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