一个堆排序问题

题目：在N个不相等的整数中找出最大的第K个数(N>K)。

思路：首先，用前K个整数构造容量为K的最小堆。然后，将后N-K个整数依次与堆顶元素比较，若比堆顶元素大，则替换堆顶元素并调整最小堆结构；反之，则继续比较下一个整数。最终，最小堆存储最大的k个数，其堆顶元素即为所求。

代码：

#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <iostream>

#define N 90
#define K 13


void HeapAdjust (int *heap, int beginidx, int endidx);
void HeapConstruct (int *heap);

void SetData (int *data);
void ShowData (int *data);

int main (int argc, char **argv)
{
    int i;
    int h[N + 1];

    SetData(h);
    ShowData(h);

    HeapConstruct(h);
    for (i = K + 1; i <= N; i++)
    {
        if (h[i] > h[1])
        {
            h[1] = h[i];
            HeapAdjust(h, 1, K);
        }
    }

    printf("The Kth biggest number: %d
", h[1]);
    return 0;
}

void HeapAdjust (int *heap, int beginidx, int endidx)
{
    int &current = beginidx;
    int tmp, left, right, data = heap[current];

    while (left = (current << 1), left <= endidx)
    {
        right = left | 1;
        if ((left == endidx) || (heap[left] < heap[right]))
        {
            tmp = left;
        }
        else
        {
            tmp = right;
        }
        if (data > heap[tmp])
        {
            heap[current] = heap[tmp];
            current = tmp;
        }
        else
        {
            break;
        }
    }
    heap[current] = data;
}

void HeapConstruct (int *heap)
{
    int i;
    for (i = K/2; i > 0; i--)
    {
        HeapAdjust(heap, i, K);
    }
}

void SetData (int *data)
{
    bool *bdata = new bool[N + 1];
    memset(bdata, false, N + 1);
    srand(time(NULL));
    data[0] = -1;
    for (int i = 1; i <= N; i++)
    {
        data[i] = rand() % N + 1;
        while (bdata[data[i]])
        {
            data[i] = rand() % N + 1;
        }
        bdata[data[i]] = true;
    }
    delete []bdata;
}

void ShowData (int *data)
{
    for (int i = 1; i <= N; i++)
    {
        printf("%02d ", data[i]);
    }
    puts("");
}

时间复杂度：O((N-K+1)*K*lgK).