[Leetcode] Find Median from data stream finding the median of a stream

Median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value. The median is the mean of the middle value.

Examples:

[2,3,4], the median is3

[2,3], the median is(2 + 3) / 2 = 2.5

Design a data structure that supports the following and the operations:

• void addnum (int num)-Add A integer number from the data stream to the data structure.
• Double Findmedian ()-Return The median of all elements so far.

For example:

Add (1) Add (2) Findmedian () 1.5add (3) Findmedian () 2

Credits:
Special thanks to @Louis1992 for adding this problem and creating all test cases.

This problem gives us a stream of data, let's find the median, because the data in the stream is not ordered, so we should first think of a way to make it orderly. If we use vectors to store data streams, it is not efficient to sort the arrays in each new data. So the thought of using multiset this data structure, is ordered to save information, but it can not use subscript direct access to elements, find the median number is not efficient. The solution used here is very ingenious, we use the size of the heap to solve the problem, where the large heap to save the right half of the larger number, a small heap to save the left half of the smaller array. So the whole array is divided into two sections, because the heap is kept in the way from large to small, we hope that the data inside the large heap is small to large, so that the first to calculate the median number of convenient. We use a little trick, that is, the number that is stored in a large heap is first reversed, so that the order from the big to the small is actually what we want in order from small to large. When the large heap and the number in the small heap as long, we take out a lot of small heap of the first element to average, when the small heap of elements, the first element of the small heap is the median, see the code is as follows:

Solution One:

classMedianfinder { Public:    //Adds A number into the data structure.    voidAddnum (intnum)        {Small.push (num); Large.push (-small.top ());        Small.pop (); if(Small.size () <large.size ()) {Small.push (-large.top ());        Large.pop (); }    }    //Returns The median of the current data stream    DoubleFindmedian () {returnSmall.size () > Large.size ()? Small.top ():0.5* (Small.top ()-large.top ()); }Private: Priority_queue<Long>small, Large;};

The above method uses priority_queue to implement the heap function, we can also use Multiset to implement the heap, see the code as follows:

Solution Two:

classMedianfinder { Public:    //Adds A number into the data structure.    voidAddnum (intnum)        {Small.insert (num); Large.insert (-*Small.begin ());        Small.erase (Small.begin ()); if(Small.size () <large.size ()) {Small.insert (-*Large.begin ());        Large.erase (Large.begin ()); }    }    //Returns The median of the current data stream    DoubleFindmedian () {returnSmall.size () > Large.size ()? *small.begin ():0.5* (*small.begin ()-*Large.begin ()); }Private: Multiset<Long>small, Large;};

Resources:

Https://leetcode.com/discuss/64850/short-simple-java-c-python-o-log-n-o-1

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[Leetcode] Find Median from data stream finding the median of a stream