凡是为民造福的事一定要千方百计办好
???????? ??? ??? ??????, ????????? ???-?????? ?????? ?? ????? ??????, ????? ???? ?? ?????, ????? ?? ??? ????????? ??????????.[1][2][3][4] ????? ????? ???? ???? ?????????, ?? ??? ?? ???? ??-????? (????, ?? ????? ??????? ?? "????? ?? ?????? ???? ????") ????? ???? ?? ?? ????????? ?????????? (????, ?? ????? ????? ?????). ???????? ???? ???? ????? ?????? ?? ??? ????? ????? ?????? ?? ????????, ?? ?????? ?? ?????, ?????? ?? ???? ???. ????-??? ???? ???? ?? ?????? ???? ????? ????? ???????? ?? ????? ????? ?????? ???? ??????? ?????? ?????. ????????? ??? ???????? ????? ?? ???? ?????? ???????? ????? ??? ?? ???? ????? ?????? ?? ????? ???? ?????, ??? ???? ?????? ??????? ?? ???? ???? ??????? ?????? ???? ?????? ????? ????? ????? ?????????.
?? ?????? ???? ??? ????????, ?? ???? ?? ??????????. ?????? ?? ?? ??????????? ?? ?????? ??????. ??? ???? ?????? ?? ??? ??????? ?? "????? ???????", ???? "?????" ??????? ???????, ???????, ???? ?? ????????. ?????? ????????, ??? ??? ????????? ????????? ?????? ????? ????????? ?????? ??? ??????? ???? ??? ?????? ?? ???. ???, ???? ???????? ??? ?? ??? ??? ???????? ???? ??????, ?????, ?? ?????? ??????? ?????? ????.
?????? ?????? ??????? ??? ???? ????? ????????? ?????, ???? ??????? ????? ??? (??? ???? ????? ????? ?????? ?? ???? ????????). ??? ???, ??????? ?? ????? ?????? ?????? ?????????? ?????, ??? ?????? ????? ?? ?????? ???????????, ????? ????? ?????? ??????. ?????? ???? ????? ????? ??????? ?? ?????????? (???? ????? ???????? ???????) ??-?? ???? ???????? ??????? ?????? ????????? ???????? ?? ???? ???? ?????????. ??????, ??? ???? ????? ?? ????????? ???? ????? ???? ??? ????, ????????? ????? ??? ????. ????? ?????? ?????????? ?"??????" ?? ??? ????? ???? ???????? ????? ???? ????.
????? ??????? ???????????? ???? ??????? ????? ?????.
???? ?????
????????? ????? ?????? ?????? ?? ?? ????????? ????? ??????? ?? ???? ???????, ????? ??? ???? ??-?'???????.[5] ??? ?????? ???? ???????. ???? ???? ?? ????? ????? ????? ???????, ???? ??? ?? ?? ?'??????? ?"?????????" (??? ????? ????? ?????? ????? ?????? ???? ?-?', ???? ? -?, ????? ??? ????? ???? ?-? ???? ?-?' -?????? ???????? ????? ?-th ??? ???-?'???????? ??? ????-?????'???), ???????? ??? ????? ?????? ????? ???? ?? ????? ???? ?????. ????? ?????? ????? ???? ??? ??? - "????? ??-?'??? ???-???????". ?? ?? ????, ????? ??????, ??-?'???, ??? ??? ???? ??????? ????? ???? ?? ?????? ?? ??? ???? ????.
?????? ?? ??????????
???????????? ???????, ?????? ????????? ??? ?????? ???????? ?? ????? ???????: ???? ?? ??? ??? ???? ???? ????????? ???? ?? ???? ???? ?????, ??? ???? ??????, ?????? ???? ????? ??? ?????? ??????. ??????? ????? ?? ?????? ????? ?????? ????? ?????? ????? ?? ????? ????? ?? ????? ??????? ????? ?????? ?????? ???.
????? ???? ????? ????????? ????? ???? ?? ???, ???? ??????? ????? ??????? ?? ????????? ?????? ?????? ?????? ????????. ?? ???, ?????? ??????? ???? ??????? ????? ??????? ???? ???? (????, ????? ?????? ?? ?????) ????? ?????? ?? ?????????? ????? ???? ???????? ??? ????? ????? ??? ??? ?????.
??? ????? ????? ?????????? ??? ?????? ??????????? ???????????? (???????: deterministic algorithm) ???????????? ??????? (?????????, ???????: randomized algorithm). ???????? ??????? ??????? ??????????? ??? ?????? ????? ???? ???? (?????, ??? ?????? ?? ????????? ?? ??? ??? ????? ???? ?? ???? ??????), ????? ???????? ?????? ??????? ??????????? ??? ?????? "????? ??????", ??????: ???? ?????? ?????? (?????? ????? ???? ?????? ?? ????????? ?? ???? ???? ????? ?????? ?????). ???? ??? ????? ??????? ?? ?????????? ???????: ????????? ????? ????, ??? ??????? ????? ??? ????? ?????? ??? ??????? (????, ???????? ????-????), ?????????? ??? ???? ??? ??? ????? ?????, ?? ???? ????? ??? ???? ????? ???? ???? ???? ????. ???? ??????? ???? ?????????? ???? ??????? ?????? ?????? ??? ????, ?? ????? ???? ????????? ???? ?????.
?????? ?????? ?? ?????????? ??????? ?? ?? "???? ??????", ?? ?????? ?????, ????? ?? ??????? ????. ?????? ??? ??????: ?????????? ?????????? ???? ?????????? ???? ????? (divide and conquer), ?????????? ??????, ????????? ????? ????? (???????: dynamic programming, ????? ?? ????? ?? ??????? ???? ?? ?????? ??? ????? ??????).
????, ????? ?? ?????????? ????? ????? ???????? ????? ?????, ???? ?????????? ????, ???????? ?????????? ????? (approximation algorithms ???????) ?????? ????? ????? ????? ???????? - ?? ?? ??? ?? ??? ???? ?? ??? ????? ?? ????????? ?? ?? ??? ???? ????? ???? ???? ????? ??? ??? ?????? (?????: NP-???).
??????? ???????????
?????- ???????? ???????, ?????? ???? ????? ???????, ????? ????? ?? ???????, "???????", ????? ????????? ????? ?????.
- ???? ?? ????????, ?????? ?????? ????????.
- ???????? ????-???? - ????? ????? ?????? ?????? ????? ??? ???? ???? ??? ??????.
- ?????????? ????? ?????? ??????? ?? ???? ???.
- ???????? ????????, ????? ?????? ????? ?? ????? ???????.
- ???? ?????? ?? ???? - ???????? ?????? ??????? ?? ????? ??????? ?????????.
- ???????? ?????? ????? ?? ????? ?????? ??????, ???? ???????? ?????? ?? ?????.
- ????????? ?? ???????? ?????? ????? ??? ???? ??????? ????? ????? ???? ?????? ??? ?????? ?? ??????? ???? ?????? ??.
- ?????????? ????? ?? ?????? ?????? ??????? ??????? (?? ?????????? ???? ?????? ???).
- ???? ??????-????? ?????? ???? ?? ??????? ?????. ??? ????? ?????? ?????????? ?????? ???????, ???? ?????? ????????? ?? ?????? ?? ???? ?????, ???? "???? ???????? ???? ?- ".
- ???????? ????? - ???????? ?????? ??????
- ???????? ???? ?????? (COBWEB) ???? ?????? ????? ????? ??? ????? ??????? ?? ????? ??????????.
?????? ????
?????- ??? ????? – ?????? ????
?????? ????? ?????? ?? ?????????? ??? ????? ?????? ???? ????? ???. ???? ???????, ??????? ????? ????? ?? ??? ????? ????? ??????? ?? ???? ????? ??????? ?? ???????? ???? ???? ??. ???? ?????? ????? ?????? ??????? ?? ???????? ??????? ???? ????? ???? ?????? ?????? ??? - ????? ?????? ?????????? ?? ???? ?????, ?? ????? ?????? ?? ??? ??? ??? ?????? ?? ??? ????.
??? ?'??'-??????? ????? ??? ?????? ???????? ?? ???????? ????? ????? ?????? ?? ??? ????? ???????, ???? ???????? ?????? ?? ??? ?????? ????. ???? ????? ??? ???????? ???? ?????? ??????? ????, ??? ?????? ???? ????? ????????.
??? ??
?????
????? ?? ?????? ????? ???? ????? ??? ??? ??? ??????? ??????? ????? ?????. ???? ????? ?? ??????? ?? ????? ????? ?? ????, ????? ???? ?????, ?????? ?????? ????. |
?????? ?????
?????- ?????, ????????, ?????, ???? ???????????, ????? MIT, ????? ?????? ?? ??? ??????????? ??????.
- ?'? ???????, ???? ?????? ????? ???????????, ????? ????? ???? "???? ???????????".
- ?'?? ????????, ???? ??????, ????? ??????????, ????? "Addison Wesley", ????? ?????? ?? ??? ??????????? ??????.
??????? ????????
?????- ????????, ???? ??????????? ???????? (???????)
- ???? ??????????? ?-ArsDigita (?????? ??????? ??????? ???????)
- ????????, ???? MathWorld (???????)
- ????????, ???? ??????????? ???????? (???????)
- ??????????, ?? ??? ??????? ???????
- Donald E. Knuth, Algorithms, Scientific American, Vol. 236, No. 4 (April 1977), pp. 63-81, in JSTOR
????? ??????
?????- ^ Donald E. Knuth, The Art of Computer Programming. Vol. 1: Fundamental Algorithms. 3rd ed., Reading, MA: Addison-Wesley, 1997, ??' 1-9
- ^ Thomas H. Cormen, Charles E. Leiserson, Ronald Rivest, Clifford Stein, Introduction to Algorithms. 3rd ed., Cambridge, MA: MIT Press, 2009, ??' 5-10, ISBN 978-0-262-53305-8
- ^ A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, Proceedings of the London Mathematical Society s2-42, 1937, ??' 230–265 doi: 10.1112/plms/s2-42.1.230
- ^ Edsger W. Dijkstra, A Discipline of Programming, Upper Saddle River, NJ: Prentice-Hall, 1976
- ^ Tarleton Gillespie, Digital Keywords, Princeton: Princeton University Press, 2025-08-06, ??' 18–30, ISBN 978-1-4008-8055-3