Problem:
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Priority Queue

A priority queue is a data structure which maintains a set $S$ of elements, each of with an associated value (key), and supports the following operations:

$insert(S, k)$: insert an element $k$ into the set $S$

$extractMax(S)$: remove and return the element of $S$ with the largest key

Write a program which performs the $insert(S, k)$ and $extractMax(S)$ operations to a priority queue $S$.
The priority queue manages a set of integers, which are also keys for the priority.

Input

Multiple operations to the priority queue $S$ are given. Each operation is given by "insert $k$", "extract" or "end" in a line. Here, $k$ represents an integer element to be inserted to the priority queue.

The input ends with "end" operation.

Output

For each "extract" operation, print the element extracted from the priority queue $S$ in a line.

Constraints

The number of operations $\leq 2,000,000$

$0 \leq k \leq 2,000,000,000$

Sample Input 1

insert 8
insert 2
extract
insert 10
extract
insert 11
extract
extract
end

Sample Output 1

8
10
11
2

Solution in C++ (judge verdict: Accepted)

#include <iostream>
#include <cstdio>
#include <cstdlib>
using namespace std;

int H = 0;

int parent(int i) { return (i - 1) / 2; }
int left(int i) { return (i + 1) * 2 - 1; }
int right(int i) { return (i + 1) * 2; }

void maxHeapify(int N, int A[], int i) {
    if (i >= N) {
        return;
    }
    int l = left(i);
    int r = right(i);
    int largest = i;
    if (l < N && A[l] > A[i]) {
        largest = l;
    }
    if (r < N && A[r] > A[largest]) {
        largest = r;
    }
    
    if (largest != i) {
        int temp = A[i];
        A[i] = A[largest];
        A[largest] = temp;
        maxHeapify(N, A, largest);
    }
}

int extractMax(int A[]) {
    int max = A[0];
    A[0] = A[H - 1];
    maxHeapify(H - 1, A, 0);

    H--;
    return max;
}

void insert(int A[], int key) {
    A[H] = key;
    int parentK = parent(H);
    int childK = H;
    
    while (parentK >= 0 && A[parentK] < A[childK]) {
        swap(A[parentK], A[childK]);
        childK = parentK;
        parentK = parent(parentK);
    }
    
    H++;
    return;
}

int main() {
    int A[2000000];
    char cmd[20];
    int key;
    
    while(true) {
        scanf("%s", cmd);
        
        if (cmd[0] == 'i') {
            scanf("%d", &key);
            insert(A, key);
            continue;
        }

        if (cmd[0] == 'e' && cmd[1] == 'x') {
            cout << extractMax(A) << endl;
            continue;
        }

        if (cmd[0] == 'e' && cmd[1] == 'n') {
            break;
        }
    }

    return 0;
}