leetcode-215. Kth Largest Element in an Array（基于堆排序）

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#leetcode #堆排序

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本文介绍了一种使用最大堆实现寻找未排序数组中第K大元素的方法。通过构建最大堆并逐步移除堆顶元素，最终找到目标元素。此方法效率高，适用于各类编程面试和技术挑战。

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原题

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.

基于堆排序思想

 public class SolutionHeapFindKthLargest
        {
            public int FindKthLargest(int[] nums, int k)
            {
                build_max_heap(nums);
                for (int i = 0; i < k; i++)
                {
                    swap(nums, 0, heap_size - 1);
                    heap_size--;
                    max_heapify(nums, 0);
                }
                return nums[heap_size];
            }

            private int left(int idx)
            {
                return (idx << 1) + 1;
            }
            private int right(int idx)
            {
                return (idx << 1) + 2;
            }
            private void max_heapify(int[] nums, int idx)
            {
                int largest = idx;
                int l = left(idx), r = right(idx);
                if (l < heap_size && nums[l] > nums[largest]) largest = l;
                if (r < heap_size && nums[r] > nums[largest]) largest = r;
                if (largest != idx)
                {
                    swap(nums, idx, largest);
                    max_heapify(nums, largest);
                }
            }
            private void build_max_heap(int[] nums)
            {
                heap_size = nums.Length;
                for (int i = (heap_size >> 1) - 1; i >= 0; i--)
                    max_heapify(nums, i);
            }

            private void swap(int[] nums, int i, int j)
            {
                int tmp = nums[i];
                nums[i] = nums[j];
                nums[j] = tmp;
            }
            private int heap_size;
        }