Skip to main content
Log in

A taxonomy of binary tree traversals

  • Part I Computer Science
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

A survey of the literature shows that eleven binary tree traversals have been defined. We systematize this work by proposing a classification that consists of twenty-six traversals grouped into seven categories. Three generator schemas are provided that allow all of the traversals to be implemented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. N. Adams,Another representation of binary tree traversal, Inf. Proc. Letters 2 (1973), 52–54.

    Article  Google Scholar 

  2. R. R. Atkinson, B. H. Liskov and R. W. Scheifler,Aspects of implementing CLU, Proc. ACM Annual Conf., Washington DC, 1978, pp. 123–129.

  3. A. T. Berztiss,Data Structures: Theory and Practice, 2nd ed. Academic Press, New York, 1975.

    Google Scholar 

  4. A. T. Berztiss,Depth-first K-trees and critical path analysis, Acta Inf. 13 (1980), 325–346.

    Article  Google Scholar 

  5. A. T. Berztiss,Data abstraction, controlled iteration, and communicating processes, Proc. ACM Annual Conf., Nashville TN, 1980, pp. 197–203.

  6. A. Blikle,Addressless units for carrying on loop-free computations, J. ACM 19 (1972), 136–157.

    Article  Google Scholar 

  7. W. A. Burkhard,Nonrecursive tree traversal algorithms, Computer J. 18 (1975), 227–230.

    Article  Google Scholar 

  8. J. A. Goguen, J. W. Thatcher and E. G. Wagner,An initial algebra approach to the specification, correctness, and implementation of abstract data types, in Current Trends in Programming Methodology, Vol. 4: Data Structuring (R. T. Yeh, ed.). Prentice-Hall, Englewood Cliffs NJ, 1978, pp. 80–149.

    Google Scholar 

  9. R. E. Griswold and M. T. Griswold,The Icon Programming Language. Prentice-Hall, Englewood Cliffs NJ, 1983.

    Google Scholar 

  10. D. Gries and N. Gehani,Some ideas on data types in high-level languages, Comm. ACM 20 (1977), 414–420.

    Article  Google Scholar 

  11. J. V. Guttag, E. Horowitz and D. R. Musser,The design of data type specifications, in Current Trends in Programming Methodology, Vol. 4: Data Structuring (R. T. Yeh, ed.). Prentice-Hall, Englewood Cliffs NJ, 1978, pp. 60–79.

    Google Scholar 

  12. D. E. Knuth,The Art of Computer Programming, Vol. 1: Fundamental Algorithms. Addison-Wesley, Reading MA, 1968, p. 329 (Exercise 4).

    Google Scholar 

  13. D. E. Knuth,The Art of Computer Programming, Vol. 3: Sorting and Searching. Addison-Wesley, Reading MA, 1973.

    Google Scholar 

  14. B. W. Lampson, J. J. Horning, R. L. London, J. G. Mitchell and G. J. Popek,Report on the programming language Euclid, ACM SIGPLAN Notices 12, 2 (Feb. 1977).

  15. L. S. Levy,Ordering of trees — simplified proofs, Proc. 7th Ann. Princeton Conf. Inf. Sciences and Systems 1973, 400–402.

  16. B. Liskov, R. Atkinson, T. Bloom, E. Moss, J. C. Schaffert, R. Scheifler and A. Snyder,CLU Reference Manual. Springer-Verlag LNCS 114, Springer-Verlag, Berlin, 1981.

    Google Scholar 

  17. W. J. Meyers,Linear representation of tree structure, Proc. 3rd Ann. ACM Symp. Theory Computing 1971, 50–62.

  18. Z. Pawlak,New class of mathematical languagues and organization of addressless computers. Proc. Colloq. Foundations Math., Math. Machines and their Applications, Tihany, Hungary, 1962, 227–238.

  19. L. A. Rowe and K. A. Shoens,Data abstraction, views and updates in Rigel, Proc. ACM SIGMOD 1979 Internat. Conf. Management Data, 71–81.

  20. M. Shaw (ed.),Alphard: Form and Content. Springer-Verlag, New York, 1981.

    Google Scholar 

  21. R. Tarjan,Depth-first search and linear graph algorithms, SIAM J. Comput 1 (1972), 146–160.

    Article  Google Scholar 

  22. L. E. Thorelli,Marking algorithms, BIT 12 (1972), 555–568.

    Google Scholar 

  23. J. P. Tremblay and P. G. Sorenson,An Introduction to Data Structures with Applications. McGraw-Hill, New York, 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berztiss, A. A taxonomy of binary tree traversals. BIT 26, 266–276 (1986). https://doi.org/10.1007/BF01933706

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01933706

CR categories

Keywords and phrases

Navigation