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();
			}
		}
	}
}