std::priority_queue is a container adaptor that provides constant time lookup of the largest (by default) element, at the expense of logarithmic insertion and extraction.

Essential for algorithms like Dijkstra's, Prim's, and "Top K elements" problems.

• Top element access: $O(1)$
• Insertion: $O(\log N)$
• Removal of top: $O(\log N)$

cpp Standard
#include <queue>
#include <vector>

// Max-heap (default)
std::priority_queue<int> maxHeap;
maxHeap.push(10);
maxHeap.push(30);
maxHeap.push(20);

std::cout << maxHeap.top(); // 30

// Min-heap
std::priority_queue<int, std::vector<int>, std::greater<int>> minHeap;
minHeap.push(10);
minHeap.push(30);
std::cout << minHeap.top(); // 10

• Default Behavior: Forgetting that it's a max-heap by default.
• Efficiency: Overusing it when a simple sorted vector or std::set might suffice.
• Updating Elements: C++ std::priority_queue does not support updating an internal element (you must re-insert or use a different container).