aspose file tools
The moose likes C / C++ and the fly likes Problem regarding time complexity Big Moose Saloon
  Search | Java FAQ | Recent Topics | Flagged Topics | Hot Topics | Zero Replies
Register / Login

Win a copy of Elasticsearch in Action this week in the Big Data forum!
JavaRanch » Java Forums » Languages » C / C++
Bookmark "Problem regarding time complexity" Watch "Problem regarding time complexity" New topic

Problem regarding time complexity

naved momin
Ranch Hand

Joined: Jul 03, 2011
Posts: 692

I was reading a book which tellls that the outer loops time complexity is O(n-m) whereas for inner loop the books gives explanation as

" The inner while
loop goes around at most m times, and potentially far less when the pattern match
fails. This, plus two other statements, lies within the outer for loop. The outer loop
goes around at most n−m times, since no complete alignment is possible once we
get too far to the right of the text. The time complexity of nested loops multiplies,
so this gives a worst-case running time of O((n − m)(m + 2)). "

i didn't understand for what reason the time complexity of inner loop is O(m+2) instead of O(m) ?please help thanks

The Only way to learn is!
Visit my blog
Jason Reaves

Joined: Feb 15, 2013
Posts: 3

Algorithm books like to be confusing. The for loop in your example will run n-m+1 times so that becomes the complexity and it'll be multiplied by the complexity of the inner loop. I'll try to demonstrate.

I'll use an example of two while loops because basically a while loop comes out to be the same thing as a for loop in time analysis.

Basically the time analysis on a while loop amounts to

twhile being the time of the while loop
tbody being the time of the body of the while loop
tcond being the time of the conditional of the while loop
"r" being how many times the body is to be run

The reason tcond is there at the end is because it will be ran again and become false at the end of loop.

So if you have loops inside of loops for instance:

Then we'll call the first while loop T1while and the second while loop T2while so T1 become

I agree. Here's the link:
subject: Problem regarding time complexity