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 <string.h>
#include <limits.h>

#define MAX 2000000

int left(int);
int right(int);
int parent(int);
void swap(int [],int,int);
void buildMaxHeap(int []);
void maxHeapify(int [],int);
void insert(int [],int);
void heapIncreaseKey(int [],int,int);
int heapExtract(int []);

int H,A[MAX];

int main(){
  char com[20];
  int ans;
  int key;

  while (1){
    scanf("%s",com);

    if (strcmp(com,"insert") == 0){
      scanf("%d",&key);
      insert(A,key);
    }

    else if (strcmp(com,"extract") == 0){
      ans = heapExtract(A);
      printf("%d\n",ans);
    }

    else if (strcmp(com,"end") == 0)
      break;
  }
  return 0;
}

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

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

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

void swap(int A[],int a,int b){
  int temp;

  temp = A[a];
  A[a] = A[b];
  A[b] = temp;
}

void buildMaxHeap(int A[]){
  int i;

  for (i = H/2;i >= 1;i--)
    maxHeapify(A,i);
}

void maxHeapify(int A[],int i){
  int l,r,largest;

  l = left(i);
  r = right(i);

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

  else
    largest = i;

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

  if (largest != i){
    swap(A,i,largest);
    maxHeapify(A,largest);
  }
  
}

void insert(int A[],int key){
  H++;
  A[H] = -INT_MAX;
  heapIncreaseKey(A,H,key);
}

void heapIncreaseKey(int A[],int i,int key){
  if (key < A[i]){
    fprintf(stderr,"新しいキーは現在のキーよりも小さい\n");
    exit(1);
  }

  A[i] = key;

  while (i > 1 && A[parent(i)] < A[i]){
    swap(A,i,parent(i));
    i = parent(i);
  }
}

int heapExtract(int A[]){
  int max;
  
  if (H < 1){
    fprintf(stderr,"ヒープアンダーフロー\n");
    exit(2);
  }

  max = A[1];
  A[1] = A[H];
  H--;
  maxHeapify(A,1);

  return max;
}