堆有关的面试题（后续补充）

//*********************************************************//面试题：N个数找出最大的前K个（N超级大）////思路：用前K个数建个小堆，然后向后遍历其余数，凡是遇到比堆根节点大的，//      就替换根节点，然后向下调整，使之始终保持小堆，然后继续遍历，//      直至访问完数据。这样就将前K个大的数据全放在了堆中。////时间复杂度：建堆+遍历（KlgK+(N-K)lgN） ->NlgK//*********************************************************#include<iostream>#include<algorithm>#include<functional>using namespace std;const int N = 10000;const int K = 10;void AdjustDown(int* a)   //向下调整{    int father = 0;    int child = (a[father * 2 + 1] < a[father * 2 + 2] ? (father * 2 + 1) : (father * 2 + 2));    while (a[father] > a[child] && child < K)    {        swap(a[father], a[child]);        father = child;        if (father * 2 + 1 == K - 1)            child = father * 2 + 1;        if(father*2+1 < K-1)            child = (a[father * 2 + 1] < a[father * 2 + 2] ? (father * 2 + 1) : (father * 2 + 2));    }}int main(){    int a[N] = { 0 };    for (int i = 0; i < N; ++i)    {        a[i] = rand()%100;  //赋值为小于100的随机值    }    a[54] = 111;    a[542] = 122;    a[2] = 3124;    a[393] = 999;    a[333] = 888;    a[1001] = 789;    a[3214] = 1131;    a[3245] = 1115;    a[3924] = 911;    a[112] = 112;    make_heap(a, a+K,greater<int>());  //建小堆    cout << "make_heap:" << endl;    for (int i = 0; i < K; ++i)    {        cout << a[i] << " ";    }    cout << endl;    for (int i = K; i < N; ++i)    {        if (a[i] >= a[0])        {            a[0] = a[i];            AdjustDown(&a[0]);        }    }    cout << "make_heap:" << endl;    for (int i = 0; i < K; ++i)    {        cout << a[i] << " ";    }    cout << endl;    system("pause");    return 0;}

////////////////////////////////////////////////////////////堆排序（选择排序的一种）////思路：1，升序：先建一个大堆(0,n-1)，然后将堆顶节点（值最大的节点）//               与堆最后一个节点交换，然后就形成了两部分：有序区//              （n-1）和 无序区(0,n-2),然后将无序区调整为堆，循环//               以上步骤，直至最后一个节点//      2，降序：建一个小堆，其余和升序本质一样。////时间复杂度：N*logN/////////////////////////////////////////////////////////////升序void HeadSort(int* a, size_t n){    for (int i = n; i > 0; i--)    {        make_heap(a, a+i);    //建大堆        swap(a[0], a[i - 1]);   //交换堆顶节点与堆尾节点    }}int main(){    int a[10] = { 0 };    for (int i = 0; i < 10; ++i)    {        a[i] = 10 - i;    }    HeadSort(a, 10);    for (int i = 0; i < 10; ++i)    {        cout << a[i] << " ";    }    cout << endl;    system("pause");    return 0;}