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Recursion In this Chapter we Study: Recursion Divide and Conquer Dynamic Programming

Recursion In this Chapter we Study: Recursion Divide and Conquer Dynamic Programming. Recursion involves: Self-reference (as in a recursive definition, or in a recursive method) Each recursive call to a function should conduct to a problem of smaller size.

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Recursion

Recursion. Recursion. Definition: when a function invokes itself A function that invokes itself is said to be Recursive Syntax & Semantics: nothing new. Thinking Non-Recursively. Divide and Conquer: A common problem solving technique:

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Recursion

Recursion. Recursion is a powerful programming tool The idea behind recursion is that the solution to a problem is solved by solving a small instance of the problem We accomplish this by placing one or more calls to the same method but with smaller sized data

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??????????????? JIT ?????

??????????????? JIT ?????. ???????? 2008/4/16 ????. ??. ???? ??????????? Range Coder ????? ?????????? FFT ?????? ( ?????? ) JIT ??????? ???????????? toy VM ???. ????. ?????????? & ??? ?????? (mp3 ????? ) MPEG 2 Video, MPEG4 ??? CPU Pentium, Athlon, PowerPC ???????

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Programming Interest Group comp.hkbu.hk/~chxw/pig/index.htm

Programming Interest Group http://www.comp.hkbu.edu.hk/~chxw/pig/index.htm. Tutorial Six Divide and Conquer and Backtracking. Outline. Recursion Divide and Conquer Backtracking Examples Constructing all subsets Constructing all permutations Pruning Eight-Queens Problem. Recursion.

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Lecture 25

Lecture 25. What will I learn in this lecture?. Recursive Functions Related Chapter: ABC 5.14, 5.15. Recursive Functions.

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????? KMP ??

????? KMP ??. Zn http://spaces.msn.com/znzhou/. OUTLINE. ??????? ?????? KMP ?? ???? ????????. OUTLINE. ??????? ?????? KMP ?? ???? ????????. ?????????????. the The quick brown fox jumps over the lazy dog jay The quick brown fox j umps over the l a z y dog. ????.

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n??????????? ????

n??????????? ????. 200703006 ????? ?????. ????????. ??????????????????????????????? ???????????????????????????????????. N ???????????? ??????????????? ?????????????. ?????????. ???????????. ????????????????????????. ????????????. ????? n ??????????. N ??????????????

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2.3 ???????????

2.3 ???????????. 1. ???? ?????????????????? ????????????????? ?????? ???????. ?????. ????? rear, ????????. ?? ?????????????? LA ? LB ???????????????????????????????? LA ?. p = A->next; q = B->next; A->next = q->next; B->next = p; A = B; free(q);. 2. ???? (Double Linked List)

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Exercise 3

Exercise 3. CS 110 S12. Consider the following recursive function: int what ( int x, int y) { if (x > y) return what (x-y , y); else if (y > x) return what (x , y-x); else return x; } Trace the above function for the following calls: what (104,16) what (15,35) what (63,18)

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Chap7

Chap7. Recursive. Recursive. ?? Recursive ?????? ( ?????? ) ?????????? ???????????? , ????? , ??????????. ??????. ??????. ??????. ??????. ??????. ??????. ??????. ???? , ???. ??????. ???. ??????. N ?? (N!). long Factorial(long n) { if ( n == 1 || n== 0) return (1);

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Chapter 12

Chapter 12. Collection Class A little data structure. Package java.util.

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CSC 213

CSC 213. Lecture 16: Strings and Pattern Matching. Announcements. Last quiz results were not good Good news: neighbors did not read book either Scores were universally poor Bad news: neighbors are also unlucky Average score was 4.2 Flipping a coin would produce an average of 5

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CS100J February 21 Recursion

CS100J February 21 Recursion. Read: pp. 403-408 but SKIP sect. 15.1.2 Look in ProgramLive CD, page 15-3, for some interesting recursive methods. Download presented algorithms from the website. Recursive definition : A definition that is defined in terms of itself.

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FOR i := 0...N-1 DO summa := summa + A[i] tulo := tulo * A[i] ENDFOR

FOR i := 0...N-1 DO summa := summa + A[i] tulo := tulo * A[i] ENDFOR. FOR i := 1 ... N DO FOR j:= 0 ... N-1 DO maara := maara + 1 ENDFOR ENDFOR. FOR i := 0 ... N DO A[i] := 0 ENDFOR FOR i := 0 ... N-1 DO FOR j:= 1 ... N DO A[i] := A[i] + j * i ENDFOR ENDFOR.

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