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>
  
int heap[2000000];
int size;
  
void max_heapify(int heap[], int i) {
    int l = 2 * i + 1;
    int r = 2 * i + 2;
    int largest;
  
    if (l <= size && heap[l] > heap[i]) {
        largest = l;
    } else {
        largest = i;
    }
    if (r <= size && heap[r] > heap[largest]) {
        largest = r;
    }
  
    if (largest != i) {
        int tmp = heap[i];
        heap[i] = heap[largest];
        heap[largest] = tmp;
        max_heapify(heap, largest);
    }
}
  
void insert(int k){
    int child = size;
    int parent = (child - 1) / 2;
  
    heap[size] = k;
  
    while(1){
        if(heap[parent] > heap[child] || child == 0)
            break;
        int tmp = heap[child];
        heap[child] = heap[parent];
        heap[parent] = tmp;
  
        child = parent;
        parent = (child - 1) / 2;
    }
  
    size++;
}
  
int extract_max(){
    int ret = heap[0];
    heap[0] = heap[size-1];
    size--;
    max_heapify(heap, 0);
    return ret;
}
  
int main(){
    char cmd[8];
    int k;
  
    while(1) {
        scanf("%s", cmd);
        if(cmd[0] == 'i'){
            scanf("%d", &k);
            insert(k);
        }else if(cmd[1] == 'x'){
            printf("%d\n", extract_max());
        }else{
            return 0;
        }
    }
}