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>
#include <string.h>

#define MAX_H 2000000
#define INF INT_MIN

int H;

int heapExtractMax(int*);
void maxHeapify(int*,int);
void maxHeapInsert(int*,int);
void heapIncreseKey(int*,int,int);
void swap(int*,int*);

int main(){
  int val;
  static int a[MAX_H];
  char command[8];
  H = 0;
  while(1){
    scanf("%s",command);
    if(!strcmp(command,"end")){
      break;
    }else if(!strcmp(command,"insert")){
      scanf("%d",&val);
      maxHeapInsert(a,val);
    }else{
      printf("%d\n",heapExtractMax(a));
    }
  }

  return 0;
}

int heapExtractMax(int *A){
  int max;
  if(H < 1){ return -1; }
  max = A[0];
  A[0] = A[H-1]; H--;
  maxHeapify(A,0);
  return max;
}

void maxHeapify(int *A,int i){
  int l = i*2+1, r = i*2+2;
  int largest;
  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],&A[largest]);
    maxHeapify(A,largest);
  }
}

void maxHeapInsert(int *A,int val){
  H++;
  A[H-1] = INF;
  heapIncreseKey(A,H-1,val);
}

void heapIncreseKey(int *A,int i,int val){
  int j;
  if(val < A[i]){ return; }
  A[i] = val;
  j = (i & 1 ? i/2 : (i-1)/2);
  while(i > 0 && A[j] < A[i]){
    swap(&A[i],&A[j]);
    i = j;
    j = (i & 1 ? i/2 : (i-1)/2);
  }
}

void swap(int *a,int *b){
  int tmp;
  tmp = *a;
  *a = *b;
  *b = tmp;
}