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<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
#define MAX 2000000
#define INFTY (1<<30)

int H, A[MAX + 1];

void maxHeapify(int i) {
    int l, r, largest;
    l = 2 * i;
    r = 2 * i + 1;
    
    if(l <= H && A[l] > A[i]) largest = l;
    else largest = i;
    if(r <= H && A[r] > A[largest]) largest = r;
    
    if(largest != i) {
        swap(A[i], A[largest]);
        maxHeapify(largest);
    }
}

int extract() {
    int maxv;
    if(H < 1) return -INFTY;
    maxv = A[1];
    A[1] = A[H--];
    maxHeapify(1);
    return maxv;
}

void increaseKey(int i, int key) {
    if(key < A[i]) return;
    A[i] = key;
    while(i > 1 && A[i / 2] < A[i]) {
        swap(A[i], A[i / 2]);
        i = i / 2;
    }
}

void insert(int key) {
    H++;
    A[H] = -INFTY;
    increaseKey(H, key);
}

int main() {
    int key;
    char com[10];
    
    while(1) {
        scanf("%s", com);
        if(com[0] == 'e' && com[1] == 'n') break;
        if(com[0] == 'i') {
            scanf("%d", &key);
            insert(key);
        }else {
            printf("%d\n", extract());
        }
    }
    
    return 0;
}