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 2000001
 
int size=0;
int A[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++;
  A[size] = INT_MIN;
  HeapIncreaseKey(size,key);
}
 
void HeapIncreaseKey(int i, int key){
 
  int tmp;
 
  if(key < A[i])
    printf("error\n");
  A[i] = key;
  while(i > 1 && A[Parent(i)] < A[i]){
    tmp = A[i];
    A[i] = A[Parent(i)];
    A[Parent(i)] = tmp;
    i = Parent(i);
  }
}
 
int HeapExtractMax(){
 
  int max;
 
  max = A[1];
  A[1] = A[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 left,right,largest,tmp;
  
    left = Left(i);
    right = Right(i);
    if(left <= size && A[left] > A[i])
        largest = left;
    else
        largest = i;
    if(right <= size && A[right] > A[largest])
        largest = right;
    if(largest != i){
        tmp = A[i];
        A[i] = A[largest];
        A[largest] = tmp;
        MaxHeapify(largest);
    }
}