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: Time Limit Exceeded)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <limits.h>

#define N 100

void Merge(long *A, long left, long mid, long right) {
  long n1,n2,*L,*R,i,j,k;
  n1 = mid -left;
  n2 = right - mid;
  L = (long*)malloc(sizeof(long) * (n1+1));
  R = (long*)malloc(sizeof(long) * (n2+1));
  for (i = 0; i< n1; i++) {
    L[i] = A[left+i];
  }
  for (i = 0; i < n2; i++) {
    R[i] = A[mid+i];
  }
  L[n1] = LONG_MAX; R[n2] = LONG_MAX;
  i = 0;j = 0;
  for(k = left; k < right; k++) {
    if (L[i] < R[j]) {
      A[k] = L[i];
      i++;
    }else {
      A[k] = R[j];
      j++;
    }
  }
  free(L);
  free(R);
}

void Merge_Sort(long *A, long left, long right) {
  if(left+1 < right) {
    long mid = (left + right)/2;
    Merge_Sort(A,left,mid);
    Merge_Sort(A,mid,right);
    Merge(A,left,mid,right);
  }
}


int main()
{
  long i,key,**S,*length,max,maxi;
  char command[8],*flag;
  S = (long**)calloc(N,sizeof(long*));
  flag = (char*)calloc(N,sizeof(char));
  length = (long*)calloc(N,sizeof(long));
  for (i = 0; i < N; i++) {
    S[i] = (long*)calloc(1000000,sizeof(long));
  }

  while(1) {
    scanf("%s",command);
    if(strcmp(command,"insert") == 0) {
      scanf("%ld",&key);
      i = key % N;
      S[i][length[i]] = key;
      length[i]++;
      flag[i] = 1;
    }
    if(strcmp(command,"extract") == 0) {
      for (i = 0; i < N; i++) {
	if(flag[i] != 0) {
	  Merge_Sort(S[i],0,length[i]);
	  flag[i] = 0;
	}
      }
      max = 0;
      for(i = 0; i < N; i++) {
	if(length[i] > 0 && S[i][length[i]-1] > max) {
	  max = S[i][length[i]-1];
	  maxi = i;
	}
      }
      length[maxi]--;
      printf("%ld\n",max);
    }
    if(strcmp(command,"end") == 0) break;
  }

  for (i = 0; i < N; i++) {
    free(S[i]);
  }
  free(S);
  free(flag);
  free(length);
  return 0;
}