/**
 * @param {number[]} nums
 * @param {number} k
 * @return {number}
 */
const findKthLargest = function (nums, k) {
  // 将数组的前k个元素作为堆，然后将其堆化
  const heap = nums.slice(0, k);
  // 从最后一个非叶子节点遍历，自底向上下沉堆化
  for (let i = Math.floor(k / 2 - 1); i >= 0; i--) {
    siftDown(heap, i, k);
  }
  // 处理剩余元素
  for (let i = k; i < nums.length; i++) {
    // 如果剩余元素大于堆顶元素，替换然后下沉维护堆
    if (nums[i] > heap[0]) {
      heap[0] = nums[i];
      siftDown(heap, 0, k);
    }
  }

  return heap[0];
};

// 下沉函数（维护堆性质）
function siftDown(heap, start, heapSize) {
  let cur = start;
  while (true) {
    const left = 2 * cur + 1;
    const right = 2 * cur + 2;
    let smallest = cur;

    if (left < heapSize && heap[left] < heap[smallest]) smallest = left;
    if (right < heapSize && heap[right] < heap[smallest]) smallest = right;

    if (smallest === cur) break;

    [heap[cur], heap[smallest]] = [heap[smallest], heap[cur]];
    cur = smallest;
  }
}