Contest6 The K-th largest number

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本文介绍了一种在大规模数据集中查找第K大的数的方法，并提供了一个时间复杂度为O(NlogK)的算法实现示例。该算法适用于数据集非常大（如100万到1000万之间）的情况。

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Problem B: The K-th largest number

Time Limit: 2 Sec Memory Limit: 40 MB
Submit: 856 Solved: 233
[ Submit][ Status][ Web Board]

Description

Given N integer numbers, find the K-th largest number.
Requirement: design an algorithm with the time complexity O(NlogK).

Input

The first line contains N, K. In the following N lines, each line contains an integer value.
Note that N could be very large ( 1000000 <= N <= 10000000). You should allocate the memory dynamically and design the algorithm with the time complexity O(NlogK).

Output

Output the K-th largest number.

Sample Input

Sample Output

HINT

If the memory is not enough, you may apply a sliding window to split the batchs of input and sort in each batch.

#include <stdio.h>
#include <time.h>
#include <stdlib.h>


void qsort2(int* a, int l, int r, int rank) {
	int m;
	if (l < r) {
		m = partition2(a, l, r);
	}
	if (r - m + 1 == rank) return;
	else if (r - m + 1 > rank) qsort2(a, m + 1, r, rank); 
	else qsort2(a, l, m - 1, rank - (r - m + 1));
}

int partition2(int* a, int l, int r) {
	int i = l;
	int j = r;
	int pivot = a[l];
	while (i < j) {
		while ((a[j] >= pivot) & (i < j)) --j;
		a[i] = a[j];
		while ((a[i] <= pivot) & (i < j)) ++i;
		a[j] = a[i];
	}
	return j;
}

int main() {
	srand(time(NULL));
	int n, rank;
	scanf("%d %d", &n, &rank);
	int* a = (int*) malloc(n * sizeof(int));
	for (int i = 0; i != n; ++i) {
		scanf("%d", a + i);
	}
	qsort2(a, 0, n - 1, rank);
	printf("%d\n", a[n - rank]);
	return 0;
}