寻找最小的K个数

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解法一：排序法：

//解法一：全部排序//时间复杂度：O(n*n);#include <iostream>using namespace std;template<class T>void Sort(T array[], size_t size, int k){    for (int i = 0; i < size; i++)      {          for (int j = i + 1; j < size; j++)          {              if (array[i] > array[j])              {                  swap(array[i], array[j]);              }          }      }     for(int idx=0; idx<k; idx++)        cout<<array[idx];    cout<<endl;}void FunTest(){    int arr[] = {1, 11, 12, 13, 14, 15, 16, 17, 18, 19,        20,  2,  3,  4,  5,  6,  7,  8,  9, 10,        71, 72, 73, 74, 75, 76, 77, 78, 79, 80,        21, 22, 23, 24, 25, 26, 27, 28, 29, 30,        31, 32, 33, 34, 35, 36, 37, 38, 39, 40,        41, 42, 43, 44, 45, 46, 47, 48, 49, 50,        51, 52, 53, 54, 55, 56, 57, 58, 59, 60,        61, 62, 63, 64, 65, 66, 67, 68, 69, 70,        81, 82, 83, 84, 85, 86, 87, 88, 89, 90};    Sort(arr, sizeof(arr)/sizeof(arr[0]), 5);}int main(){    FunTest();    system("pause");    return 0;}

解法二：创建大堆（k个），取堆顶，调整
（1）用容量为k的最大堆存储最先遍历的k个数，假设他们是最小的k个数，建堆用时O(k)，建好堆后堆中的元素是有序的，可令K1

//解法二：创建大堆（k个），取堆顶，调整#include <vector>#include <iostream>using namespace std;#include <assert.h>template<class T>struct Less{    bool operator()(const T& left, const T& right)//仿函数    {        return left<right;    }};template<class T>struct Greater{    bool operator()(const T& left, const T& right)//仿函数    {        return left>right;    }};//模板参数template<class T, class Compare = Less<T>>class Heap{public:    // 创建一个空堆    Heap()    {}    Heap(const T array[], size_t size)    {        _heap.resize(size);  //一次性开辟足够的空间        for(size_t idx=0; idx<size; ++idx)        {            //_heap.push_back(array[idx]);  //先开辟有限个，若不够，再开辟            _heap[idx] = array[idx]; //如果没有扩容，就是没有开辟空间，导致程序崩溃        }        int root = (_heap.size() - 2)>>1;  //找到最后一个非叶子节点        for(; root>=0; root--)        {            _AdjustDown(root);        }    }    size_t Size()const    {        return _heap.size();    }    bool Empty()const    {        return _heap.empty();    }    void Insert(const T& data)    {        _heap.push_back(data);          if(_heap.size()>1)            _AdjustUp();    }    T& Top()    {        assert(!Empty());        return _heap[0];    }    void Remove()    {        assert(!_heap.empty());        size_t last = _heap.size()-1;        swap(_heap[last], _heap[0]);        _heap.pop_back();        _AdjustDown(0);    }protected:    void _AdjustDown(size_t parent)    {        size_t size = _heap.size();        size_t child = 2*parent+1;   //左孩子结点        while(child<size)        {            child = 2*parent+1;             //右孩子存在，找出左右孩子中小的节点            Compare com;            if(child+1 < size && com(_heap[child+1], _heap[child]))            {                child+= 1; //child指向右孩子            }            if(com(_heap[child], _heap[parent]))            {                swap(_heap[child], _heap[parent]);                parent = child;                child = parent*2+1;            }            else            {                break;            }        }    }    void _AdjustUp()    {        size_t child = _heap.size()-1;        size_t parent = (child-1)>>1;        while(child != 0)        {            Compare com;            if(com(_heap[child], _heap[parent]))            {                swap(_heap[child], _heap[parent]);                child = parent;                parent = (child-1)>>1;            }            else                return;        }    }protected:    std::vector<T> _heap;};void FunTest(){    int array[] = {100, 99, 98, 97, 96, 95, 94, 93, 92, 91};    Heap<int, Greater<int>> hp(array, sizeof(array)/sizeof(array[0]));    int arr[] = {1, 11, 12, 13, 14, 15, 16, 17, 18, 19,                20,  2,  3,  4,  5,  6,  7,  8,  9, 10,                 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,                 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,                 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,                 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,                 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,                 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,                 81, 82, 83, 84, 85, 86, 87, 88, 89, 90};    int len = sizeof(arr)/sizeof(arr[0]);    for(int i=0; i<len; ++i)    {        int ret = arr[i];        if(hp.Top() > ret)        {            hp.Remove();            hp.Insert(ret);        }    }}int main(){    FunTest();    system("pause");    return 0;}

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