# Median of Stream of Running Integers using STL | Set 2

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 10Explanation:

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**element insert^{th}**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);` `}` |

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

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