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<limits.h>
#define MAX 2000000

int size=0;
int heap[MAX];

void maxHeapInsert(int);
void heapIncreaseKey(int ,int);
void maxHeapify(int);
int heapExtractMax();
int parent(int);
int left(int);
int right(int);

int main(){

  int n,i,tmp,x;
  char com[20];

  while(1){
    scanf("%s",com);
    if(com[0] == 'i'){
      scanf("%d",&x);
      maxHeapInsert(x);
    }
    else if(com[0] == 'e' && com[1] == 'x'){
      printf("%d\n",heapExtractMax());
    }
    else if(com[0] == 'e' && com[1] == 'n')
      break;
  }
  

  return 0;
}

void maxHeapInsert(int key){

  size++;
  heap[size] = INT_MIN;
  heapIncreaseKey(size,key);
}

void heapIncreaseKey(int i, int key){

  int tmp;

  if(key < heap[i])
    printf("error\n");
  heap[i] = key;
  while(i > 1 && heap[parent(i)] < heap[i]){
    tmp = heap[i];
    heap[i] = heap[parent(i)];
    heap[parent(i)] = tmp;
    i = parent(i);
  }
}

int heapExtractMax(){

  int max;

  max = heap[1];
  heap[1] = heap[size];
  size--;
  maxHeapify(1);
  return max;
}

int parent(int i){
  return i / 2;
  }

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

void maxHeapify(int i){
    int l,r,largest,tmp;
 
    l = left(i);
    r = right(i);
    if(l <= size && heap[l] > heap[i])
        largest = l;
    else
        largest = i;
    if(r <= size && heap[r] > heap[largest])
        largest = r;
    if(largest != i){
        tmp = heap[i];
        heap[i] = heap[largest];
        heap[largest] = tmp;
        maxHeapify(largest);
    }
}