215. 数组中的第K个最大元素

和414的题是一样，我就是想用一下bfprt。可以代码一直有问题，下面第二个死机。

class Solution {
public:
void partition(vector<int>& a, int left, int right, int &less, int &more)
{if(left>=right)return;int cur = left, index = right;less = left-1, more = right;while(cur<more){if(a[cur]<a[index])swap(a[cur++], a[++less]);else if(a[cur]==a[index])++cur;elseswap(a[cur], a[--more]);}swap(a[index], a[more++]);return;
}int findKthLargest(vector<int>& nums, int k) {int less=0, more=0, left=0,right=nums.size()-1;k = nums.size() - k;while(left<right){partition(nums, left, right, less, more);if(k<=less)right=less;else if(k>=more)left=more;elsereturn nums[k];}return nums[left];
}};

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
#if 0
int medIndex(vector<int>a, vector<int>index, int left, int right)///<返回数组中位数的下标
{for(int i=1; i<right-left+1; ++i)for(int j=i; j>0 && a[index[j-1]]<a[index[j]]; --j)swap(index[j-1],index[j]);return index[(index.size()-1)/2];
}int bfprt(vector<int>a, vector<int>index, int left, int right)
{if(left>=right)return right;vector<int>vecbfprt;for(size_t i=0; i<index.size()/5; ++i)vecbfprt.push_back(medIndex(a, index, i*5, i*5+4));if(0!=index.size()%5)vecbfprt.push_back(medIndex(a, index, index.size()/5*5, index.size()-1));return bfprt(a, vecbfprt, 0, a.size()-1);
}
#endif
///<获取闭区间[left,right]范围内中位数的下标
int getMidIndex(const vector<int>mapa, int left, int right)
{vector<int>index;for(int i=left; i<=right; ++i)index.push_back(i);for(int i=left+1; i<=right; ++i)for(int j=i; j>left && mapa[index[j-1]]<=mapa[index[j]]; --j)swap(index[j-1], index[j]);return index[index.size()/2];
}int bfprt(const vector<int>mapa, const vector<int>index)
{if(1==index.size())return mapa[index[0]];vector<int>newIndex;  for(int i=0; i<(int)index.size()/5; ++i)newIndex.push_back(getMidIndex(mapa, i*5, i*5+4));if(0!=index.size()%5)newIndex.push_back(getMidIndex(mapa, index.size()/5*5, index.size()-1));auto bb = bfprt(mapa, newIndex);return bb;
}
void partition(vector<int>& a, int left, int right, int &less, int &more)
{if(left>=right)return;vector<int>vecbfprt;for(int i=left;i<=right;++i)vecbfprt.push_back(i);auto x = bfprt(a, vecbfprt);swap(a[x], a[right]);int cur = left, index = right;less = left-1, more = right;while(cur<more){if(a[cur]<a[index])swap(a[cur++], a[++less]);else if(a[cur]==a[index])++cur;elseswap(a[cur], a[--more]);}swap(a[index], a[more++]);return;
}int findKthLargest(vector<int>& nums, int k) {int less=0, more=0, left=0,right=nums.size()-1;k = nums.size() - k;while(left<right){partition(nums, left, right, less, more);if(k<=less)right=less;else if(k>=more)left=more;elsereturn nums[k];}return nums[left];
}int main(void)
{vector<int>a={3,2,3,1,2,4,5,5,6};cout<<findKthLargest(a, 2)<<endl;return 0;
}

第K小的数是从1开始的，没有第0小的数。所有数没有重复的，如果有重复的可以用hash_set去重。

1.方法

法一：

这个方法不仅简单而且效率高。用类似于解决荷兰国旗问题partition问题的方法。随机选一个数作为划分值，小于这个数的放左边，等于这个数的放中间，大于这个数的放右边。假如等于区是200~500，我要找第300小的数就直接找到了。如果我要找第700小的数，就把大于区递归重新分配一下。

时间复杂度是个数学期望，结果是O(N)。最好情况是小于区和大于区大小一样。

法二：

BFPRT算法就求这个问题时间复杂度是稳定的O(N)，连期望都不是，它就是在选择partition问题的那个数的时候做了文章。法一中选择那个数不是随机的嘛，所以产生了期望，如果我要是能用O(N)的时间找到一个不会偏缀的数，结果就稳定了。BFPRT就是在找这样一个数。

因为不管怎么找结果肯定不会错，顶天就是偏缀嘛，所以只要证明我找这个数的时间复杂度是O(N)就行。先说方法，再求时间复杂度。

2.操作

1）先把一组数每5个一组分组，分成N/5组，最后一组如果不满5个也成一组。其实这步其实没啥实际操作，就是变换下标而已。

2）每组的组内进行排序，组间不排序。

3）把这N/5个数组的中位数拿出来单独形成一个数组。最后一组不满5个的拿上中位数或下中位数都行，不满5个的组只有一个，完全不影响复杂度。

4）找着N/5个数的中位数。这里找中位数是递归调用BFPRT实现的。BFPRT函数的格式就是两个形参，一个是数组arr，一个是第k小数的k，返回值是数。int BFPRT(vectora,int k)。假设N/5的数组叫做arr，递归的时候可以写成BFPRT(arr,arr.size()/2)，中位数嘛，所以一定是数组长度的一半。这个中位数记为

5）用这个进行partition。

6）如果命中K了就返回这个数，没命中就选择一侧走。

3.复杂度分析

1）O(1)

2)O(N)，因为每组内只有5个数是O(1)，一共有O(N/5)个数

3）O(N)

4）T(N/5)，因为是N/5个数进行递归，找到中位数p

5）O(N)，单纯的partition过程

6）判断是走左边还是走右边，用了BFPRT以后，左侧和右侧的规模就能够估计出来了。

估计的时候肯定是要估计最差的情况，最差的情况指的就是小于p的最多能有多少个数，这个不好求，可以变成求最少能有多少个数比p大，N再减去这个数就行了。怎么求，看下图

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)]

上图为一个排好序的数组，每组从上到小依次变大。每组的中位数提出来，这个中位数数组的大小是N/5，因为每组5个数嘛。对于中位数数组的中位数p而言，一共有1/2个数比它大，而这个数组大小为N/5，所以一共有N/10组数比P要大。每组一共有5个数，比该组中位数大的有两个，加上这个中位数一共是三个数，就是数所有中位数比p大的组中至少有3个数会比p要大。总共有N/10组，所以比p大的数至少有3N/10个。

再举个例子

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这里比7大的数就不止3N/10个，以为10和11都比7大。但10和11位置上的数可能比7小吗？可能，所以说至少有多少个，至少就只包括8、9、12、13和14。

有上述求解可知，小于区最大为7N/10，大于区至少也为7N/10，因此，该部分的时间复杂度为T(7N/10)。

所以总共的时间复杂度为

T(N)=O(N)+T(N/5)+T(7N/10)

不用数学推了，反正用5个数一组分T(N)是可以收敛到O(N)的，3个数也行，7个数也行，别的行不行我就不知道了，要看具体的数学证明，5个肯定是可以的。如果是3个一组呢？中位数数组的大小为N/3，所以1一共有N/6组数比p大，每组数中至少有两个数比p大，所以至少有有N/3个数比p要大，至多有2N/3个数比p要小。结果就是

T(N)=O(N)+T(N/3)+T(2N/3)

4.应用

取前k小的数，如果用堆做时间复杂度就是NlogN，我这样找到第k小的数，比它小的都要就行了。时间复杂度是O(N)。至于哈希那里有一道题是说读取流中前10大的数，那就不行了，因为流的数据太大，只能用堆。

5.我的代码

法一：

https://leetcode-cn.com/problems/kth-largest-element-in-an-array/

class Solution {
public:
void partition(vector<int>& a, int left, int right, int &less, int &more)
{if(left>=right)return;int cur = left, index = right;less = left-1, more = right;while(cur<more){if(a[cur]<a[index])swap(a[cur++], a[++less]);else if(a[cur]==a[index])++cur;elseswap(a[cur], a[--more]);}swap(a[index], a[more++]);return;
}int findKthLargest(vector<int>& nums, int k) {int less=0, more=0, left=0,right=nums.size()-1;k = nums.size() - k;while(left<right){partition(nums, left, right, less, more);if(k<=less)right=less;else if(k>=more)left=more;elsereturn nums[k];}return nums[left];
}};

法二：

我把对数器也写出来了，求的是第n大的，第n小的只要把求test1时的输入改改就行，其它代码都不变。LeetCode中需要单独去重。

#include<iostream>
#include<vector>
#include<algorithm>
#include<ctime>
using namespace std;
int BFPRT(vector<int>a, int begin, int end, int k);int getMedian(vector<int>a, int begin, int end)//获取中位数
{sort(a.begin() + begin, a.begin() + end+1);//加一是因为sort不包括最后一个return a[(begin+end)/2];
}
int MedianOfMedians(vector<int>a, int begin, int end)//找到中位数数组的中位数
{int n = end - begin + 1;int offset =(0 == n % 5) ? 0 : 1;int groupcount = n/5 + offset;vector<int>arr;for (int i = 0; i < groupcount; ++i){int beginI = begin + i * 5;int endI = beginI + 4;arr.push_back(getMedian(a,beginI,min(end,endI)));//将beginI和endI之间的中位数返回，并推入中位数数组中}return BFPRT(arr,0,arr.size()-1,arr.size()/2);//在0和arr.size()-1的范围上求中位数
}
int *partition(vector<int>&a, int left, int right,int key)//用可以对从begin到end的a进行分割
{int ll = left - 1;//ll是小于区和等于区的分界，属于小于区int rr = right + 1;//rr是等于区和大于区的分界，属于大于区int mid = left;while (mid < rr){if (a[mid] > key)swap(a[mid], a[--rr]);else if (a[mid] < key)swap(a[mid++], a[++ll]);else++mid;}int *p = (int*)malloc(8);*p = ll;*(p + 1) = mid;return p;
}
int BFPRT(vector<int>a, int begin, int end, int k)//在begin和end的范围上求第k小的数
{if (end == begin)return a[begin];int p = MedianOfMedians(a,begin,end);//求中文数int *pp = partition(a,begin,end,p);//partition的同时进行排序int less = *pp, more = *(pp+1);//小于区和大于区的位置，中间就是等于区。less属于小于区，more属于大于区，所以下面k<=less有等于号，k<more没有等于号free(pp);if (k <= less)//小于区return BFPRT(a, begin, less, k);else if (k < more)//等于区return a[k];else//大于区return BFPRT(a,more,end,k);
}
int GetMinKByBFPRT(vector<int>a, int k)
{return BFPRT(a,0,a.size()-1,k-1);//因为没有第0小的数，所以要k-1
}
void print(vector<int>a)
{for (int i = 0; i < a.size(); ++i)cout << a[i] << ",";
}
int main(void)//带有对数器
{srand((unsigned)time(NULL));for (int times = 0; times < 10000; ++times){vector<int>a;int n = rand() % 100 + 2;//数组长度为1~100的随机数n = 10;for (int i = 0; i < n; ++i)//数组长度为na.push_back(rand() % 100+1);//数组中的元素时从1到100的随机数vector<int>primitive(a.begin(), a.end());//因为正确的方法和待检测的方法都会对数组进行修改，但是为了能够打印出原始的，所以我留一个/*正确的方法*/vector<int>b(a.begin(),a.end());int k = rand() % n + 1;//1~n的随机数,第K大的数，这个数必须小于n啊sort(b.begin(),b.end(),less<int>());/*正确的方法结束*///test2是待检测的方法k = 1;int test1 = GetMinKByBFPRT(a, n + 1 - k);int test2 = b[n - k];if (test1 != test2){print(primitive);cout << endl;cout << "k==" << k << endl;while(1);}}cout << "true" << endl;while(1);return 0;
}

https://leetcode-cn.com/problems/third-maximum-number/submissions/