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年識料 ˍˍˍˍˍˍ 不 80 1.25 2 1~80 不 1 列 array A n n matrix 零 lower triangular matrix 列來 n n(n+1)/2 n(n 1)/2 n n 2 例行 Y[1][3] 列 INT Y[4][4]; FOR(I=0; I<4; I++) FOR(J=0; J<4; J++) Y[I][J]=2*I*J+1; Y[2][1] Y[2][2] Y[2][3] Y[3][1] 3 A[1 m][1 n] 列 byte addressable A element 2-bytes A[5][2] 1900 A[2][3] 1930 A[3][15] 2362 2364 2366 2368 4 Knuth-Morris-Pratt 度 n 串度 p 串 p<n 狀度 O(n+p) O(n log p) O(n p) O(n 2 ) 5 列料數 tree 列 queue stack 列 array 6 列料列 circular queue void addq(int front, int *rear, element item) { rear=(*rear+1)% MAX QUEUE SIZE; if(front= = *rear){ queue full(rear); return;} queue[ ------ ]=item; } rear *rear (*rear)+ (*rear)++ 7 列料不串列 linear list tree 列 queue stack 列 array 8 stack 行連串 push pop push a push b push c pop push b push c pop 行 abb bba abc cba 9 ABCDEFGHI prefix DCBEAGFHI infix postfix 列 DCBEHIFGA BCDAEFGHI BEDCAFGHI DCEBGHIFA 10 prefix /*+abc/d-ef infix 列 (a+b)*c/d/(e-f) a+b*c/(d/(e-f)) (a+b)*c/(d/e-f) (a+b)*c/(d/(e-f)) 11 (x,y) x y 兩 (0,4),(3,1),(6,10),(8,9),(7,4),(6,8),(3,5),(2,11),(11,0) 列 {0,2,3,5} {6,8,9,10,11} {1,3,5,8} 0,1,2,3,4,5,6,7,8,9,10,11 12 不

年識料 12 C 類 typedef struct list_node *list_pointer; typedef struct list_node { char data[4]; list_pointer link; }; 數 Bytes 列 list_node 度 4 串 list_node 8 Bytes link list_node 類數 ptr list_node Null list_pointer ptr=0 13 C 什 #include<stdio.h> void main() { int a = 100, *p, **ptr; p = &a; ptr = &p; *p = 200; **ptr = 250; printf( a = %d, *p = %d, **ptr = %d\n, a, *p, **ptr); } a = 250, *p = 250, **ptr = 250 a = 100, *p = 250, **ptr = 250 a = 250, *p = 200, **ptr = 250 a = 100, *p = 200, **ptr = 250 14 列 Array 串列 Linked List 兩列 Linked List 若來數列 a 1,a 2,,a n O(log 2 n) 度數 k 數列 Array 來 Linked List Linked List Array Linked List 料度 O(log 2 n) 若 Array Linked List 數列若數 k 數列 Array 15 Priority Queue 若不料來 Insertion Deletion Time 不 Queue n Priority Queue 列若 Unordered Array 來 Insertion Time = O(n), Deletion Time = O(1) 若 Sorted Array 來 Insertion Time = O(n), Deletion Time = O(1) 若 Sorted Linked List 來 Insertion Time = O(n), Deletion Time = O(1) 若 Max Heap 來 Insertion Time = O(log 2 n), Deletion Time = O(log 2 n) 16 度 Depth k Full Binary Treek1 k 2 k 2 k 1 2 k-1 17 n Node Complete Binary Tree 度 Height n1 n n log 2 n + 1 n log 2 log 2

年識料 18 Max Heap 13 列 Heap 19 1,2,3,4,5 Push Stack Push Pop Stack 5 都陸 Pop 來列 Permutation 列列不 12345 31425 23145 45321 20 狀 Node Subtree 數 Root Degree Leaf Level 21 列拓列 topological order 3,0,1,2,4,6,7,8,5,9,10 0,3,1,2,4,6,7,5,9,8,10 3,5,0,1,2,4,6,8,7,9,10 0,1,2,3,4,5,6,7,8,9,10 22 n nodes e 連 edges 列 Dijkstras algorithm 路 shortest path 度 time complexity O(n 2 ) O(n log n) O(ne) O(e log e) 23 略 Kruskals algorithmdivide and conquer method Dijkstras algorithm dynamic programming quick sort branch and bound method binary search greedy method 24 連路連行若拓列 0 1 2 3 4 5 6 7 8 0 2 1 3 5 4 6 7 8 0 1 2 4 3 5 7 6 8 0 3 5 2 1 4 7 6 8 25 列不度 breadth first search 1 5 6 2 3 4 1 2 6 5 4 3 1 6 2 3 4 5 1 5 2 6 4 3

年識料 26 n nodes e 連 edgesundirected graph G MAX( e ) = n (n-1) e 連數 tree graph 若 G adjacency matrix 度 depth first search O(n e) 若 G 串列 adjacency list 度 depth first search O(n+e) 27 列 sort 料 heap sort bubble sort merge sort selection sort 28 quick sort 料 5,4,6,2,8,3 pass 料理料列列 5,4,6,2,8,3 4,5,2,6,3,8 4,2,5,3,6,8 2,4,3,5,6,8 2,3,4,5,6,8 5,4,6,2,8,3 3,4,2,5,8,6 2,3,4,5,6,8 2,3,4,5,6,8 5,4,6,2,8,3 5,4,6,2,3,8 5,4,3,2,6,8 2,4,3,5,6,8 2,3,4,5,6,8 5,4,6,2,8,3 4,5,6,2,8,3 2,4,5,6,8,3 2,3,4,5,6,8 29 insertion sort selection sort quick sort heap sortrecursive 來 30 selection sort worst case 度 time complexity O(n log n) average case 度 time complexity O(n 2 ) best case 度 time complexity O(1) 不 unstable 31 18,10,31,20,27 立 3 B B-Tree of order 3 裂 31 裂 Root 兩 32 列 Oct Aug Dec Mar Sep 33 列度 AVL Tree 度 1 n 度 O(log n) Insert Delete 度 O(log n) Search 度 O(log n) 34 Huffman 2,3,7,9,11 路度 Weighted External Path Length 32 48 69 101

年識料 35 列 Internal Search 行 External Search 行 Static Search 料不 Dynamic Search 料 36 列索 Index 索料索索料不索錄 Record 數料錄數 37 列 DEAP Complete Binary Tree Root Left Subtree Min-Heap 度 O(log n) 38 Division 數 Hashing Function 數數便 Hash Table 率 Collision 不 39 利 Division 數 Hashing Function 12,33,125,78,64 7 bucket slot 0 6 若 Linear Probing 來理列 Collision 度 5/7 2 64 6 125 40 若 Min-Max Heap 3 1 2 3 4 41 列 special word Fortran keyword C keyword C++ reserved word keyword Jave special word 42 參數不列數數邏 43 列 Prolog 不 Prolog The closed world assumption Prolog NOT operator logical NOT Prolog goal-driven 行 Prolog declarative semantics 44 Smalltalk method 列不 variables message expressions block expressions exception parts 45 object class instance message class method 來行六

年六識料 46 行錄列料狀 tree 列 queue stack graph 47 數 counter 行參數數數數 48 列串串 regular set {a i b j gcd(i,j)=1} {a n ba n n1} {L * L is a subset of 0 * } {a i b n c n i 1,n1} 49 列 Lisp 不 (cdr (cdr(a b c))) (c) (car (car((a b) b c))) a (atom? (car(a b))) F (null? (car(() b c))) T 50 scheme 列不 (define (map f x) (cond ((null? x) ()) (else (cons (f (car x))(map f(cdr x)))) )) (map list (a b c)(1 2 3)) ((a 1)(b 2)(c 3)) (map car ((a 1)(b 2)(c 3)(d 4))) (a b c d) (map square (1 2 3 4 5)) (1 4 9 16 25) (map cdr ((a 1)(b 2)(c 3)(d 4))) (1 2 3 4) 51 C int *foo[20]; 列 foo foo foo 數數 foo 20 數 foo 20 數數 52 數 Type Compatibility 列 Name Equivalence Structure Equivalence Declaration Equivalence Dynamic Equivalence 53 了行率了 array operation constructs 列不列 array operation APL Fortran 77 Fortran 90 Matlab 54 Java 列 C++ friend package applet thread class 55 Ada 95 C++ Java 列留不來 subclass extend public protected subtype 56 C++ class 留來 private properties class(es) public friend protected private 57 列不行錄 return point global variable 參數 actual parameter 料 local data 58 out mode 參數參數 actual parameter 數 constant 數 variable arithmetic expression 邏 logical expression 59 流不列參數 60 行 call by name 參數 APL LISP ALGOL 60 FORTRAN

年識料 61 PASCAL 行 Program main Var x: integer; Procedure A(var x: integer); {call-by-address parameter} Begin x : = x + 10; End; Procedure B(x: integer); {call-by-value-in parameter} Begin A(x); x : =x+5; End; Begin {of main} x : = 5; B(x); Writeln(x) End. 5 10 15 20 62 若 Procedure B parameter call-by-address 5 10 15 20 63 列 Java language 例理 exception handling 例 exception 類 class 例 static scoping 例 procedure calls 不行例 64 列數 dynamic scoping Scheme ML LISP Haskell 65 列 compiled programs 行率 execution efficiency interpreted programs compiled programs flexibilityinterpreted programs C Fortran 邏 Java assembly language 66 易行行不易漏洞 67 列 Java 數 Java 邏 Java Java assembly language 68 列不易不易漏洞行行 69 Java library 列 Thread class method main sleep suspend synchronized

年識料 70 不數 Aliases 列 Fortran 77 Equivalence Aliases C++pointer Aliases Java 不 pointer 不 Aliases Aliases 參數 71 lost object 列 reclaim storage Reference Counting Approach Garbage Collection Mark & Sweep Method Locks-and-Keys method proposed in UW-Pascal 72 理 dangling pointer 列 ANSI C Tombstone Approach non-recursive program 理 73 C++ Inheritance super class private variable private inheritance private properties class(es) 74 列 C++ subclasses 都 subtypes class constructor method class destructor method 75 列不 case multi-selector C ADA LISP PASCAL 76 FORTRAN 90 若行列令 break change proceed continue 77 列理列 arrays 料 C++ APL PL/1 COBOL 78 列數 (define (f3 n) (f3c n id)) (define (id n) n) (define (f3c n c) (if (= n 0) (c 1) (f3c (- n 1) (lambda (x) (c (* n x))) ))) 行數 (f3 4) 4 10 24 64 79 列 axiomatic semantics 來 programming environments denotational semantics 來 operational sematics 來數理邏理 80 列 functional languages imperative languages 不 functional languages 行度 functional languages functional languages functional languages concurrent execution 易