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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 $O (n)$
edited | 276 views

Aspi R Osa ji,

Very good observation. But i think question needs some correction. Because  in sorted list they are finding median in O(1) time (or their list has properties simillar to array).

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
the median.
Median = (max(ar1[0], ar2[0]) + min(ar1[1], ar2[1]))/2
Time complexity O(logn)

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

edited by
its given lists. why can we use arrays then?

Aspi R Osa ji,

Very good observation. But i think question needs some correction. Because  in sorted list they are finding median in O(1) time (or their list has properties simillar to array).