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;
}