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 <stdio.h>
#include <stdlib.h>
 
void maxheap(int *,int);

int main(int argc,char *argv[]) {
    int *heap, key, index, half, tmp;
    char cmd[20];
 
    heap = malloc(sizeof(int) * 2000001);
    heap[0] = 1;
    while (1) {
        scanf("%s %d ", cmd, &key);
        if (cmd[0] == 'i') {
            heap[0]++;
            index = heap[0];
            heap[index] = key;
 
            half = index / 2;
            while (index > 1 && heap[half] < heap[index]) {
                tmp = heap[index];
                heap[index] = heap[half];
                heap[half] = tmp;
                index /= 2;
                half = index / 2;
            }
        } else if (cmd[1] == 'x') {
            printf("%d\n", heap[1]);
            heap[1] = heap[heap[0]];
            heap[0]--;
            maxheap(heap, 1);
        } else {
            return 0;
        }
    }
    return 0;
}
void maxheap(int *heap, int i) {
  int heapsize, l, r, largest, tmp;
  
  heapsize = heap[0];
  l = 2*i;
  r = 2*i + 1;
  if (l <= heapsize && heap[l] > heap[i]) 
      largest = l;
  else 
      largest = i;
  if (r <= heapsize && heap[r] > heap[largest]) 
      largest = r;
  if (largest != i) 
    {
      tmp = heap[i];
      heap[i] = heap[largest];
      heap[largest] = tmp;
      maxheap(heap, largest);
    }
}