Data Structures: Binary Min-Heap & Continuous Stream Median

Construct a custom Binary Heap from scratch and solve the continuous Running Stream Median problem:

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  Private std::vector<int> heap.
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  void push(int val): Adds element and performs sift-up to preserve min-heap invariant.
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  void pop(): Replaces root with last element and performs sift-down.
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  int top() const: Returns minimum element in $O(1)$.
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  int size() const and bool empty() const.

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  Uses a Max-Heap for lower half numbers and a Min-Heap for upper half numbers.
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  void addNum(int num): Inserts number and rebalances heap sizes in $O(\log N)$.
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  double findMedian() const: Returns exact median in $O(1)$ time.

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  Test MinHeap operations (push, pop, top).
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  Stream numbers: 5, 15, 1, 3, 2, 8, 7 and display running median after each insertion.