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 <string.h>
#define MAX_HEAP 2000000
#define NEG_INF -100000

int heap_size = 1;
/* 木の移動 */
int parent(int);
int left(int);
int right(int);

void maxHeapfy(int *, int);
void maxHeapInsert(int *, int);
void heapIncreaseKey(int *, int, int);
int heapExtractMax(int *);

int main(void) {
  int key;
  int ary[MAX_HEAP];
  char order[10];

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

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 *A, int i) {
  int l = left(i);
  int r = right(i);
  int largest;

  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) {
    /* A[i]とA[largest]の値を交換 */
    int tmp = A[largest];
    A[largest] = A[i];
    A[i] = tmp;

    maxHeapify(A, largest);
  }
}

void maxHeapInsert(int *A, int key) {
  heap_size++;
  A[heap_size] = NEG_INF;
  heapIncreaseKey(A, heap_size, key);
}

void heapIncreaseKey(int *A, int i, int key) {
  if (key < A[i]) {             /* 新しいキーは現在のキーより小さい */
    return;
  }

  A[i] = key;
  while (i > 1 && A[parent(i)] < A[i]) {
    /* 親と子を入れ替える */
    int tmp = A[i];
    A[i] = A[parent(i)];
    A[parent(i)] = tmp;
    i = parent(i);
  }
}

int heapExtractMax(int *A) {
  if (heap_size < 1) {          /* ヒープアンダーフロー */
    return -1;
  }

  int max = A[1];
  A[1] = A[heap_size];
  heap_size--;
  maxHeapify(A, 1);
  return max;
}