No215. Kth Largest Element in an Array

一、题目描述

Find the kth largest element in anunsorted array. Note that it is the kth largest element in the sorted order,not the kth distinct element.

For example,

Given [3,2,1,5,6,4] and k = 2, return 5.

Note:

You may assume k is always valid, 1 ≤ k ≤ array's length.

二、方法一

写法最简单的方法，调用sort函数从小到大排序，再输出数组的第n-k位，该方法的时间复杂度是O(nlogn)。

class Solution {public:    int findKthLargest(vector<int>& nums, int k) {        sort(nums.begin(),nums.end());        return nums[nums.size()-k];    }};

三、方法二

对排序进行优化，分别用快排和堆排实现：

快排：

class Solution {public:    int patition(vector<int>& nums,int left,int right){        int l=left+1,r=right;        while(l<=r){            if(nums[l]<nums[left]&&nums[r]>nums[left]){                swap(nums[l],nums[r]);                l++;                r--;            }            if(nums[l]>=nums[left]) l++;            if(nums[r]<=nums[left]) r--;        }        swap(nums[r],nums[left]);        return r;    }    int findKthLargest(vector<int>& nums, int k) {        int left=0,right=nums.size()-1;        while(true){            int pos = patition(nums,left,right);            if(pos==k-1) return nums[pos];            else if(pos>k-1) right=pos-1;            else left=pos+1;        }    }};

堆排：

class Solution {public:    void maxheap(vector<int>& nums,int index){        int large =index;        int left = index*2+1,right=index*2+2;        if(left<heapsize&&nums[large]<nums[left]) large=left;        if(right<heapsize&&nums[large]<nums[right]) large=right;        if(large!=index){           swap(nums[index],nums[large]);           maxheap(nums,large);        }     }    void buildheap(vector<int>& nums){        heapsize=nums.size();        for(int i=(heapsize/2-1);i>=0;i--)            maxheap(nums,i);    }    int findKthLargest(vector<int>& nums, int k) {        buildheap(nums);        heapsize=nums.size();        for(int i=0;i<k;i++){            swap(nums[0],nums[heapsize-1]);            heapsize--;            maxheap(nums,0);        }        return nums[heapsize];    }private:    int heapsize;    };