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2
3 - transformaces geomtricas 2d ,
1
= 1 0 0 1 1 0 1
001
x0,y0 = origem xd,yd = destino Tx,Ty = distncia = ngulo em radianos Sx,Sy = fator de multiplicao
1 =
0 00 0
0 0 1
001
1
= 0 0
0 0 1
001
1 =
1 0 00 1 00 0 1
001
Flip horizontal
1 =
1 0 00 1 00 0 1
001
Flip vertical
Translao
Rotao
Escala
x
y
4 - transformaces geomtricas 3d ,
1
=
1 0 0 0 1 0 00
00
1 0 1
0001
1
=
0 0 00 0 0
00
00
0 0 1
0001
Translao
Rotao eixo z
Escala
1
=
0 0 0 0
00
00
1 0 0 1
0001
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1
=
0 0 0 0
00
00
1 0 0 1
0001
1
=
1 0 0 00 000
0
0 0 1
0001
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1
=
0 0 0 0
00
00
1 0 0 1
0001
1
=
1 0 0 00 000
0
0 0 1
0001
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1
=
0 00 1 0 0
0
00
00 1
0001
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1
=
0 0 0 0
00
00
1 0 0 1
0001
1
=
0 00 1 0 0
0
00
00 1
0001
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Rotao eixo x
Rotao eixo y
x0,y0,z0 = origem xd,yd,zd = destino Tx,Ty,Tz = distncia = ngulo em radianos sx,sy,sz = fator de multiplicao
x
y
z
3
5 - sistemas numricos base 10, 16 E 2
Decimal Hexa Binrio Decimal Hexa Binrio Decimal Hexa Binrio Decimal Hexa Binrio
0 0 0000 0000 64 40 0100 0000 128 80 1000 0000 192 C0 1100 0000
1 1 0000 0001 65 41 0100 0001 129 81 1000 0001 193 C1 1100 0001
2 2 0000 0010 66 42 0100 0010 130 82 1000 0010 194 C2 1100 0010
3 3 0000 0011 67 43 0100 0011 131 83 100 00011 195 C3 1100 0011
4 4 0000 0100 68 44 0100 0100 132 84 1000 0100 196 C4 1100 0100
5 5 0000 0101 69 45 0100 0101 133 85 1000 0101 197 C5 1100 0101
6 6 0000 0110 70 46 0100 0110 134 86 1000 0110 198 C6 1100 0110
7 7 0000 0111 71 47 0100 0111 135 87 1000 0111 199 C7 1100 0111
8 8 0000 1000 72 48 0100 1000 136 88 1000 1000 200 C8 1100 1000
9 9 0000 1001 73 49 0100 1001 137 89 1000 1001 201 C9 1100 1001
10 A 0000 1010 74 4A 0100 1010 138 8A 1000 1010 202 CA 1100 1010
11 B 0000 1011 75 4B 0100 1011 139 8B 1000 1011 203 CB 1100 1011
12 C 0000 1100 76 4C 0100 1100 140 8C 1000 1100 204 CC 1100 1100
13 D 0000 1101 77 4D 0100 1101 141 8D 1000 1101 205 CD 1100 1101
14 E 0000 1110 78 4E 0100 1110 142 8E 1000 1110 206 CE 1100 1110
15 F 0000 1111 79 4F 0100 1111 143 8F 1000 1111 207 CF 1100 1111
16 10 0001 0000 80 50 0101 0000 144 90 1001 0000 208 D0 1101 0000
17 11 0001 0001 81 51 0101 0001 145 91 1001 0001 209 D1 1101 0001
18 12 0001 0010 82 52 0101 0010 146 92 1001 0010 210 D2 1101 0010
19 13 0001 0011 83 53 0101 0011 147 93 1001 0011 211 D3 1101 0011
20 14 0001 0100 84 54 0101 0100 148 94 1001 0100 212 D4 1101 0100
21 15 0001 0101 85 55 0101 0101 149 95 1001 0101 213 D5 1101 0101
22 16 0001 0110 86 56 0101 0110 150 96 1001 0110 214 D6 1101 0110
23 17 0001 0111 87 57 0101 0111 151 97 1001 0111 215 D7 1101 0111
24 18 0001 1000 88 58 0101 1000 152 98 1001 1000 216 D8 1101 1000
25 19 0001 1001 89 59 0101 1001 153 99 1001 1001 217 D9 1101 1001
26 1A 0001 1010 90 5A 0101 1010 154 9A 1001 1010 218 DA 1101 1010
27 1B 0001 1011 91 5B 0101 1011 155 9B 1001 1011 219 DB 1101 1011
28 1C 0001 1100 92 5C 0101 1100 156 9C 1001 1100 220 DC 1101 1100
29 1D 0001 1101 93 5D 0101 1101 157 9D 1001 1101 221 DD 1101 1101
30 1E 0001 1110 94 5E 0101 1110 158 9E 1001 1110 222 DE 1101 1110
31 1F 0001 1111 95 5F 0101 1111 159 9F 1001 1111 223 DF 1101 1111
32 20 0010 0000 96 60 0110 0000 160 A0 1010 0000 224 E0 1110 0000
33 21 0010 0001 97 61 0110 0001 161 A1 1010 0001 225 E1 1110 0001
34 22 0010 0010 98 62 0110 0010 162 A2 1010 0010 226 E2 1110 0010
35 23 0010 0011 99 63 0110 0011 163 A3 1010 0011 227 E3 1110 0011
36 24 0010 0100 100 64 0110 0100 164 A4 1010 0100 228 E4 1110 0100
37 25 0010 0101 101 65 0110 0101 165 A5 1010 0101 229 E5 1110 0101
38 26 0010 0110 102 66 0110 0110 166 A6 1010 0110 230 E6 1110 0110
39 27 0010 0111 103 67 0110 0111 167 A7 1010 0111 231 E7 1110 0111
40 28 0010 1000 104 68 0110 1000 168 A8 1010 1000 232 E8 1110 1000
41 29 0010 1001 105 69 0110 1001 169 A9 1010 1001 233 E9 1110 1001
42 2A 0010 1010 106 6A 0110 1010 170 AA 10101010 234 EA 1110 1010
43 2B 0010 1011 107 6B 0110 1011 171 AB 1010 1011 235 EB 1110 1011
44 2C 0010 1100 108 6C 0110 1100 172 AC 1010 1100 236 EC 1110 1100
45 2D 0010 1101 109 6D 0110 1101 173 AD 1010 1101 237 ED 1110 1101
46 2E 0010 1110 110 6E 0110 1110 174 AE 1010 1110 238 EE 1110 1110
47 2F 0010 1111 111 6F 0110 1111 175 AF 1010 1111 239 EF 1110 1111
48 30 0011 0000 112 70 0111 0000 176 B0 1011 0000 240 F0 1111 0000
49 31 0011 0001 113 71 0111 0001 177 B1 1011 0001 241 F1 1111 0001
50 32 0011 0010 114 72 0111 0010 178 B2 1011 0010 242 F2 1111 0010
51 33 0011 0011 115 73 0111 0011 179 B3 1011 0011 243 F3 1111 0011
52 34 0011 0100 116 74 0111 0100 180 B4 1011 0100 244 F4 1111 0100
53 35 0011 0101 117 75 0111 0101 181 B5 1011 0101 245 F5 1111 0101
54 36 0011 0110 118 76 0111 0110 182 B6 1011 0110 246 F6 1111 0110
55 37 0011 0111 119 77 0111 0111 183 B7 1011 0111 247 F7 1111 0111
56 38 0011 1000 120 78 0111 1000 184 B8 1011 1000 248 F8 1111 1000
57 39 0011 1001 121 79 0111 1001 185 B9 1011 1001 249 F9 1111 1001
58 3A 0011 1010 122 7A 0111 1010 186 BA 1011 1010 250 FA 1111 1010
59 3B 0011 1011 123 7B 0111 1011 187 BB 1011 1011 251 FB 1111 1011
60 3C 0011 1100 124 7C 0111 1100 188 BC 1011 1100 252 FC 1111 1100
61 3D 0011 1101 125 7D 0111 1101 189 BD 1011 1101 253 FD 1111 1101
62 3E 0011 1110 126 7E 0111 1110 190 BE 1011 1110 254 FE 1111 1110
63 3F 0011 1111 127 7F 0111 1111 191 BF 1011 1111 255 FF 1111 1111
4
6 - potncias de 2
7 potncias de 16
n 16n n 16n
0 1 17 295 147 905 179 352 825 856
1 16 18 4 722 366 482 869 645 213 696
2 256 19 75 557 863 725 914 323 419 136
3 4 096 20 1 208 925 819 614 629 174 706 176
4 65 536 21 19 342 813 113 834 066 795 298 816
5 1 048 576 22 309 485 009 821 345 068 724 781 056
6 16 777 216 23 4 951 760 157 141 521 099 596 496 896
7 268 435 456 24 79 228 162 514 264 337 593 543 950 336
8 4 294 967 296 25 1 267 650 600 228 229 401 496 703 205 376
9 68 719 476 736 26 20 282 409 603 651 670 423 947 251 286 016
10 1 099 511 627 776 27 324 518 553 658 426 726 783 156 020 576 256
11 17 592 186 044 416 28 5 192 296 858 534 827 628 530 496 329 220 096
12 281 474 976 710 656 29 83 076 749 736 557 242 056 487 941 267 521 536
13 4 503 599 627 370 496 30 1 329 227 995 784 915 872 903 807 060 280 344 576
14 72 057 594 037 927 936 31 21 267 647 932 558 653 966 460 912 964 485 513 216
15 1 152 921 504 606 846 976 32 340 282 366 920 938 463 463 374 607 431 768 211 456
16 18 446 744 073 709 551 616 33 5 444 517 870 735 015 415 413 993 718 908 291 383 296
n 2n n 2n
0 1 34 17 179 869 184
1 2 35 34 359 738 368
2 4 36 68 719 476 736
3 8 37 137 438 953 472
4 16 38 274 877 906 944
5 32 39 549 755 813 888
6 64 40 1 099 511 627 776
7 128 41 2 199 023 255 552
8 256 42 4 398 046 511 104
9 512 43 8 796 093 022 208
10 1 024 44 17 592 186 044 416
11 2 048 45 35 184 372 088 832
12 4 096 46 70 368 744 177 664
13 8 192 47 140 737 488 355 328
14 16 384 48 281 474 976 710 656
15 32 768 49 562 949 953 421 312
16 65 536 50 1 125 899 906 842 624
17 131 072 51 2 251 799 813 685 248
18 262 144 52 4 503 599 627 370 496
19 524 288 53 9 007 199 254 740 992
20 1 048 576 54 18 014 398 509 481 984
21 2 097 152 55 36 028 797 018 963 968
22 4 194 304 56 72 057 594 037 927 936
23 8 388 608 57 144 115 188 075 855 872
24 16 777 216 58 288 230 376 151 711 744
25 33 554 432 59 576 460 752 303 423 488
26 67 108 864 60 1 152 921 504 606 846 976
27 134 217 728 61 2 305 843 009 213 693 952
28 268 435 456 62 4 611 686 018 427 387 904
29 536 870 912 63 9 223 372 036 854 775 808
30 1 073 741 824 64 18 446 744 073 709 551 616
31 2 147 483 648 65 36 893 488 147 419 103 232
32 4 294 967 296 66 73 786 976 294 838 206 464
33 8 589 934 592 67 147 573 952 589 676 412 928
5
8 - tabela ascii - para PC
Dec Hex Dec Hex Char Dec Hex Char Dec Hex Char
0 0 NUL (null) 64 40 @ 128 80 192 C0
1 1 SOH (start of heading) 65 41 A 129 81 193 C1
2 2 STX (start of text) 66 42 B 130 82 194 C2
3 3 ETX (end of text) 67 43 C 131 83 195 C3
4 4 EOT (end of transmission) 68 44 D 132 84 196 C4
5 5 ENQ (enquiry) 69 45 E 133 85 197 C5
6 6 ACK (acknowledge) 70 46 F 134 86 198 C6
7 7 BEL (bell) 71 47 G 135 87 199 C7
8 8 BS (backspace) 72 48 H 136 88 200 C8
9 9 TAB (horizontal tab) 73 49 I 137 89 201 C9
10 A LF (line feed) 74 4A J 138 8A 202 CA
11 B VT (vertical Tab) 75 4B K 139 8B 203 CB
12 C FF (form feed) 76 4C L 140 8C 204 CC
13 D CR (carriage return) 77 4D M 141 8D 205 CD
14 E SO (shift out) 78 4E N 142 8E 206 CE
15 F SI (shift in) 79 4F O 143 8F 207 CF
16 10 DLE (data link escape) 80 50 P 144 90 208 D0
17 11 DC1 (device control 1) 81 51 Q 145 91 209 D1
18 12 DC2 (device control 2) 82 52 R 146 92 210 D2
19 13 DC3 (device control 3) 83 53 S 147 93 211 D3
20 14 DC4 (device control 4) 84 54 T 148 94 212 D4
21 15 NAK (negative acknowledge) 85 55 U 149 95 213 D5
22 16 SYN (synchronous idle) 86 56 V 150 96 214 D6
23 17 ETB (end of transmission block) 87 57 W 151 97 215 D7
24 18 CAN (cancel) 88 58 X 152 98 216 D8
25 19 EM (end of medium) 89 59 Y 153 99 217 D9
26 1A SUB (substitute) 90 5A Z 154 9A 218 DA
27 1B ESC (escape) 91 5B [ 155 9B 219 DB
28 1C FS (file separator) 92 5C \ 156 9C 220 DC
29 1D GS (group separator) 93 5D ] 157 9D 221 DD
30 1E RS (record separator) 94 5E ^ 158 9E 222 DE
31 1F US (unit separator) 95 5F _ 159 9F 223 DF
32 20 Space 96 60 ` 160 A0 224 E0 a
33 21 ! 97 61 a 161 A1 225 E1 b
34 22 " 98 62 b 162 A2 226 E2 G
35 23 # 99 63 c 163 A3 227 E3 p
36 24 $ 100 64 d 164 A4 228 E4 S
37 25 % 101 65 e 165 A5 229 E5 s
38 26 & 102 66 f 166 A6 230 E6
39 27 ' 103 67 g 167 A7 231 E7 t
40 28 ( 104 68 h 168 A8 232 E8 f
41 29 ) 105 69 i 169 A9 233 E9
42 2A * 106 6A j 170 AA 234 EA W
43 2B + 107 6B k 171 AB 235 EB d
44 2C , 108 6C l 172 AC 236 EC
45 2D - 109 6D m 173 AD 237 ED
46 2E . 110 6E n 174 AE 238 EE
47 2F / 111 6F o 175 AF 239 EF
48 30 0 112 70 p 176 B0 240 F0
49 31 1 113 71 q 177 B1 241 F1
50 32 2 114 72 r 178 B2 242 F2
51 33 3 115 73 s 179 B3 243 F3
52 34 4 116 74 t 180 B4 244 F4
53 35 5 117 75 u 181 B5 245 F5
54 36 6 118 76 v 182 B6 246 F6
55 37 7 119 77 w 183 B7 247 F7
56 38 8 120 78 x 184 B8 248 F8
57 39 9 121 79 y 185 B9 249 F9
58 3A : 122 7A z 186 BA 250 FA
59 3B ; 123 7B { 187 BB 251 FB
60 3C < 124 7C | 188 BC 252 FC h
61 3D = 125 7D } 189 BD 253 FD 2
62 3E > 126 7E ~ 190 BE 254 FE
63 3F ? 127 7F del 191 BF 255 FF
charDec Hex Dec Hex Char Dec Hex Char Dec Hex Charchar
6
9 - tabela ebcdic - para mainframe
Dec Hex char Dec Hex Char Dec Hex Char Dec Hex Char
0 0 NUL (null) 64 40 SP (space) 128 80 192 C0 {
1 1 SOH (start of heading) 65 41 129 81 a 193 C1 A
2 2 STX (start of text) 66 42 130 82 b 194 C2 B
3 3 ETX (end of text) 67 43 131 83 c 195 C3 C
4 4 PF (punch off) 68 44 132 84 d 196 C4 D
5 5 HT (horizontal tab) 69 45 133 85 e 197 C5 E
6 6 LC (lower case) 70 46 134 86 f 198 C6 F
7 7 DEL (delete) 71 47 135 87 g 199 C7 G
8 8 GE 72 48 136 88 h 200 C8 H
9 9 RLF 73 49 137 89 i 201 C9 I
10 A SMM (start of manual message) 74 4A 138 8A 202 CA
11 B VT (vertical tab) 75 4B . 139 8B 203 CB
12 C FF (form feed) 76 4C < 140 8C 204 CC
13 D CR (carriage return) 77 4D ( 141 8D 205 CD
14 E SO (shift out) 78 4E + 142 8E 206 CE
15 F SI (shift in) 79 4F | 143 8F 207 CF
16 10 DLE (data link escape) 80 50 & 144 90 208 D0 }
17 11 DC1 (device control 1) 81 51 145 91 j 209 D1 J
18 12 DC2 (device control 2) 82 52 146 92 k 210 D2 K
19 13 TM (tape mark) 83 53 147 93 l 211 D3 L
20 14 RES (restore) 84 54 148 94 m 212 D4 M
21 15 NL (new line) 85 55 149 95 n 213 D5 N
22 16 BS (back space) 86 56 150 96 o 214 D6 O
23 17 IL (idle) 87 57 151 97 p 215 D7 P
24 18 CAN (cancel) 88 58 152 98 q 216 D8 Q
25 19 EM (end of medium) 89 59 153 99 r 217 D9 R
26 1A CC (cursor control) 90 5A ! 154 9A 218 DA
27 1B CU1 (customer use 1) 91 5B $ 155 9B 219 DB
28 1C IFS (interchange file separator) 92 5C * 156 9C 220 DC
29 1D IGS (interchange group separator) 93 5D ) 157 9D 221 DD
30 1E IRS (interchange record separator) 94 5E ; 158 9E 222 DE
31 1F IUS (interchange unit separator) 95 5F 159 9F 223 DF
32 20 DS (digit select) 96 60 - 160 A0 224 E0 \
33 21 SOS (start of significance) 97 61 / 161 A1 ~ 225 E1
34 22 FS (field separator) 98 62 162 A2 s 226 E2 S
35 23 99 63 163 A3 t 227 E3 T
36 24 BYP (bypass) 100 64 164 A4 u 228 E4 U
37 25 LF (line feed) 101 65 165 A5 v 229 E5 V
38 26 ETB (end of transmission block) 102 66 166 A6 w 230 E6 W
39 27 ESC (escape) 103 67 167 A7 x 231 E7 X
40 28 104 68 168 A8 y 232 E8 Y
41 29 105 69 169 A9 z 233 E9 Z
42 2A SM (set mode) 106 6A 170 AA 234 EA
43 2B CU2 (customer use 2) 107 6B , 171 AB 235 EB
44 2C 108 6C % 172 AC 236 EC
45 2D ENQ (enquiry) 109 6D _ 173 AD 237 ED
46 2E ACK (acknowledge) 110 6E > 174 AE 238 EE
47 2F BEL (bell) 111 6F ? 175 AF 239 EF
48 30 112 70 176 B0 240 F0 0
49 31 113 71 177 B1 241 F1 1
50 32 SYN (synchronous idle) 114 72 178 B2 242 F2 2
51 33 115 73 179 B3 243 F3 3
52 34 PN (punch on) 116 74 180 B4 244 F4 4
53 35 RS (reader stop) 117 75 181 B5 245 F5 5
54 36 UC (upper case) 118 76 182 B6 246 F6 6
55 37 EOT (end of transmission) 119 77 183 B7 247 F7 7
56 38 120 78 184 B8 248 F8 8
57 39 121 79 ` 185 B9 249 F9 9
58 3A 122 7A : 186 BA 250 FA
59 3B CU3 (customer use 3) 123 7B # 187 BB 251 FB
60 3C DC4 (device control 4) 124 7C @ 188 BC 252 FC
61 3D NAK (negative acknowledge) 125 7D ' 189 BD 253 FD
62 3E 126 7E = 190 BE 254 FE
63 3F SUB (substitute) 127 7F " 191 BF 255 FF
7
10 - medida da informaco (SI / IEC)
11 aritmticos e relacionais
Sobre o autor
Prof. Nelson G. de Oliveira, Cientista da Computao pelo IMES-SCS, Especialista em Telecomunicaes pela FAAP-SP, mestrando em Cincia da Computao pela UFABC-SP. Iniciou a carreira como desenvolvedor de software em 1987, especializando-se em COBOL para Mainframes IBM. Professor universitrio desde 2000, leciona diversas disciplinas nos cursos de Cincia da Computao e Informtica. Em 2008 fundou a Grande Porte com o objetivo de difundir essa experincia para o mercado. O objetivo do Carto de Referncia dar ao aluno da graduao um guia de consulta rpida para tpicos teis durante a sua formao.
Aritmtico Prioridade Significado Relacional Significado
( ) 0 Parnteses = igualdade
^ 1 Exponenciao == igualdade
** 1 Exponenciao diferente
/ 2 Diviso real != direfente
\ 2 Diviso inteira > maior que
% 2 Resto da diviso < menor que
* 2 Multiplicao >= maior ou igual
+ 3 Adio menor ou igual
Nome SI Smbolo SI Valor (quantidade de bytes)
Kilobyte kB 1003 = 1.000 este k deve ser minsculo
Megabyte MB 1006 = 1. 000. 000
Gigabyte GB 1009 = 1. 000. 000. 000
Terabyte TB 1012 = 1. 000. 000. 000. 000
Petabyte PB 1015 = 1. 000. 000. 000. 000. 000
Exabyte EB 1018 = 1. 000. 000. 000. 000. 000. 000
Zettabyte ZB 1021 = 1. 000. 000. 000. 000. 000. 000. 000
Yottabyte YB 1024 = 1. 000. 000. 000. 000. 000. 000. 000. 000
Nome IEC Smbolo IEC Valor (quantidade de bytes)
Kibibyte KiB 210 = 1.024
Mebibyte MiB 220 = 1.048.576
Gibibyte GiB 230 = 1.073.741.824
Tebibyte TiB 240 = 1.099.511.627.776
Pebibyte PiB 250 = 1.125.899.906.842.624
Exbibyte EiB 260 = 1.152.921.504.606.846.976
Zebibyte ZiB 270 = 1.180.591.620.717.411.303.424
Yobibyte YiB 280 = 1.208.925.819.614.629.174.706.176
em uso
Kilobyte
Megabyte
Gigabyte
Terabyte
Petabyte
Exabyte
Zettabyte
Yottabyte
9
12 - tabela verdade
Conectivo Smbolo Prioridade
NOT 0
AND 1
OR 2
A B AB 0 0 0
0 1 0
1 0 0
1 1 1
A B AB 0 0 0
0 1 1
1 0 1
1 1 1
A A
0 1
1 0
0 false
1 true
13 - equivalncias lgicas
A B AB AB AB AB 0 0 1 1 0 1
0 1 1 0 1 0
1 0 0 0 1 0
1 1 1 1 0 1
AB = AB
AB = (AB) (AB)
AB = (AB) (AB)AB = (AB) = ((AB)(AB))
14 tabela verdade abreviada
AB 000
001
100
111
AB 000
011
110
111
A
10
01
AB = AB 010 1010
011 1011
100 0100
111 0111
AB = (AB)(AB) 0 1 0 1010 1 01 1 0
0 0 1 1011 0 00 0 1
1 0 0 0100 0 11 1 0
1 1 1 0111 1 11 0 1
AB = (AB)(AB) 0 0 0 000 0 1 000
0 1 1 011 1 1 001
1 1 0 110 1 1 100
1 0 1 111 0 0 111
AB = (AB) = ((AB)(AB)) 010 1 0 0 0 1 000 0 1 000
001 0 0 1 1 0 011 1 1 001
100 0 1 1 0 0 110 1 1 100
111 1 1 0 1 1 111 0 0 111
valor inicial
valor intermedirio valor final
10
15 PROPRIEDADES lgicas
A0 = A
A1 = 1 Tautologia
A1 = A
A0 = 0 Contradio
AA = A Idempotncia
AA = A Idempotncia
AB = BA Comutativa
AB = BA Comutativa
A(AB) = A Absoro
A(AB) = A Absoro
(AB)C = A(BC) Associativa
(AB)C = A(BC) Associativa
A(BC) = (AB)(AC) Morgan
A(BC) = (AB)(AC) Morgan
16 - lgebra proposicional
Nome Sequncia
Modus Ponens ((p q ) p ) q
Modus Tollens ((p q ) q ) p
Silogismo Hipottico ((p q ) (q r )) (p r )
Silogismo Disjuntivo ((p q ) p ) q
Dilema Construtivo ((p q ) (r s ) (p r )) (q s )
Dilema Destrutivo ((p q ) (r s ) (q s )) (p r )
Simplificao (p q ) p
Conjuno p , q (p q )
Adio p (p q )
Composio ((p q ) (p r )) (p (q r ))
Teorema de De Morgan (1) (p q ) (p q )
Teorema de De Morgan (2) (p q ) (p q )
Comutao (1) (p q ) (q p )
Comutao (2) (p q ) (q p )
Associatividade (1) (p (q r )) ((p q ) r )
Associatividade (2) (p (q r )) ((p q ) r )
Distributividade (1) (p (q r )) ((p q ) (p r ))
Distributividade (2) (p (q r )) ((p q ) (p r ))
Dupla Negao p p
Transposio (p q ) (q p )
Implicao Material (p q ) (p q )
Equivalncia Material (1) (p q ) ((p q ) (q p ))
Equivalncia Material (2) (p q ) ((p q ) (q p ))
Equivalncia Material (3) (p q ) ((p q ) (q p ))
Exportao ((p q ) r ) (p (q r ))
Importao (p (q r )) ((p q ) r )
Tautologia (1) p (p p )
Tautologia (2) p (p p )
Tertium non datur (p p )
11
17 - algoritmos de sort
Bubble Sort
template
void bubblesort (T data[], int n) {
for (int i = 0; i < n-1; i++)
for (int j = n-1; j > i; --j)
if (data[j] < data[j-1])
swap(data[j],data[j-1]);
}
INSERTION Sort
template
void insertionsort(T data[], int n) {
for (int i = 1, j; i < n; i++) {
T tmp = data[i];
for (j = i; j > 0 && tmp < data[j-1]; j--)
data[j] = data[j-1];
data[j] = tmp;
}
}
SELECTION Sort
template
void selectionsort(T data[], int n) {
for (int i = 0, j, least; i < n-1; i++) {
for (j = i+1, least = i; j < n; j++)
if (data[j] < data[least])
least = j;
swap (data[least],data[i]);
}
}
Quick sort
template
void quicksort(T data[], int first, int last) {
int lower = first+1, upper = last;
swap(data[first],data[(first+last)/2]);
T bound = data[first];
while (lower