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Airline Gate Queue OverviewAn airline control center tracks aircraft waiting to reach a gate. Each aircraft has a unique integer id and a priority equal to its ETA (in minutes). A smaller ETA means higher dispatch priority. The system supports adding new aircraft (insert), decreasing an aircraft’s ETA (decreaseKey), and dispatching the aircraft with the smallest ETA (extractMin). Data Model• The priority queue is a min-heap stored in an array, using 0-based indexing.• The heap stores nodes directly: each entry is {priority, id}, both integers.• One hash map (key: current index, value: reference to heap array) accompanies the heap to allow decreaseKey to be implemented in O(log n).• Priorities (ETAs) are guaranteed to be unique at all times; the aircraft with the smallest priority is always the one dispatched (no tie-breaking needed). Provided Helpers (assumed present and correct and you don’t need to implement these)• heapify_up(i): restores heap order upward from index i.• heapify_down(i): restores heap order downward from index i. Functions to Implement flight_add(int id, int priority)Purpose: introduces an aircraft with the specified id and initial ETA. Inserts a node {priority, id} into the 0-indexed min-heap and records the heap index for this id. decrease_flight_key(int id, int newPriority)Purpose: updates the priority of the specified aircraft from its current ETA to a strictly smaller ETA. The aircraft remains in the heap; only its priority changes. The effect is that its relative order may improve according to the heap’s ordering by priority. flight_pop() -> intPurpose: removes and returns the id of the aircraft with the smallest ETA (priority) from the min-heap, restoring the heap property afterward. Example flight_add(42,9); flight_add(17,12); flight_add(11,13); decrease_flight_key(11,7); flight_pop(); decrease_flight_key(42,6); flight_pop(); flight_pop(); Expected outputs when calling in order:[11, 42, 17] Structure of the Problem class AirlineGateQueue {public:    struct Node { int pr, id; };    vector heap;    unordered_map idx;    void heapify_up(int i);    void heapify_down(int i);    void decrease_flight_key(int id, int newPriority);    void flight_add(int id, int priority);    int flight_pop();}; You can use the following compilers to test your code: 1. https://cpp.sh/2. https://my.newtonschool.co/playgrounds/cpp-compiler3. https://www.w3schools.com/cpp/trycpp.asp?filename=demo_compiler

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