前k个小的元素

假如有一个数组（无序），让你找出里面前k个小的元素，设计一个算法

思路1：

快速排序的思想，找出第k位置的元素，在此元素左边都比他小，输出即可，时间复杂度为O（n）

思路2：
查找前k小，构建最大值堆，先将k个元素构建一个最大值堆，然后再遍历剩余元素，若剩余元素比堆顶小，让堆顶等于这个小的元素，再调整一下位置，这样遍历结束，前k个最小的元素都在堆中了。时间复杂度O（n）

下面将两个思路整合在一起了

class Solution {
private:
	vector<int> heap;
	int leftChild(int pos)
	{
		return 2 * pos + 1;
	}
	int rightChild(int pos)
	{
		return 2 * pos + 2;
	}
	bool isLeaf(int pos)
	{
		return (pos >= heap.size() / 2) && (pos < heap.size());
	}
	void siftDown(int pos)
	{
		while (!isLeaf(pos))
		{
			int left = leftChild(pos);
			int right = rightChild(pos);
			if (right<heap.size() && heap[right]<heap[left])
				right = left;
			if (heap[pos] > heap[right])
				return;
			swap(heap[pos], heap[right]);
			pos = right;
		}
	}
	void buildHeap(int size)
	{
		for (int i = size / 2 - 1; i >= 0; --i)
			siftDown(i);
	}
	int randomInRange(vector<int>& nums, int start, int end)
	{
		if (start == end)
			return nums[start];
		srand((unsigned)time(NULL));
		if (start > end)
			return rand() % (start - end + 1) + end;
		else
			return rand() % (end - start + 1) + start;
	}
	int partition(vector<int>&nums, int start, int end)
	{
		if (start == end)
			return nums[start];
		int index = randomInRange(nums, start, end);
		swap(nums[index], nums[end]);
		int small = start - 1;
		for (int i = start; i < end; ++i)
		{
			if (nums[i] < nums[end])
			{
				small++;
				if (small != i)
					swap(nums[small], nums[i]);
			}
		}
		small++;
		swap(nums[small], nums[end]);
		return small;
	}

public:
	void findKthLargest(vector<int>& nums, int k)
	{
		int start = 0, end = nums.size() - 1;
		int index = partition(nums, start, end);
		while (index != k - 1)
		{
			if (index > k - 1)
				end = index - 1;
			else
				start = index + 1;
			index = partition(nums, start, end);
		}
		for (int i = 0; i <= index; ++i)
			cout << nums[i] << " ";
	}
	void heapFindK(vector<int>& nums, int k)
	{
		for (int i = 0; i < k; ++i)
			heap.push_back(nums[i]);
		buildHeap(heap.size());
		for (int i = k; i < nums.size(); ++i)
		{
			if (heap[0] > nums[i])
			{
				heap[0] = nums[i];
				siftDown(0);
			}
		}
		for (int i = 0; i < k; ++i)
			cout << heap[i] << " ";
	}
};