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 MAX 3000001
#define MINI -1
int parent(int);
int left(int);
int right(int);
void maxHeapify(int*, int);
void buildMaxHeap(int*);
void insert(int*, int);
void heapIncreaseKey(int*, int);
int extractMax(int*);
int n=0;
int main(){
  int *T, key;
  char func[7];
  T = (int*)malloc(sizeof(int) * MAX);
  while(1){
    scanf("%s",func);
    if(func[2] == 'd') break;
    else if(func[0] == 'i'){
      scanf("%d",&key);
      insert(T, key);
    }
    else if(func[0] == 'e') printf("%d\n",extractMax(T));
  }
  return 0;
}
int parent(int x){
  return x/2;
}
int left(int x){
  return 2*x;
}
int right(int x){
  return 2*x+1;
}
  void maxHeapify(int *A, int i){
    int l=left(i), r=right(i), largest, temp;
    if(l <= n && A[l] > A[i]) largest = l;
    else largest = i;
    if(r <= n && A[r] > A[largest]) largest = r;
    if(largest != i){
      temp = A[i];
      A[i] = A[largest];
      A[largest] = temp;
      maxHeapify(A,largest);
    }
  }
  void buildMaxHeap(int *A){
    int i;
    for(i=n/2; i>0; i--) maxHeapify(A,i);
  }
  void insert(int *A, int key){
    n++;
    A[n] = MINI;
    heapIncreaseKey(A, key);
  }
  void heapIncreaseKey(int *A, int key){
    int temp, i=n;
    if(key < A[i]) printf("Error\n");
    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);
    }
  }
  int extractMax(int *A){
    int max;
    if(n < 1) printf("Error\n");
    max = A[1];
    A[1] = A[n];
    n--;
    maxHeapify(A,1);
    return max;
  }