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>
#include <limits.h>

int extractMax(int []);
void insert(int [], int);
void increaseKey(int [], int, int);
void maxHeapify(int [], int);
int parent(int);
int left(int);
int right(int);

int A[1000000], H = 0;

int main(){
  char s[10];
  int k;

  while(1){
    scanf("%s", s);
    
    if(s[0] == 'e' && s[1] == 'n') break;
    else if(s[0] == 'e') printf("%d\n", extractMax(A));
    else if(s[0] == 'i'){
      scanf("%d", &k);
      insert(A, k);
    }
  }
  
  return 0;
}

int extractMax(int A[]){
  int max;
  
  if(H < 1) exit(1);
  
  max = A[1];
  A[1] = A[H];
  H--;
  maxHeapify(A, 1);
  return max;
}

void insert(int A[], int key){
  H++;
  A[H] = INT_MIN;
  increaseKey(A, H, key);
}

void increaseKey(int A[], int i, int key){
  int temp;
  
  if(key < A[i]) exit(1);
  A[i] = key;
  while(i > 1 && A[parent(i)] < A[i]){
    temp = A[i];
    A[i] = A[parent(i)];
    A[parent(i)] = temp;
    i = parent(i);
  }
}

void maxHeapify(int A[], int i){
  int l = left(i);
  int r = right(i);
  int large, temp;

  if(l <= H && A[l] > A[i]) large = l;
  else large = i;

  if(r <= H && A[r] > A[large]) large = r;

  if(large != i){
    temp = A[i];
    A[i] = A[large];
    A[large] = temp;
    maxHeapify(A, large);
  }
}

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

int left(int i){ return i*2; }

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