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>

#define N 2000001

void maxHeapify(int A[N],int i);
void maxHeapInsert(int A[N], int key);
void heapIncreaseKey(int A[N], int i, int key);
int heapExtractMax(int A[N]);

int heap_size = 0;
//int A[N];

int main(){
  int A[N];
  int i,j,key,max;
  char com[20];
  
  //heap_size = N;

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




void maxHeapInsert(int A[],int key){
  
  
  
  heap_size +=1;
  A[heap_size] = (-1000000000);
  heapIncreaseKey(A, heap_size, key);
  
  
}


void heapIncreaseKey(int A[], int i, int key){
  int temp;
  
  
  if(key < A[i]) printf("error\n");
  
  A[i] = key;
  while(i > 1 && A[i/2] < A[i]){
    temp = A[i];
    A[i] = A[i/2];
    A[i/2] = temp;
    i = i/2;
    
    
  } 
}

int heapExtractMax(int A[]){
  int max;

  if(heap_size < 1) printf("heap under \n");
  
  max = A[1];
  A[1] = A[heap_size];
  heap_size -= 1;
  maxHeapify(A, 1);
  return max;
  
}


void maxHeapify(int A[],int i){
  int l,r,largest,temp;
  
  l = 2*i;
  r = 2*i + 1;
  if(l <= heap_size && A[l] > A[i]){
    largest = l;
  }
  else largest = i;
  
  if(r <= heap_size && A[r] > A[largest]){
    largest = r;
  }
  
  if(largest != i){
    temp = A[i];
    A[i] = A[largest];
    A[largest] = temp;
    maxHeapify(A,largest);
  }
  
  
}