to the left of the pivot location
             if (arr[i] <pivot)
             {         
                 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 <k )
             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> length)
         {
             Console.WriteLine( "Index out of bound" );
         }
         else
         {
             //find kth smallest value
             Console.WriteLine( "K-th smallest element in array : " + 
                                 kthSmallest(arraycopy, 0, length - 1, kPosition - 1)); 
         } 
     }
}
  
//This code is contributed by 29AjayKumar

输出如下：

K-th smallest element is 6

重要事项：

  1. 与快速排序类似, 它在实践中速度很快, 但最坏情况下的性能却很差。它用于
  2. 分区过程与QuickSort相同, 只是递归代码不同。
  3. 有一种算法可以找到最坏cas中O(n)中第k个最小元素e, 但QuickSelect的平均效果更好。

相关的C++函数：C++中的std::nth_element

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