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<stdlib.h>

#define MAX 2000001
#define INF 2147483647
int A[MAX];
int h=0;

void heapIncreaseKey(int i, int k);

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,temp;
  
  l = left(i);
  r = right(i);
  
  // choose max node among left child, me, and right child
  
  if(l <= h && A[l] > A[i])
    largest = l;
  else 
    largest = i;
  
  if(r <= h && A[r] > A[largest])
    largest = r;
  
  if(largest != i){ // A[i] > A[l],A[r]
    temp = A[i];
    A[i] = A[largest];
    A[largest] = temp;
    maxHeapify(largest);
  }
}
void buildMaxHeap(){
  int i;
  for(i=h/2;i>0;i--)
    maxHeapify(i);
}

void maxHeapInsert(int k){
  h++;
  A[h] = -INF;
  heapIncreaseKey(h,k);
}

void heapIncreaseKey(int i, int k){

  int temp;

  /*  // 例外処理
  if(k < A[i]){
    printf("new key is smaller than current key\n");
    exit(0);
    }*/
  
  A[i] = k;
  while(i>1 && A[parent(i)] < A[i]){
    temp = A[i];
    A[i] = A[parent(i)];
    A[parent(i)] = temp;
    i = parent(i);
  }
  
  
  
}
int extract(){
  
  /*  // 例外処理
  if(h<1){
    printf("heap underflow\n");
    exit(0);
    }*/
  
  int max = A[1];
  A[1] = A[h];
  h--;
  maxHeapify(1);
  
  return max;
}
int main(){
  
  int i,k;
  char cmd[10];
  
  // 入力
  while(1){
    scanf("%s",cmd);
    
    if(strcmp(cmd,"insert") == 0){
      scanf("%d",&k);
      maxHeapInsert(k);
    }
    else if(strcmp(cmd,"extract") == 0){
      printf("%d\n",extract());
    }
    else if(strcmp(cmd,"end") == 0){
      break;
    }
  }
  return 0;
}