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It takes $O(n)$ time to find the median in a list of $n$ elements, which are not necessarily in sorted order while it takes only $O(1)$ time to find the median in a list of $n$ sorted elements. How much time does it take to find the median of $2n$ elements which are given as two lists of $n$ sorted elements each?

1. $O (1)$
2. $O \left(\log n\right)$ but not $O (1)$
3. $O (\sqrt{n})$ but not $O \left(\log n\right)$
4. $O (n)$ but not $O (\sqrt{n})$
5. $O \left(n \log n\right)$ but not $O (n)$

### 4 Comments

finding median of n elements (unsorted) takes O(n) time so for 2n elements also it will be O(n)
CORMEN Exercise problem

chapter-9 medians and order statistics page no-223  9.3-8

## 2 Answers

Best answer
1. Calculate the medians $m1$ and $m2$ of the input arrays $ar1[\ ]$ and $ar2[ \ ]$ respectively.
2. If $m1$ and $m2$ both are equal,
return $m1$ (or $m2$)
3. If $m1$ is greater than $m2$, then median is present in one of the below two subarrays.
(a)  From first element of $ar1$ to $m1$ $(ar1[0$ to $n/2])$
(b)  From $m2$ to last element of $ar2$  $(ar2[n/2$ to $n-1])$
4. If $m2$ is greater than $m1$, then median is present in one of the below two subarrays.
(a)  From $m1$ to last element of $ar1$  $(ar1[n/2$ to $n-1])$
(b)  From first element of $ar2$ to $m2$ $(ar2[0$ to $n/2])$
5. Repeat the above process until size of both the subarrays becomes $2$.
6. If size of the two arrays is $2$ then,
Median $= (\max(ar1[0], ar2[0]) + \min(ar1[1], ar2[1]))/2$
Time complexity $O(\log n)$

http://www.geeksforgeeks.org/median-of-two-sorted-arrays/

Correct Answer: $B$

### 4 Comments

1. Merge sort is having O(nlogn), simply merging two sorted arrays take only O(n)
2. When we can achieve TC as logn, why will we go for nlogn?
@vaibhavkedia968 2 sorted arrays after merging doesn’t guarantees that they are by default getting sorted. For eg. {11,18,22,31,40}  and {23,45,57,67,82}.
I am not getting it how it is O(logn) from this algo I am getting  O(n) time ??
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