703

public class KthLargest {
    private readonly PriorityQueue<int, int> pq = new();
    private readonly int k;
 
    public KthLargest(int k, int[] nums) {
        this.k = k;
 
        foreach (int x in nums)
            InsertAndTrim(x);
    }
 
    public int Add(int val) {
        InsertAndTrim(val);
        return pq.Peek();
    }
 
    private void InsertAndTrim(int x) {
        pq.Enqueue(x, x);
        if (pq.Count > k) pq.Dequeue();
    }
}

Min Heap for Kth largest pattern.
We insert in the heap, and if heap is greater than k, we remove minimum element. This way, we always have K largest elements in the heap, and the top node is exactly the Kth largest since this is a min heap.