programming-examples/java/Data_Structures/NthElement.java
2019-11-15 12:59:38 +01:00

106 lines
2.6 KiB
Java

import java.util.*;
import java.util.stream.IntStream;
public class NthElement {
// See: http://www.cplusplus.com/reference/algorithm/nth_element
// O(n) on average
public static void nth_element(int[] a, int low, int high, int n, Random rnd) {
while (true) {
int k = partition(a, low, high, low + rnd.nextInt(high - low));
if (n < k)
high = k;
else if (n > k)
low = k + 1;
else
return;
}
}
static int partition(int[] a, int fromInclusive, int toExclusive, int separatorIndex) {
int i = fromInclusive;
int j = toExclusive - 1;
if (i >= j) return j;
int separator = a[separatorIndex];
swap(a, i++, separatorIndex);
while (i <= j) {
while (i <= j && a[i] < separator)
++i;
while (i <= j && a[j] > separator)
--j;
if (i >= j)
break;
swap(a, i++, j--);
}
swap(a, j, fromInclusive);
return j;
}
static void swap(int[] a, int i, int j) {
int t = a[j];
a[j] = a[i];
a[i] = t;
}
// O(n) worst case. See Cormen et al
public static void nth_element2(int[] a, int low, int high, int n) {
if (high - low <= 1)
return;
while (true) {
int[] a5 = new int[(high - low + 4) / 5];
for (int i = low, cnt = 0; i < high; i += 5) {
int j = Math.min(i + 5, high);
for (int iteration = 0; iteration < 3; iteration++) {
for (int k = i; k + 1 < j; k++) {
if (a[k] > a[k + 1]) {
int t = a[k];
a[k] = a[k + 1];
a[k + 1] = t;
}
}
}
a5[cnt++] = a[(i + j) >>> 1];
}
nth_element2(a5, 0, a5.length, a5.length / 2);
int separatorIndex = IntStream.range(low, high).filter(i -> a[i] == a5[a5.length / 2]).findFirst().getAsInt();
int k = partition(a, low, high, separatorIndex);
if (n < k)
high = k;
else if (n > k)
low = k + 1;
else
return;
}
}
// Random test
public static void main(String[] args) {
Random rnd = new Random(1);
int len = 1000_000;
nth_element(new int[len], 0, len, 0, rnd);
nth_element2(new int[len], 0, len, 0);
for (int step = 0; step < 100_000; step++) {
int n = rnd.nextInt(10) + 1;
int[] a = rnd.ints(n, 0, 10).toArray();
int[] b = a.clone();
int k = rnd.nextInt(n);
nth_element(a, 0, n, k, rnd);
nth_element2(b, 0, n, k);
int[] sa = a.clone();
Arrays.sort(sa);
int[] sb = b.clone();
Arrays.sort(sb);
if (!Arrays.equals(sa, sb))
throw new RuntimeException();
if (a[k] != sa[k] || b[k] != sb[k])
throw new RuntimeException();
for (int i = 0; i < n; i++) {
if (i < k && a[i] > a[k] || i > k && a[i] < a[k])
throw new RuntimeException();
if (i < k && b[i] > b[k] || i > k && b[i] < b[k])
throw new RuntimeException();
}
}
}
}