215. Kth Largest Element in an Array

最新推荐文章于 2022-07-02 13:48:51 发布

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本文介绍了三种不同的算法来解决寻找未排序数组中第K大的元素的问题。这些方法包括使用优先队列、类似快速排序的方法及堆排序。每种方法都有其特定的时间复杂度和空间复杂度，适用于不同场景。

Find the kth largest element in an unsorted 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.

Solution 1 PriorityQueue

//O(N lg K) running time + O(K) memory
	public static int findKthLargest(int[] nums, int k) {
		final PriorityQueue<Integer> pq = new PriorityQueue<>();
		for (int val : nums) {
			pq.offer(val);
			if (pq.size() > k) {
				pq.poll();
			}
		}
		return pq.peek();
	}

Solution 2

//similar idea with quick sort
	public static int findKthLargest2(int[] nums, int k) {
		//shuffle(nums);
        k = nums.length - k;
        int start = 0;
        int end = nums.length - 1;
        while(start < end){
            int j = partition(nums, start, end);
            if(j < k){
                start = j + 1;
            }else if(j > k){
                end = j - 1;
            }else{
                break;
            }
        }
        return nums[k];
    }
    public static int partition(int [] nums, int start, int end){
        int i = start;
        int j = end + 1;
        while(true){
            while(i < end && (nums[++i] < nums[start]));
               
            while(j > start && (nums[start] < nums[--j]));
            if(i >= j){
                break;
            }
            swap(nums, i, j);
        }
        swap(nums, start, j);
        return j;
    }
    public static void swap(int [] nums, int i, int j){
        int temp = nums[i];
        nums[i] = nums[j];
        nums[j] = temp;
    }
    
    private static void shuffle(int a[]) {

        Random random = new Random();
        for(int ind = 1; ind < a.length; ind++) {
            final int r = random.nextInt(ind + 1);
            swap(a, ind, r);
        }
    }

Solution 3 Heap sort

//Heap sort
    private static int L;
    public static int findKthLargest3(int[] nums, int k) 
    {
        heapSort(nums);
        return nums[nums.length - k];
    }

    private static void heapSort(int[] nums)
    {
       buildHeap(nums);
       for(int i = L;i >=1; i--)
       {
           swap(nums, 0, i);
           L = L - 1;
          heapify(nums, 0);
       }
    }

    private static void buildHeap(int[] nums)
    {
        L = nums.length-1;
        for(int i = L/2; i >=0; i--)
            heapify(nums, i);
    }

    //max-heap
    private static void heapify(int[] nums, int i)
    {
        int l = 2 * i;
        int r = l + 1;
        int largest = i;
        if((l <= L) && (nums[l] > nums[largest]))
            largest = l;
        if((r <= L) && (nums[r] > nums[largest]))
            largest = r;
        if(largest != i)
        {
            swap(nums, i, largest);
            heapify(nums, largest);
        }
    }