Median of Stream of Running Integers using STL

Given an array arr[] of size N representing integers required to be read as a data stream, the task is to calculate and print the median after reading every integer.

Examples:

Input: arr[] = { 5, 10, 15 } Output: 5 7.5 10 Explanation: After reading arr[0] from the data stream, the median is 5. After reading arr[1] from the data stream, the median is 7.5. After reading arr[2] from the data stream, the median is 10.

Input: arr[] = { 1, 2, 3, 4 } Output: 1 1.5 2 2.5

Approach: The problem can be solved using Ordered Set. Follow the steps below to solve the problem:

Initialize a multi Ordered Set say, mst to store the array elements in a sorted order.
Traverse the array using variable i. For every i^th element insert arr[i] into mst and check if the variable i is even or not. If found to be true then print the median using (*mst.find_by_order(i / 2)).
Otherwise, print the median by taking the average of (*mst.find_by_order(i / 2)) and (*mst.find_by_order((i + 1) / 2)).

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach

#include <iostream>
#include <ext/pb_ds/assoc_container.hpp> 
#include <ext/pb_ds/tree_policy.hpp> 
using namespace __gnu_pbds; 
using namespace std;
typedef tree<int, null_type, 
less_equal<int>, rb_tree_tag,
tree_order_statistics_node_update> idxmst;



// Function to find the median
// of running integers
void findMedian(int arr[], int N)
{
    // Initialise a multi ordered set
    // to store the array elements 
    // in sorted order
    idxmst mst;
    
    // Traverse the array
    for (int i = 0; i < N; i++) {

        // Insert arr[i] into mst
        mst.insert(arr[i]);

        // If i is an odd number
        if (i % 2 != 0) {

            // Stores the first middle
            // element of mst
            double res 
             = *mst.find_by_order(i / 2);

            // Stores the second middle
            // element of mst
            double res1 
              = *mst.find_by_order(
                             (i + 1) / 2);

            cout<< (res + res1) / 2.0<<" ";
        }
        else {

            // Stores middle element of mst
            double res
               = *mst.find_by_order(i / 2);

            // Print median
            cout << res << " ";
        }
    }
}

// Driver Code
int main()
{
    // Given stream of integers
    int arr[] = { 1, 2, 3, 3, 4 };

    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call
    findMedian(arr, N);
}

Python3

# Python program to implement the approach for finding the median of running integers

# Import the necessary module for Ordered Dict
from collections import OrderedDict

def find_median(arr):
  # Initialize an ordered dictionary to store the elements in sorted order
  ordered_dict = OrderedDict()
  
  # Traverse the array
  for i in range(len(arr)):
    # Insert arr[i] into ordered_dict
    ordered_dict[arr[i]] = ordered_dict.get(arr[i], 0) + 1
    
    # If i is an odd number
    if i % 2 != 0:
      # Find the middle elements and store them in a list
      mid = list(ordered_dict.keys())[i//2:i//2 + 2]
      
      # Calculate the median by taking the average of the middle elements
      median = (mid[0] + mid[1]) / 2
      
      # Print median
      print("%.1f" % median, end=" ")
    else:
      # Find the middle element
      mid = list(ordered_dict.keys())[i//2]
      
      # Print median
      print(mid, end=" ")

# Given stream of integers
arr = [1, 2, 3, 3, 4]

# Function call
find_median(arr)
# This code is contributed by Shivam Tiwari

JavaScript

// JavaScript program to implement the approach for finding the median of running integers

// Initialize an object to store the elements in sorted order
let orderedObj = {};

function find_median(arr) {
  // Traverse the array
  for (let i = 0; i < arr.length; i++) {
    // Insert arr[i] into orderedObj
    orderedObj[arr[i]] = (orderedObj[arr[i]] || 0) + 1;

    // If i is an odd number
    if (i % 2 !== 0) {
      // Find the middle elements and store them in a list
      let mid = Object.keys(orderedObj).slice(i / 2, i / 2 + 2);

      // Calculate the median by taking the average of the middle elements
      let median = (parseInt(mid[0]) + parseInt(mid[1])) / 2;

      // Print median
      process.stdout.write(median.toFixed(1) + " ");
    } else {
      // Find the middle element
      let mid = Object.keys(orderedObj)[i / 2];

      // Print median
      process.stdout.write(mid + " ");
    }
  }
}

// Given stream of integers
let arr = [1, 2, 3, 3, 4];

// Function call
find_median(arr);


// This code is contributed by sdeadityasharma

Java

import java.util.*;

public class GFG {

    // Function to find the median
    // of running integers
    public static void findMedian(int[] arr) {
        // Initialize an ordered dictionary to store the elements in sorted order
        Map<Integer, Integer> ordered_dict = new TreeMap<>();

        // Traverse the array
        for (int i = 0; i < arr.length; i++) {
            // Insert arr[i] into ordered_dict
            ordered_dict.put(arr[i], ordered_dict.getOrDefault(arr[i], 0) + 1);

            // If i is an odd number
            if (i % 2 != 0) {
                // Find the middle elements and store them in a list
                List<Integer> mid = new ArrayList<>(ordered_dict.keySet()).subList(i / 2, i / 2 + 2);

                // Calculate the median by taking the average of the middle elements
                double median = (mid.get(0) + mid.get(1)) / 2.0;

                // Print median
                System.out.print(String.format("%.1f", median) + " ");
            } else {
                // Find the middle element
                int mid = new ArrayList<>(ordered_dict.keySet()).get(i / 2);

                // Print median
                System.out.print(mid + " ");
            }
        }
    }

    // Driver Code
    public static void main(String[] args) {
        // Given stream of integers
        int[] arr = {1, 2, 3, 3, 4};

        // Function call
        findMedian(arr);
    }
}
// This code is contributed By Shivam Tiwari

//C# program to implement the approach for finding the median of running integers
using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        // Given stream of integers
        int[] arr = { 1, 2, 3, 3, 4 };

        // Function call
        find_median(arr);
    }

    // Function to find the median of running integers
    static void find_median(int[] arr)
    {
        // Initialize an ordered dictionary to store the elements in sorted order
        Dictionary<int, int> ordered_dict = new Dictionary<int, int>();

        // Traverse the array
        for (int i = 0; i < arr.Length; i++)
        {
            // Insert arr[i] into ordered_dict
            if (ordered_dict.ContainsKey(arr[i]))
            {
                ordered_dict[arr[i]]++;
            }
            else
            {
                ordered_dict[arr[i]] = 1;
            }

            // If i is an odd number
            if (i % 2 != 0)
            {
                // Find the middle elements and store them in a list
                var mid = ordered_dict.Keys.ToList().GetRange(i / 2, 2);

                // Calculate the median by taking the average of the middle elements
                var median = (mid[0] + mid[1]) / 2.0;

                // Print median
                Console.Write("{0:F1} ", median);
            }
            else
            {
                // Find the middle element
                var mid = ordered_dict.Keys.ToList().GetRange(i / 2, 1);

                // Print median
                Console.Write("{0} ", mid[0]);
            }
        }

        
    }
}
// This code is contributed by shivamsharma215

Output

1 1.5 2 2.5 3

Time Complexity: O(N * log(N))
Auxiliary Space: O(N)

Median of Stream of Running Integers using STL | Set 2

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