Editing Rope (data structure) (section)

==Comparison with monolithic arrays==
{| class="wikitable floatright"
|+ Complexity{{citation needed|date=October 2010}}
! Operation !! Rope !! String
|- align="center"
| Index<ref name="Boehm" /> || {{bad|O(log n)}} || {{yes|O(1)}}
|- align="center"
| Split<ref name="Boehm" /> || {{bad|O(log n)}} || {{yes|O(1)}} 
|- align="center"
| Concatenate || {{yes|O(1) amortized, O(log n) worst case}}{{Citation needed|date=June 2022|reason=earlier this article claims "A concatenation can be performed simply by ... which is constant time.", or O(1).}} || {{bad|O(n)}}
|- align="center"
| Iterate over each character<ref name="Boehm" />
| {{okay|O(n)}} || {{okay|O(n)}}
|- align="center"
| Insert<ref name=":0" />{{Failed verification|date=September 2023}} || {{yes|O(log n)}} || {{bad|O(n)}}
|- align="center"
| Append<ref name=":0">{{Cite web|url=https://www.sgi.com/tech/stl/ropeimpl.html|title=Rope Implementation Overview|website=www.sgi.com|access-date=2017-03-01
|archive-url=https://web.archive.org/web/20171219030153/https://www.sgi.com/tech/stl/ropeimpl.html
|archive-date=2017-12-19
}}</ref>{{Failed verification|date=September 2023}} || {{yes|O(1) amortized, O(log n) worst case}} || {{bad|O(1) amortized, O(n) worst case}}
|- align="center"
| Delete || {{yes|O(log n)}} || {{bad|O(n)}}
|- align="center"
| Report || {{bad|O(j + log n)}} || {{yes|O(j)}}
|- align="center"
| Build || {{okay|O(n)}} || {{okay|O(n)}}
|}

Advantages:
* Ropes enable much faster insertion and deletion of text than monolithic string arrays, on which operations have time complexity O(n).
* Ropes do not require O(n) extra memory when operated upon (arrays need that for copying operations).
* Ropes do not require large contiguous memory spaces.
* If only nondestructive versions of operations are used, rope is a [[persistent data structure]]. For the text editing program example, this leads to an easy support for multiple [[undo]] levels.

Disadvantages:
* Greater overall space use when not being operated on, mainly to store parent nodes. There is a trade-off between how much of the total memory is such overhead and how long pieces of data are being processed as strings. The strings in example figures above are unrealistically short for modern architectures. The overhead is always O(n), but the constant can be made arbitrarily small.
* Increase in time to manage the extra storage
* Increased complexity of source code; greater risk of bugs

This table compares the ''algorithmic'' traits of string and rope implementations, not their ''raw speed''.  Array-based strings have smaller overhead, so (for example) concatenation and split operations are faster on small datasets. However, when array-based strings are used for longer strings, time complexity and memory use for inserting and deleting characters becomes unacceptably large. In contrast, a rope data structure has stable performance regardless of data size. Further, the space complexity for ropes and arrays are both O(n). In summary, ropes are preferable when the data is large and modified often.