quickselectとして知られているアルゴリズムの github でこのコードを見つけましたorder-statistics。このコードは正常に動作します。
medianOf3最初、中間、最後のインデックスをソート順に並べる方法がわかりません。しかし、実際には、メソッドを呼び出した後に配列を出力するときはそうではありませんmedianof3。の最後の呼び出しを除いて、このメソッドが何をしているのかについては、このメソッドに従うことができますswap(list, centerIndex, rightIndex - 1);。誰かがなぜこれが呼び出されたのか説明できますか?
import java.util.Arrays;
/**
* This program determines the kth order statistic (the kth smallest number in a
* list) in O(n) time in the average case and O(n^2) time in the worst case. It
* achieves this through the Quickselect algorithm.
*
* @author John Kurlak <john@kurlak.com>
* @date 1/17/2013
*/
public class Quickselect {
/**
* Runs the program with an example list.
*
* @param args The command-line arguments.
*/
public static void main(String[] args) {
int[] list = { 3, 5, 9, 10, 7, 40, 23, 45, 21, 2 };
int k = 6;
int median = medianOf3(list, 0, list.length-1);
System.out.println(median);
System.out.println("list is "+ Arrays.toString(list));
Integer kthSmallest = quickselect(list, k);
if (kthSmallest != null) {
System.out.println("The kth smallest element in the list where k=" + k + " is " + kthSmallest + ".");
} else {
System.out.println("There is no kth smallest element in the list where k=" + k + ".");
}
System.out.println(Arrays.toString(list));
}
/**
* Determines the kth order statistic for the given list.
*
* @param list The list.
* @param k The k value to use.
* @return The kth order statistic for the list.
*/
public static Integer quickselect(int[] list, int k) {
return quickselect(list, 0, list.length - 1, k);
}
/**
* Recursively determines the kth order statistic for the given list.
*
* @param list The list.
* @param leftIndex The left index of the current sublist.
* @param rightIndex The right index of the current sublist.
* @param k The k value to use.
* @return The kth order statistic for the list.
*/
public static Integer quickselect(int[] list, int leftIndex, int rightIndex, int k) {
// Edge case
if (k < 1 || k > list.length) {
return null;
}
// Base case
if (leftIndex == rightIndex) {
return list[leftIndex];
}
// Partition the sublist into two halves
int pivotIndex = randomPartition(list, leftIndex, rightIndex);
int sizeLeft = pivotIndex - leftIndex + 1;
// Perform comparisons and recurse in binary search / quicksort fashion
if (sizeLeft == k) {
return list[pivotIndex];
} else if (sizeLeft > k) {
return quickselect(list, leftIndex, pivotIndex - 1, k);
} else {
return quickselect(list, pivotIndex + 1, rightIndex, k - sizeLeft);
}
}
/**
* Randomly partitions a set about a pivot such that the values to the left
* of the pivot are less than or equal to the pivot and the values to the
* right of the pivot are greater than the pivot.
*
* @param list The list.
* @param leftIndex The left index of the current sublist.
* @param rightIndex The right index of the current sublist.
* @return The index of the pivot.
*/
public static int randomPartition(int[] list, int leftIndex, int rightIndex) {
int pivotIndex = medianOf3(list, leftIndex, rightIndex);
int pivotValue = list[pivotIndex];
int storeIndex = leftIndex;
swap(list, pivotIndex, rightIndex);
for (int i = leftIndex; i < rightIndex; i++) {
if (list[i] <= pivotValue) {
swap(list, storeIndex, i);
storeIndex++;
}
}
swap(list, rightIndex, storeIndex);
return storeIndex;
}
/**
* Computes the median of the first value, middle value, and last value
* of a list. Also rearranges the first, middle, and last values of the
* list to be in sorted order.
*
* @param list The list.
* @param leftIndex The left index of the current sublist.
* @param rightIndex The right index of the current sublist.
* @return The index of the median value.
*/
public static int medianOf3(int[] list, int leftIndex, int rightIndex) {
int centerIndex = (leftIndex + rightIndex) / 2;
if (list[leftIndex] > list[rightIndex]) {
swap(list, leftIndex, centerIndex);
}
if (list[leftIndex] > list[rightIndex]) {
swap(list, leftIndex, rightIndex);
}
if (list[centerIndex] > list[rightIndex]) {
swap(list, centerIndex, rightIndex);
}
swap(list, centerIndex, rightIndex - 1);
return rightIndex - 1;
}
/**
* Swaps two elements in a list.
*
* @param list The list.
* @param index1 The index of the first element to swap.
* @param index2 The index of the second element to swap.
*/
public static void swap(int[] list, int index1, int index2) {
int temp = list[index1];
list[index1] = list[index2];
list[index2] = temp;
}
}