Doubt in merge sort?

#1

explain the time complexity of the merge sort?

#2

@mehulbhandari358
for mergesort, this is the formula for time complexity with array size of N
T(N) = 2T(N/2) + O(N)
because we call mergesort for both halves(costing 2T(N/2) ) and then merge them (costing O(N) )
now when we expand this formula,
we get T(N) = O(N) + 2O(N/2) + 4O(N/4) + … upto logN terms
hence T(N) = O(N)xlogN = O(NlogN).

#3

what is T AND O here are they diiferent ?

#4

T is the complexity of a function(merge sort in this case) and O is complexity of any operation.
T(N) = O(NlogN) means that a function with input size N takes time complexity of NlogN.

#5

then how merge sort takes o(n) complexity ?

#6

merge sort has a complexity of NlogN only!

#7

no i am asking for merging the two arrays how does it takes o(n) time ?

#8

@mehulbhandari358
we do this in mergesort
mergesort(a,s,mid)
mergesort(a,mid+1,e)
// now here the array from s to mid and mid+1 to e is already sorted!
hence now merging two sorted arrays takes linear time!

#9

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