使用优先级队列计算中位数

Question

我需要计算中位数。有人告诉我，在这个特定的应用程序中，最好的方法是使用优先级队列。我不知道如何继续。我真的很感激任何帮助。

Answer 1

这应该可以。维护两个大于和小于中值的数字的优先级队列。在两个队列之间移动值，使它们保持平衡或接近平衡，并根据优先级队列的顶部值定义中值。

#include <queue>
#include <vector>
#include <functional>
#include <limits>
#include <iostream>

template<class T>
class RunningMedian {
 private:
  //Values greater than the median sorted so that smallest is on top
  std::priority_queue<T, std::vector<T>, std::greater<T> > upper;
  //Values smaller than the median sorted so that greatest is on top
  std::priority_queue<T, std::vector<T>, std::less<T> > lower;

 public:
  RunningMedian(){
    //Seed the queues
    upper.push(std::numeric_limits<T>::max());
    lower.push (std::numeric_limits<T>::min());
  }
  void push(T val){
    //Add number to the property queue

    //If number is greater than the least upper number, it is an upper number
    if(val>=upper.top())
      upper.push(val);
    else //Otherwise it is a lower number
      lower.push(val);

    //Rebalance
    //If the queues sizes differ by 2, they need to be rebalanced so that they
    //differ by 1.
    if(upper.size()-lower.size()==2){ //Upper queue is larger
      lower.push(upper.top());        //Move value from upper to lower
      upper.pop();                    //Remove same value from upper
    } else if(lower.size()-upper.size()==2){ //Lower queue is larger
      upper.push(lower.top());               //Move value from lower to upper
      lower.pop();                           //Remove same value
    }
  }

  T getMedian() const {
    if(upper.size()==lower.size())               //Upper and lower are same size
      return(upper.top()+lower.top())/((T)2.0);  //so median is average of least upper and greatest lower
    else if(upper.size()>lower.size())           //Upper size greater
      return upper.top();
    else                                         //Lower size greater
      return lower.top();
  }
};

int main(){
  RunningMedian<int> rm;
  rm.push(10);
  rm.push(3);
  rm.push(1);
  rm.push(20);
  rm.push(5);
  rm.push(8);
  rm.push(-1);
  std::cout<<rm.getMedian()<<std::endl; //Gives 5
}

Answer 2

@Richard 的代码产生未定义的行为。你可以参考这个。综上所述，当您在空优先级队列上调用 PQ.top 时，您将做出未定义的行为。

我会用求反的方法，让最大堆中原来上半部分的最小数成为最大。

class FindMedian{
    /* the largest number in lower half */
    std::priority_queue<int> small;
    /* the largest negative number in upper half */
    std::priority_queue<int> large;
    public:
        void add(int num) {
            small.push(num);
            large.push(-small.top());
            /*In order to rearrange small.top() later
            * e.g., assume that small = {2} and large = {-4}
            * Now, we want to push 5 into the small, so small = {5, 2} and 
            * large = {-4, -5}
            * However, the small.top() is larger than (-large.top()).
            * Thus, we need to rearrange them and first pop out in small container
            */
            small.pop();
            //we ensure that the size of small is equal to or one more than large
            if (small.size() < large.size()) {
                small.push(-large.top());
                large.pop();
            }

        }
        double findMedian() {
            return small.size() > large.size() ?
               //if total size is odd or if total size is even 
                small.top() : ((small.top() - large.top()) >> 1);
        }
    };

基本上，代码背后的原理与 Richard 的相同。

Answer 3

#包括

使用命名空间 std；

#定义尺寸 5

类队列{

私人：

int arr[size];

int rear, front;

公众：

Queue()
{
    front = -1;
    rear = -1;
}

bool isfull()
{
    return (rear == size - 1);
}

bool empty()
{
    return (front == -1 && rear == -1);
}

void enqueue(int temp)
{
    if (isfull())
    {
        cout << "Queue Overflow" << endl;
    }
    if (empty())
    {
        front = 0;
        rear = 0;
    }
    else {
        rear++;
    }
    arr[rear] = temp;
}

void dequeue()
{
    if (empty())
    {
        cout << "Queue Underflow" << endl;
    }
    if (front==rear)
    {
        front = -1;
        rear = -1;
    }
    else {
        front++;
    }
}

int peek()
{
    if (empty())
    {
        cout << "Queue is empty" << endl;
    }
    return arr[front];
}

void display()
{
    if (empty())
    {
        cout << "Queue is empty" << endl;
    }
    cout << "Queue Element=" << endl;
    for (int i = front; i <= rear; i++)
    {
        cout << arr[i] << endl;
    }
    cout << endl;
}

//Find the median of the Queue
int median()
{
    int median;
    if (empty())
    {
        cout << "Queue is empty" << endl;
        return 0;
    }
    median = arr[size / 2];
    return median;
    
}

};

int main() {

Queue q;

cout << "Insert the elements into the Queue=" << endl;

q.enqueue(1);

q.enqueue(2);

q.enqueue(3);

q.enqueue(4);

q.enqueue(5);

q.display();

cout << "Median value of Queue is=" << q.median() << endl;

return 0;

}