You could sort after each add, but that's per operation. Instead, use a min-heap of size k. The heap always contains the k largest elements seen so far. The minimum of these k elements (heap top) is the kth largest overall. When adding a new element: if it's larger than the heap top, remove the top and add the new element.
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$ curl repovive.com/roadmaps/maang-interview-prep/heaps-priority-queues/kth-largest-stream-hint
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