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Файл:Алгоритмизация в инженерных задачах. Учебное пособие
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ɋ. ȼ. ɋɬɟɩɨɲɢɧɚ, Ɉ. ɇ. Ɏɟɞɨɧɢɧ, ɋ. ɘ. ɋɴɹɧɨɜ
ȺɅȽɈɊɂɌɆɂɁȺɐɂə
ȼ ɂɇɀȿɇȿɊɇɕɏ ɁȺȾȺɑȺɏ
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ
Ɇɨɫɤɜɚ ȼɨɥɨɝɞɚ
«ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ»
2023
1
ɍȾɄ 004.421
ȻȻɄ 30.2
ɋ79
Ɋɟɰɟɧɡɟɧɬɵ:
ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ ɋ. ə. Ⱥɥɢɛɟɤɨɜ;
ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ Ⱥ. Ⱥ. Ɇɟɞɹɤɨɜ
ɋɬɟɩɨɲɢɧɚ, ɋ. ȼ.
ɋ79 Ⱥɥɝɨɪɢɬɦɢɡɚɰɢɹ ɜ ɢɧɠɟɧɟɪɧɵɯ ɡɚɞɚɱɚɯ : ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ /
ɋ. ȼ. ɋɬɟɩɨɲɢɧɚ, Ɉ. ɇ. Ɏɟɞɨɧɢɧ, ɋ. ɘ. ɋɴɹɧɨɜ. – Ɇɨɫɤɜɚ ; ȼɨɥɨɝɞɚ :
ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ, 2023. – 116 ɫ. : ɢɥ., ɬɚɛɥ.
ISBN 978-5-9729-1456-2
Ɉɩɢɫɚɧɵ ɨɫɧɨɜɧɵɟ ɤɨɧɫɬɪɭɤɰɢɢ ɹɡɵɤɚ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ
ɜɵɫɨɤɨɝɨ
ɭɪɨɜɧɹ ɋ++. Ɋɚɫɫɦɨɬɪɟɧɵ ɱɢɫɥɟɧɧɵɟ ɦɟɬɨɞɵ ɢ ɚɥɝɨɪɢɬɦɵ ɢɯ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɞɥɹ ɪɟɲɟɧɢɹ ɢɧɠɟɧɟɪɧɵɯ ɢ ɩɪɢɤɥɚɞɧɵɯ ɡɚɞɚɱ.
Ⱦɥɹ ɫɬɭɞɟɧɬɨɜ ɧɚɩɪɚɜɥɟɧɢɣ ɩɨɞɝɨɬɨɜɤɢ 15.03.04 «Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ
ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɢ ɩɪɨɢɡɜɨɞɫɬɜ», 15.03.06 «Ɇɟɯɚɬɪɨɧɢɤɚ ɢ ɪɨɛɨɬɨɬɟɯɧɢɤɚ» ɢ 27.03.04 «ɍɩɪɚɜɥɟɧɢɟ ɜ ɬɟɯɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦɚɯ».
ɍȾɄ 004.421
ȻȻɄ 30.2
ISBN 978-5-9729-1456-2 © ɋɬɟɩɨɲɢɧɚ ɋ. ȼ., Ɏɟɞɨɧɢɧ Ɉ. ɇ., ɋɴɹɧɨɜ ɋ. ɘ., 2023
© ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2023
© Ɉɮɨɪɦɥɟɧɢɟ. ɂɡɞɚɬɟɥɶɫɬɜɨ «ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ», 2023
2
ɈȽɅȺȼɅȿɇɂȿ
ɉɊȿȾɂɋɅɈȼɂȿ ........................................................................................................ 5
ȽɅȺȼȺ 1. ɈɋɇɈȼɇɕȿ ɄɈɇɋɌɊɍɄɐɂɂ əɁɕɄȺ ɋ++ ...................................... 6
1.1. ɉɨɧɹɬɢɟ ɚɥɝɨɪɢɬɦɚ ............................................................................................. 6
1.2. ɉɨɧɹɬɢɟ ɬɢɩɚ ɞɚɧɧɵɯ ....................................................................................... 10
1.3. Ɂɧɚɤɢ ɨɩɟɪɚɰɢɣ ɜ ɋ++ ...................................................................................... 12
1.4. ɉɪɢɦɟɧɟɧɢɟ ɮɭɧɤɰɢɣ ....................................................................................... 15
1.5. Ȼɚɡɨɜɵɟ ɤɨɧɫɬɪɭɤɰɢɢ ɫɬɪɭɤɬɭɪɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ............................. 16
1.6. Oɩɟɪɚɬɨɪɵ ɹɡɵɤɚ ɋ++ ...................................................................................... 18
1.7. Ɋɚɡɪɚɛɨɬɤɚ ɚɥɝɨɪɢɬɦɨɜ .................................................................................... 24
1.8. ɋɬɚɬɢɱɟɫɤɢɟ ɫɬɪɭɤɬɭɪɵ ɞɚɧɧɵɯ ...................................................................... 25
1.9. ɉɪɢɦɟɧɟɧɢɟ ɝɪɚɮɨɜ .......................................................................................... 29
1.10. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ................................................................................ 42
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ............................................................................................. 45
ȽɅȺȼȺ 2. ɑɂɋɅȿɇɇɕȿ ɆȿɌɈȾɕ Ɋȿɒȿɇɂə ɍɊȺȼɇȿɇɂɃ ...................... 46
2.1. Ɇɟɬɨɞ ɞɟɥɟɧɢɹ ɨɬɪɟɡɤɚ
2.2. Ɇɟɬɨɞ ɤɚɫɚɬɟɥɶɧɵɯ .......................................................................................... 48
2.3. Ɇɟɬɨɞ ɩɪɨɫɬɵɯ ɢɬɟɪɚɰɢɣ ................................................................................. 49
2.4. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ .................................................................................. 50
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ............................................................................................. 57
ȽɅȺȼȺ 3. ɑɂɋɅȿɇɇɕȿ ɆȿɌɈȾɕ Ɋȿɒȿɇɂə ɋɂɋɌȿɆ
ɅɂɇȿɃɇɕɏ ɍɊȺȼɇȿɇɂɃ .................................................................................. 58
3.1. Ɇɟɬɨɞ ɦɚɬɪɢɰ .................................................................................................... 58
3.2. Ɇɟɬɨɞ ɢɬɟɪɚɰɢɣ (ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɩɪɢɛɥɢɠɟɧɢɣ) .................................... 59
3.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ .................................................................................. 60
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ............................................................................................. 64
ȽɅȺȼȺ 4. ɈɉɌɂɆɂɁȺɐɂə ɐȿɅȿȼɕɏ ɎɍɇɄɐɂɃ ........................................ 65
4.1. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɦɟɬɨɞɨɜ ɨɩɬɢɦɢɡɚɰɢɢ ........................................................... 65
4.2. Ƚɪɚɞɢɟɧɬɧɵɟ ɦɟɬɨɞɵ ɞɥɹ ɨɩɬɢɦɢɡɚɰɢɢ ɮɭɧɤɰɢɢ
ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ ......................................................................................... 68
4.3. ɍɫɥɨɜɧɚɹ ɨɩɬɢɦɢɡɚɰɢɹ
Ɇɟɬɨɞ ɲɬɪɚɮɧɵɯ ɮɭɧɤɰɢɣ ..................................................................................... 72
4.4. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ .................................................................................. 73
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ............................................................................................. 80
ȽɅȺȼȺ 5. ɑɂɋɅȿɇɇɈȿ ȾɂɎɎȿɊȿɇɐɂɊɈȼȺɇɂȿ
ɂ ɂɇɌȿȽɊɂɊɈȼȺɇɂȿ .......................................................................................... 81
5.1. Ɇɟɬɨɞɵ ɱɢɫɥɟɧɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ ɮɭɧɤɰɢɣ ..................................... 81
5.2. Ɇɟɬɨɞɵ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ .................... 84
ɩɨɩɨɥɚɦ ..................................................................... 47
ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ.
3
5.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ .................................................................................. 88
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ............................................................................................. 90
ȽɅȺȼȺ 6. ɂɇɌȿɊɉɈɅəɐɂə ɂ ɗɄɋɌɊȺɉɈɅəɐɂə ɎɍɇɄɐɂɃ .................. 91
6.1. Ⱥɩɩɪɨɤɫɢɦɚɰɢɹ, ɢɧɬɟɪɩɨɥɹɰɢɹ ɢ ɷɤɫɬɪɚɩɨɥɹɰɢɹ ɮɭɧɤɰɢɣ ......................... 91
6.2. Ɇɟɬɨɞɵ ɢɧɬɟɪɩɨɥɢɪɨɜɚɧɢɹ ɮɭɧɤɰɢɣ ɩɨɥɢɧɨɦɨɦ ........................................ 93
6.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ .................................................................................. 94
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ............................................................................................. 95
ȽɅȺȼȺ 7. ɑɂɋɅȿɇɇɈȿ Ɋȿɒȿɇɂȿ ɈȻɕɄɇɈȼȿɇɇɕɏ
ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɕɏ ɍɊȺȼɇȿɇɂɃ ɉȿɊȼɈȽɈ ɉɈɊəȾɄȺ ..................... 96
7.1. Ɇɟɬɨɞ ɗɣɥɟɪɚ .................................................................................................... 97
7.2. Ɇɟɬɨɞ ɗɣɥɟɪɚ-Ʉɨɲɢ (Ɇɟɬɨɞ Ɋɭɧɝɟ-Ʉɭɬɬɚ ɜɬɨɪɨrɨ ɩɨɪɹɞɤɚ) ...................... 98
7.3. Ɇɟɬɨɞ Ɋɭɧɝɟ-Ʉɭɬɬɚ
ɱɟɬɜɟɪɬɨɝɨ ɩɨɪɹɞɤɚ ........................................................ 99
7.4. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ................................................................................ 100
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ........................................................................................... 101
ȽɅȺȼȺ 8. ɋɈɋɌȺȼɅȿɇɂȿ ɄɈɆɉɊɈɆɂɋɋɇɕɏ ɐȿɅȿȼɕɏ
ɎɍɇɄɐɂɃ ............................................................................................................. 102
8.1. Ɇɟɬɨɞɵ ɫɨɫɬɚɜɥɟɧɢɹ ɤɨɦɩɥɟɤɫɧɵɯ ɤɪɢɬɟɪɢɟɜ ɨɩɬɢɦɢɡɚɰɢɢ .................... 102
8.2. Ɉɩɪɟɞɟɥɟɧɢɟ ɨɝɪɚɧɢɱɟɧɢɣ ............................................................................. 104
8.3. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ................................................................................ 109
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ........................................................................................... 110
ɋɉɂɋɈɄ ɂɋɉɈɅɖɁɈȼȺɇɇɈɃ ɅɂɌȿɊȺɌɍɊɕ ............................................. 111
4
ɉɊȿȾɂɋɅɈȼɂȿ
Ɉɛɪɚɛɨɬɤɚ ɱɢɫɥɨɜɵɯ ɞɚɧɧɵɯ ɜ ɩɨɫɥɟɞɧɢɟ ɝɨɞɵ ɫɜɹɡɚɧɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɪɚɡɥɢɱɧɵɯ ɫɩɟɰɢɚɥɢɡɢɪɨɜɚɧɧɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɨɝɪɚɦɦ ɢ ɫɢɫɬɟɦ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɱɢɫɥɟɧɧɵɯ ɦɟɬɨɞɨɜ ɤɚɤ ɢɧɫɬɪɭɦɟɧɬɚ ɪɟɲɟɧɢɹ ɩɪɢɤɥɚɞɧɵɯ ɡɚɞɚɱ.
ɒɢɪɨɤɨɟ ɜɧɟɞɪɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɟɬɨɞɨɜ ɜ ɫɚɦɵɟ ɪɚɡɧɨɨɛɪɚɡɧɵɟ ɫɮɟɪɵ
ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɱɟɥɨɜɟɤɚ ɬɪɟɛɭɟɬ ɫɨɡɞɚɧɢɹ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ
ɢɧɫɬɪɭɦɟɧɬɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɥɹ ɪɟɲɟɧɢɹ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ
ɡɚɞɚɱ. ɋɨɜɪɟɦɟɧɧɵɟ ɱɢɫɥɟɧɧɵɟ ɦɟɬɨɞɵ ɜ
ɬɨɦɚɬɢɡɚɰɢɢ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɟɪɫɨɧɚɥɶɧɵɯ ɤɨɦɩɶɸɬɟɪɨɜ ɩɪɟɜɪɚɳɚɸɬɫɹ ɜ
ɭɧɢɜɟɪɫɚɥɶɧɵɣ ɢɧɫɬɪɭɦɟɧɬ ɞɥɹ ɪɟɲɟɧɢɹ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɡɚɞɚɱ.
ȼ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɪɚɫɫɦɨɬɪɟɧɵ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɨɫɧɨɜɵ ɱɢɫɥɟɧɧɵɯ ɦɟ-
ɬɨɞɨɜ, ɩɪɢɦɟɧɹɟɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɢɧɠɟɧɟɪɧɵɯ ɢ ɧɚɭɱɧɵɯ ɡɚɞɚɱ, – ɦɟɬɨɞɵ ɩɪɢɛɥɢɠɟɧɧɵɯ ɜɵɱɢɫɥɟɧɢɣ, ɨɩɬɢɦɢɡɚɰɢɢ ɭɫɥɨɜɧɵɯ ɢ ɛɟɡɭɫɥɨɜɧɵɯ ɰɟɥɟɜɵɯ ɮɭɧɤɰɢɣ, ɱɢɫɥɟɧɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹ ɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ.
ɍɱɟɛɧɨɟ
ɫɜɟɞɟɧɢɹ ɨɛ ɨɫɧɨɜɧɵɯ ɤɨɧɫɬɪɭɤɰɢɹɯ ɹɡɵɤɚ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɜɵɫɨɤɨɝɨ ɭɪɨɜɧɹ
ɋ++. ȼɨ ɜɬɨɪɨɣ–ɜɨɫɶɦɨɣ ɝɥɚɜɚɯ ɪɚɫɫɦɨɬɪɟɧɵ ɱɢɫɥɟɧɧɵɟ ɦɟɬɨɞɵ ɢ ɚɥɝɨɪɢɬɦɵ
ɞɥɹ ɪɟɲɟɧɢɹ ɢɧɠɟɧɟɪɧɵɯ ɢ ɧɚɭɱɧɵɯ ɡɚɞɚɱ. ȼ ɤɚɠɞɨɣ ɢɡ ɷɬɢɯ ɝɥɚɜ ɢɦɟɸɬɫɹ
ɩɪɢɦɟɪɵ ɪɟɚɥɢɡɚɰɢɢ ɱɢɫɥɟɧɧɵɯ ɦɟɬɨɞɨɜ (ɚɥɝɨɪɢɬɦ ɢ ɩɪɨɝɪɚɦɦɧɵɣ ɤɨɞ ɧɚ ɹɡɵɤɟ ɋ
++).
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɨ ɫɬɭɞɟɧɬɚɦɢ ɩɪɢ ɩɨɞɝɨɬɨɜɤɟ ɤ
ɩɪɚɤɬɢɱɟɫɤɢɦ ɪɚɛɨɬɚɦ ɩɨ ɞɢɫɰɢɩɥɢɧɚɦ «ɉɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ ɢ ɨɫɧɨɜɵ ɚɥɝɨɪɢɬɦɢɡɚɰɢɢ», «ɋɬɪɭɤɬɭɪɵ ɢ ɚɥɝɨɪɢɬɦɵ ɨɛɪɚɛɨɬɤɢ ɞɚɧɧɵɯ», «Ⱥɥɝɨɪɢɬɦɢɡɚɰɢɹ ɢɧɠɟɧɟɪɧɵɯ ɢ ɧɚɭɱɧɵɯ ɡɚɞɚɱ».
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɩɪɟɞɧɚɡɧɚɱɟɧɨ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɜɫɟɯ ɮɨɪɦ ɨɛɭɱɟɧɢɹ ɩɨ
ɧɚɩɪɚɜɥɟɧɢɹɦ ɩɨɞɝɨɬɨɜɤɢ 15.03.04 «Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ
ɢ ɩɪɨɢɡɜɨɞɫɬɜ», 15.03.06 «Ɇɟɯɚɬɪɨɧɢɤɚ ɢ ɪɨɛɨɬɨɬɟɯɧɢɤɚ» ɢ 27.03.04 «ɍɩɪɚɜɥɟɧɢɟ ɜ ɬɟɯɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦɚɯ».
ɩɨɫɨɛɢɟ ɫɨɫɬɨɢɬ ɢɡ ɜɨɫɶɦɢ ɝɥɚɜ. ȼ ɩɟɪɜɨɣ ɝɥɚɜɟ ɩɪɟɞɫɬɚɜɥɟɧɵ
ɫɨɜɨɤɭɩɧɨɫɬɢ ɫ ɜɨɡɦɨɠɧɨɫɬɶɸ ɢɯ ɚɜ-
5
ȽɅȺȼȺ 1
ɈɋɇɈȼɇɕȿ ɄɈɇɋɌɊɍɄɐɂɂ əɁɕɄȺ ɋ++
1.1. ɉɨɧɹɬɢɟ ɚɥɝɨɪɢɬɦɚ
Ⱥɥɝɨɪɢɬɦ – ɷɬɨ ɬɨɱɧɨɟ ɩɪɟɞɩɢɫɚɧɢɟ, ɨɩɪɟɞɟɥɹɸɳɟɟ ɜɵɱɢɫɥɢɬɟɥɶɧɵɣ
ɩɪɨɰɟɫɫ, ɜɟɞɭɳɢɣ ɨɬ ɜɚɪɶɢɪɭɟɦɵɯ ɧɚɱɚɥɶɧɵɯ ɞɚɧɧɵɯ ɤ ɢɫɤɨɦɨɦɭ ɪɟɡɭɥɶɬɚɬɭ.
ɉɗȼɆ ɩɪɢɯɨɞɢɬɫɹ ɧɟ ɬɨɥɶɤɨ ɫɱɢɬɵɜɚɬɶ ɢ ɜɵɩɨɥɧɹɬɶ ɨɩɪɟɞɟɥɟɧɧɵɟ ɚɥɝɨ-
ɪɢɬɦɵ, ɧɨ ɢ ɯɪɚɧɢɬɶ ɡɧɚɱɢɬɟɥɶɧɵɟ ɨɛɴɟɦɵ ɢɧɮɨɪɦɚɰɢɢ, ɤ ɤɨɬɨɪɨɣ ɧɟɨɛɯɨɞɢɦɨ
ɛɵɫɬɪɨ ɨɛɪɚɳɚɬɶɫɹ. ɗɬɚ ɢɧɮɨɪɦɚɰɢɹ ɜ ɧɟɤɨɬɨɪɨɦ ɫɦɵɫɥɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ
ɚɛɫɬɪɚɤɰɢɸ ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ
ɧɨɝɨ ɦɧɨɠɟɫɬɜɚ ɞɚɧɧɵɯ, ɨɬɧɨɫɹɳɢɯɫɹ ɤ ɤɚɤɨɣ-ɥɢɛɨ ɬɟɦɟ.
ɇɟɡɚɜɢɫɢɦɨ ɨɬ ɫɨɞɟɪɠɚɧɢɹ ɢ ɫɥɨɠɧɨɫɬɢ ɥɸɛɵɟ ɞɚɧɧɵɟ ɜ ɩɚɦɹɬɢ ɉɗȼɆ
ɩɪɟɞɫɬɚɜɥɹɸɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶɸ ɞɜɨɢɱɧɵɯ ɪɚɡɪɹɞɨɜ, ɢɥɢ ɛɢɬɨɜ, ɚ ɢɯ ɡɧɚɱɟɧɢɹɦɢ ɹɜɥɹɸɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɞɜɨɢɱɧɵɟ ɱɢɫɥɚ. Ⱦɚɧɧɵɟ, ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɟ ɜ ɜɢɞɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɛɢɬɨɜ, ɢɦɟɸɬ ɨɱɟɧɶ ɩɪɨɫɬɭɸ ɨɪɝɚɧɢɡɚɰɢɸ ɢɥɢ
ɞɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɫɥɚɛɨ ɫɬɪɭɤɬɭɪɢɪɨɜɚɧɵ.
Ɉɫɧɨɜɧɨɣ ɰɟɥɶɸ ɜɵɱɢɫɥɢɬɟɥɶɧɨɝɨ ɩɪɨɰɟɫɫɚ ɹɜɥɹɟɬɫɹ ɢɫɩɨɥɧɟɧɢɟ ɚɥɝɨ-
ɪɢɬɦɚ ɫ ɡɚɞɚɧɧɵɦɢ ɢɫɯɨɞɧɵɦɢ ɞɚɧɧɵɦɢ ɢ ɩɨɥɭɱɟɧɢɟ ɪɟɡɭɥɶɬɚɬɚ.
ȿɫɥɢ ɜɵɛɪɚɧɧɵɣ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɱɢɫɥɟɧɧɵɣ ɦɟɬɨɞ ɭɠɟ ɪɟɚɥɢɡɨɜɚɧ ɜ
ɫɬɚɧɞɚɪɬɧɨɣ ɛɢɛɥɢɨɬɟɤɟ ɩɪɨɝɪɚɦɦ, ɬɨ ɚɥɝɨɪɢɬɦɨɦ ɛɭɞɟɬ ɬɨɥɶɤɨ ɨɩɢɫɚɧɢɟ ɢ
ɜɜɨɞ ɞɚɧɧɵɯ, ɨɛɪɚɳɟɧɢɟ ɤ ɫɬɚɧɞɚɪɬɧɨɣ ɩɪɨɝɪɚɦɦɟ, ɜɵɜɨɞ ɪɟɡɭɥɶɬɚɬɨɜ ɧɚ ɩɟɱɚɬɶ ɢɥɢ
ɥɟɟ ɱɚɫɬɵ ɫɥɭɱɚɢ, ɤɨɝɞɚ ɫ ɩɨɦɨɳɶɸ ɫɬɚɧɞɚɪɬɧɵɯ ɩɪɨɝɪɚɦɦ ɪɟɲɚɸɬ ɬɨɥɶɤɨ ɤɚɤɭɸ-ɬɨ ɱɚɫɬɶ ɡɚɞɚɱɢ.
ɡɚɰɢɢ ɡɚɞɚɱɢ, ɪɚɡɛɢɟɧɢɢ ɟɺ ɧɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɩɨɞɡɚɞɚɱ (ɲɚɝɨɜ) ɢ ɩɨɫɬɪɨɟɧɢɢ ɚɥɝɨɪɢɬɦɚ ɞɥɹ ɤɚɠɞɨɝɨ ɲɚɝɚ.
(ɲɚɝɢ, ɞɢɫɤɪɟɬɵ). Ɋɟɲɟɧɢɟ ɡɚɞɚɱɢ ɫɜɨɞɢɬɫɹ ɤ ɪɟɲɟɧɢɸ ɩɪɨɫɬɵɯ ɡɚɞɚɱ, ɩɪɢ ɷɬɨɦ
ɤɚɠɞɨɟ ɞɟɣɫɬɜɢɟ ɜɵɩɨɥɧɹɟɬɫɹ ɬɨɥɶɤɨ ɩɨɫɥɟ ɬɨɝɨ, ɤɚɤ ɡɚɤɨɧɱɢɬɫɹ ɢɫɩɨɥɧɟɧɢɟ
ɩɪɟɞɵɞɭɳɟɝɨ.
ɱɬɨ ɱɺɬɤɨ ɨɩɪɟɞɟɥɺɧ ɩɨɪɹɞɨɤ ɜɵɩɨɥɧɟɧɢɹ ɚɥɝɨɪɢɬɦɚ. ɗɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɨɞɧɨ
ɡɧɚɱɧɨɫɬɶ ɪɟɡɭɥɶɬɚɬɚ ɩɪɢ ɡɚɞɚɧɧɵɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ.
ɨɩɪɟɞɟɥɺɧɧɨɟ ɱɢɫɥɨ ɲɚɝɨɜ.
ɧɵɣ, ɫɯɨɞɹɳɢɣɫɹ ɤ ɢɫɤɨɦɨɦɭ ɪɟɲɟɧɢɸ ɩɪɨɰɟɫɫ. ɉɪɨɰɟɫɫ ɨɛɪɵɜɚɟɬɫɹ, ɤɨɝɞɚ
ɨɱɟɪɟɞɧɨɟ ɩɪɢɛɥɢɠɺɧɧɨɟ ɪɟɲɟɧɢɟ ɞɨɫɬɢɝɚɟɬ ɡɚɞɚɧɧɨɣ ɬɨɱɧɨɫɬɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɡɚ ɤɨɧɟɱɧɨɟ ɱɢɫɥɨ ɲɚɝɨɜ ɞɨɫɬɢɝɚɟɬɫɹ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ.
ɷɤɪɚɧ ɞɢɫɩɥɟɹ. Ɉɞɧɚɤɨ ɩɪɢ ɪɟɲɟɧɢɢ ɧɚɭɱɧɵɯ ɢ ɢɧɠɟɧɟɪɧɵɯ ɡɚɞɚɱ ɛɨ-
Ɋɚɡɪɚɛɨɬɤɚ ɫɯɟɦɵ ɚɥɝɨɪɢɬɦɚ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɫɨɫɬɨɢɬ ɜ ɱɺɬɤɨɣ ɫɬɪɭɤɬɭɪɢ-
Ⱥɥɝɨɪɢɬɦ
− ɞɢɫɤɪɟɬɧɨɫɬɶ. ȼɟɫɶ ɜɵɱɢɫɥɢɬɟɥɶɧɵɣ ɩɪɨɰɟɫɫ ɪɚɡɛɢɬ ɧɚ ɦɟɥɤɢɟ ɷɬɚɩɵ
− ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɨɫɬɶ (ɨɩɪɟɞɟɥɺɧɧɨɫɬɶ), ɤɨɬɨɪɚɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ,
− ɪɟɡɭɥɶɬɚɬɢɜɧɨɫɬɶ. ɉɨɥɭɱɟɧɢɟ ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɺɧɧɨɝɨ ɪɟɡɭɥɶɬɚɬɚ ɡɚ
− ɤɨɧɟɱɧɨɫɬɶ. ɉɪɢ ɪɚɛɨɬɟ ɫ ɱɢɫɥɟɧɧɵɦɢ ɦɟɬɨɞɚɦɢ ɫɬɪɨɢɬɫɹ ɢɬɟɪɚɰɢɨɧ-
ɞɨɥɠɟɧ ɢɦɟɬɶ ɫɥɟɞɭɸɳɢɟ ɫɜɨɣɫɬɜɚ:
ɮɪɚɝɦɟɧɬɚ ɪɟɚɥɶɧɨɝɨ ɦɢɪɚ ɢ ɫɨɫɬɨɢɬ ɢɡ ɨɩɪɟɞɟɥɟɧ-
,
-
6
− ɦɚɫɫɨɜɨɫɬɶ. ɋ ɩɨɦɨɳɶɸ ɜɵɛɪɚɧɧɨɝɨ ɚɥɝɨɪɢɬɦɚ ɦɨɠɧɨ ɩɨɥɭɱɚɬɶ ɜɩɨɥɧɟ
ɨɩɪɟɞɟɥɺɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɧɟɤɨɬɨɪɨɝɨ ɤɥɚɫɫɚ
ɡɚɞɚɱ.
− ɮɨɪɦɚɥɶɧɨɫɬɶ. ɂɫɩɨɥɧɢɬɟɥɶ, ɧɟɡɧɚɤɨɦɵɣ ɫ ɫɨɞɟɪɠɚɧɢɟɦ ɚɥɝɨɪɢɬɦɚ, ɧɨ
ɩɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɢɜɲɢɣ ɟɝɨ ɩɪɟɞɩɢɫɚɧɢɟ, ɩɨɥɭɱɚɟɬ ɢɫɤɨɦɵɣ ɪɟɡɭɥɶɬɚɬ.
ɉɪɢ ɡɚɩɢɫɢ ɚɥɝɨɪɢɬɦɚ ɧɚ ɥɸɛɨɦ ɷɬɚɩɟ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ, ɱɬɨ ɢɫɩɨɥ-
ɧɢɬɟɥɟɦ ɛɭɞɟɬ ɤɨɦɩɶɸɬɟɪ, ɤɨɬɨɪɵɣ ɫɦɨɠɟɬ ɜɵɩɨɥɧɹɬɶ ɬɨɥɶɤɨ
ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɺɧɧɵɟ ɞɟɣɫɬɜɢɹ – ɩɪɢɫɜɚɢɜɚɧɢɟ, ɜɟɬɜɥɟɧɢɟ, ɰɢɤɥɢɱɟɫɤɨɟ ɩɨɜɬɨɪɟɧɢɟ, ɛɟɡɭɫɥɨɜɧɵɣ ɩɟɪɟɯɨɞ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɥɸɛɚɹ ɞɟɬɚɥɢɡɚɰɢɹ ɞɨɥɠɧɚ ɩɪɢɜɨɞɢɬɶ ɤ ɪɟɚɥɢɡɚɰɢɢ ɬɚɤɢɯ ɞɟɣɫɬɜɢɣ.
ɂɫɩɨɥɶɡɭɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɹɡɵɤɢ ɨɩɢɫɚɧɢɹ ɚɥɝɨɪɢɬɦɨɜ:
– ɫɥɨɜɟɫɧɚɹ ɡɚɩɢɫɶ, ɧɚɩɪɢɦɟɪ:
ɫɤɨɩɢɪɨɜɚɬɶ ɡɧɚɱɟɧɢɟ ɏ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɭɸ ɩɟɪɟɦɟɧɧɭɸ ɯ;
ɫɤɨɩɢɪɨɜɚɬɶ ɡɧɚɱɟɧɢɟ Y ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɭɸ ɩɟɪɟɦɟɧɧɭɸ y;
ɟɫɥɢ ɯy, ɩɟɪɟɣɬɢ ɤ ɩ. 4, ɢɧɚɱɟ
− ɤ ɩ. 7;
ɟɫɥɢ ɯ>y, ɩɟɪɟɣɬɢ ɤ ɩ. 5, ɢɧɚɱɟ − ɤ ɩ. 6;
ɡɚɩɢɫɚɬɶ ɜ ɯ ɪɟɡɭɥɶɬɚɬ ɜɵɱɢɫɥɟɧɢɹ (x-y) ɢ ɩɟɪɟɣɬɢ ɤ ɩ. 3;
ɡɚɩɢɫɚɬɶ ɜ ɭ ɪɟɡɭɥɶɬɚɬ ɜɵɱɢɫɥɟɧɢɹ ɜɵɪɚɠɟɧɢɹ ɭ-ɯ ɢ ɩɟɪɟɣɬɢ ɤ ɩ. 3;
ɤɨɧɟɰ. ɯ − ɪɟɡɭɥɶɬɚɬ.
– ɩɫɟɜɞɨɤɨɞ, ɧɚɩɪɢɦɟɪ:
ɇɈȾ(X, Y)
ɩɨɤɚ (xy) ɩɨɜɬɨɪɹɬɶ
ɟɫɥɢ (x>y) ɬɨ x: = x-y;
ɢɧɚɱɟ y: = y-x;
ɤɨɧɟɰ ɰɢɤɥɚ;
ɜɵɜɟɫɬɢ
ɯ;
ɤɨɧɟɰ.
– ɛɥɨɤ-ɫɯɟɦɵ.
ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦ ɹɜɥɹɟɬɫɹ ɨɩɢɫɚɧɢɟ ɚɥɝɨɪɢɬɦɨɜ, ɩɪɨɝɪɚɦɦ,
ɞɚɧɧɵɯ ɢ ɫɢɫɬɟɦ ɜ ɜɢɞɟ ɫɯɟɦɵ ɢɡ ɝɪɚɮɢɱɟɫɤɢɯ ɫɢɦɜɨɥɨɜ. Ȼɥɨɤ-ɫɯɟɦɚ – ɷɬɨ ɝɪɚɮɢɱɟɫɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɦɟɬɨɞɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɜ ɤɨɬɨɪɨɦ ɢɫɩɨɥɶɡɭɸɬɫɹ ɫɢɦɜɨɥɵ, ɨɬɨɛɪɚɠɚɸɳɢɟ ɨɩɟɪɚɰɢɢ (ɞɟɣɫɬɜɢɹ) ɢ ɞɚɧɧɵɟ.
ȼ ɛɥɨɤ-ɫɯɟɦɟ ɤɚɠɞɨɦɭ ɬɢɩɭ ɞɟɣɫɬɜɢɣ (ɧɚɩɪɢɦɟɪ: ɜɜɨɞ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ,
ɜɵɱɢɫɥɟɧɢɟ ɡɧɚɱɟɧɢɣ
ɜɵɪɚɠɟɧɢɣ, ɩɪɨɜɟɪɤɚ ɭɫɥɨɜɢɣ ɢ ɬ. ɞ.) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɝɟɨɦɟɬɪɢɱɟɫɤɚɹ ɮɢɝɭɪɚ, ɩɪɟɞɫɬɚɜɥɟɧɧɚɹ ɫɢɦɜɨɥɨɦ ɞɟɣɫɬɜɢɹ. ɋɢɦɜɨɥɵ ɞɟɣɫɬɜɢɹ
ɫɨɟɞɢɧɹɸɬ ɥɢɧɢɹɦɢ ɩɟɪɟɯɨɞɨɜ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬ ɨɱɟɪɺɞɧɨɫɬɶ ɜɵɩɨɥɧɟɧɢɹ
ɞɟɣɫɬɜɢɣ. Ɏɨɪɦɚ ɫɢɦɜɨɥɨɜ ɢ ɩɪɚɜɢɥɚ ɫɨɫɬɚɜɥɟɧɢɹ ɛɥɨɤ-ɫɯɟɦ ɭɫɬɚɧɨɜɥɟɧɵ ȿɞɢɧɨɣ ɫɢɫɬɟɦɨɣ ɩɪɨɝɪɚɦɦɧɨɣ ɞɨɤɭɦɟɧɬɚɰɢɢ (ȿɋɉȾ) ȽɈɋɌ 19701-90 [5]. ɇɚɢɛɨɥɟɟ ɱɚɫɬɨ ɭɩɨɬɪɟɛɥɹɟɦɵɟ ɫɢɦɜɨɥɵ ɞɟɣɫɬɜɢɣ ɭɤɚɡɚɧɧɨɝɨ ɫɬɚɧɞɚɪɬɚ ɩɪɢɜɟɞɟɧɵ ɜ
ɬɚɛɥɢɰɟ 1.
7
Ɍɚɛɥɢɰɚ 1
ɋɢɦɜɨɥɵ ɛɥɨɤ-ɫɯɟɦ ɚɥɝɨɪɢɬɦɨɜ
ɇɚɡɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ ɉɨɹɫɧɟɧɢɟ
ɉɪɨɰɟɫɫ
ȼɵɩɨɥɧɟɧɢɟ ɨɩɟɪɚɰɢɢ
ɢɥɢ ɝɪɭɩɩɵ ɨɩɟɪɚɰɢɣ
ɉɪɟɞɨɩɪɟɞɟɥɟɧɧɵɣ
ɩɪɨɰɟɫɫ
Ɋɟɲɟɧɢɟ
ɉɨɞɝɨɬɨɜɤɚ
Ɍɟɪɦɢɧɚɬɨɪ
Ⱦɚɧɧɵɟ
Ⱦɨɤɭɦɟɧɬ
Ʌɢɧɢɹ
ɋɨɟɞɢɧɢɬɟɥɶ
ȼɵɩɨɥɧɟɧɢɟ
ɩɨɞɩɪɨɝɪɚɦɦɵ/ɮɭɧɤɰɢɢ
ɉɪɨɜɟɪɤɚ ɭɫɥɨɜɢɣ
Ɇɨɞɢɮɢɤɚɰɢɹ ɤɨɦɚɧɞ ɞɥɹ
ɧɟɤɨɬɨɪɨɣ ɩɨɫɥɟɞɭɸɳɟɣ
ɮɭɧɤɰɢɢ. ɂɫɩɨɥɶɡɭɟɬɫɹ
ɞɥɹ ɰɢɤɥɨɜ ɫ ɩɚɪɚɦɟɬɪɨɦ
ɇɚɱɚɥɨ ɢ ɤɨɧɟɰ
ɩɪɨɝɪɚɦɦɵ, ɜɯɨɞ ɢ ɜɵɯɨɞ
ɢɡ ɩɨɞɩɪɨɝɪɚɦɦɵ
ȼɜɨɞ ɞɚɧɧɵɯ ɢɥɢ ɜɵɜɨɞ
ɞɚɧɧɵɯ ɢ ɩɟɱɚɬɶ
ɪɟɡɭɥɶɬɚɬɨɜ
ɋɢɦɜɨɥ ɩɟɱɚɬɢ
ɪɟɡɭɥɶɬɚɬɨɜ
ɍɤɚɡɵɜɚɟɬ ɩɨɬɨɤ ɞɚɧɧɵɯ,
ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ
ɞɨɩɨɥɧɹɟɬɫɹ ɫɬɪɟɥɤɚɦɢ
ɉɪɢɦɟɧɹɟɬɫɹ ɞɥɹ ɨɛɪɵɜɚ
ɥɢɧɢɢ ɢ ɩɪɨɞɨɥɠɟɧɢɹ ɟɟ
ɜ ɞɪɭɝɨɦ ɦɟɫɬɟ (ɩɪɢɦɟɪ:
ɪɚɡɞɟɥɟɧɢɟ ɛɥɨɤ-ɫɯɟɦɵ,
ɧɟ ɩɨɦɟɳɚɸɳɟɣɫɹ
ɧɚ ɥɢɫɬɟ).
ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ
ɫɨɟɞɢɧɢɬɟɥɶɧɵɟ ɫɢɦɜɨɥɵ
ɞɨɥɠɧɵ ɢɦɟɬɶ ɨɞɧɨ
(ɭɧɢɤɚɥɶɧɨɟ)
ɨɛɨɡɧɚɱɟɧɢɟ
8
Ɉɤɨɧɱɚɧɢɟ ɬɚɛɥɢɰɵ 1
ɇɚɡɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ ɉɨɹɫɧɟɧɢɟ
ɉɪɢɦɟɧɹɟɬɫɹ
Ʉɨɦɦɟɧɬɚɪɢɣ
ɞɥɹ ɤɨɦɦɟɧɬɚɪɢɟɜ
ɢ ɩɨɹɫɧɟɧɢɣ
ɉɚɪɚɥɥɟɥɶɧɵɣ
ɪɚɡɜɟɬɜɢɬɟɥɶ
ɇɚɱɚɥɨ ɩɚɪɚɥɥɟɥɶɧɵɯ
ɜɟɬɜɟɣ ɞɟɹɬɟɥɶɧɨɫɬɢ
Ʉɨɧɟɰ ɩɚɪɚɥɥɟɥɶɧɵɯ
ɜɟɬɜɟɣ ɞɟɹɬɟɥɶɧɨɫɬɢ
Ɉɫɧɨɜɧɵɟ ɩɪɚɜɢɥɚ ɩɪɢɦɟɧɟɧɢɹ ɫɢɦɜɨɥɨɜ ɢ ɜɵɩɨɥɧɟɧɢɹ ɛɥɨɤ-ɫɯɟɦ [2, 10]:
1. ɋɢɦɜɨɥɵ ɜ ɫɯɟɦɟ ɞɨɥɠɧɵ ɛɵɬɶ ɪɚɫɩɨɥɨɠɟɧɵ ɪɚɜɧɨɦɟɪɧɨ. ɇɟɨɛɯɨɞɢɦɨ
ɩɪɢɞɟɪɠɢɜɚɬɶɫɹ ɪɚɡɭɦɧɨɣ ɞɥɢɧɵ ɫɨɟɞɢɧɟɧɢɣ ɢ ɦɢɧɢɦɚɥɶɧɨɝɨ ɱɢɫɥɚ ɞɥɢɧɧɵɯ
ɥɢɧɢɣ.
2. ɋɢɦɜɨɥɵ ɞɨɥɠɧɵ ɛɵɬɶ ɩɨ ɜɨɡɦɨɠɧɨɫɬɢ ɨɞɧɨɝɨ ɪɚɡɦɟɪɚ ɢ, ɩɪɟɞɩɨɱɬɢ-
ɬɟɥɶɧɨ, ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɪɢɟɧɬɚɰɢɢ.
3. ȼɧɭɬɪɢ ɫɢɦɜɨɥɚ ɩɨɦɟɳɚɟɬɫɹ ɦɢɧɢɦɚɥɶɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɬɟɤɫɬɚ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɩɨɧɢɦɚɧɢɹ
ɮɭɧɤɰɢɢ ɫɢɦɜɨɥɚ. Ⱦɥɹ ɡɚɩɢɫɢ ɩɪɢɦɟɧɹɟɬɫɹ ɟɫɬɟɫɬɜɟɧɧɵɣ
ɹɡɵɤ ɫ ɷɥɟɦɟɧɬɚɦɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɢɦɜɨɥɢɤɢ. ȿɫɥɢ ɨɛɴɟɦ ɬɟɤɫɬɚ ɩɪɟɜɵɲɚɟɬ
ɪɚɡɦɟɪ ɫɢɦɜɨɥɚ, ɬɨ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɦɟɧɹɬɶ ɫɢɦɜɨɥ Ʉɨɦɦɟɧɬɚɪɢɣ.
4. ɉɨɬɨɤɢ ɞɚɧɧɵɯ ɢ ɩɨɬɨɤɢ ɭɩɪɚɜɥɟɧɢɹ ɜ ɫɯɟɦɚɯ ɩɨɤɚɡɵɜɚɸɬɫɹ ɥɢɧɢɹɦɢ.
ɇɚɩɪɚɜɥɟɧɢɟ ɩɨɬɨɤɚ ɫɥɟɜɚ ɧɚɩɪɚɜɨ ɢ ɫɜɟɪɯɭ ɜɧɢɡ ɫɱɢɬɚɟɬɫɹ ɫɬɚɧɞɚɪɬɧɵɦ. ȿɫɥɢ
ɩɨɬɨɤ ɢɦɟɟɬ ɧɚɩɪɚɜɥɟɧɢɟ, ɨɬɥɢɱɧɨɟ ɨɬ ɫɬɚɧɞɚɪɬɧɨɝɨ, ɫɬɪɟɥɤɢ ɞɨɥɠɧɵ ɭɤɚɡɵ
ɜɚɬɶ ɷɬɨ ɧɚɩɪɚɜɥɟɧɢɟ.
5. Ʌɢɧɢɢ ɜ ɫɯɟɦɚɯ ɞɨɥɠɧɵ ɩɨɞɯɨɞɢɬɶ ɤ ɫɢɦɜɨɥɭ ɥɢɛɨ ɫɥɟɜɚ, ɥɢɛɨ ɫɜɟɪɯɭ,
ɚ ɢɫɯɨɞɢɬɶ ɥɢɛɨ ɫɩɪɚɜɚ, ɥɢɛɨ ɫɧɢɡɭ. Ʌɢɧɢɢ ɞɨɥɠɧɵ ɛɵɬɶ ɧɚɩɪɚɜɥɟɧɵ ɤ ɰɟɧɬɪɭ
ɫɢɦɜɨɥɚ.
6. Ʉɚɠɞɵɣ ɫɢɦɜɨɥ ɢɦɟɟɬ ɨɞɢɧ ɜɯɨɞ ɢ ɨɞɢɧ ɜɵɯɨɞ. ɂɫɤɥɸɱɟɧɢɟɦ ɹɜɥɹɟɬɫɹ
ɫɢɦɜɨɥ Ɋɟɲɟɧɢɟ, ɤɨɬɨɪɵɣ ɢɦɟɟɬ ɨɞɢɧ ɜɯɨɞ ɢ ɧɟɫɤɨɥɶɤɨ ɜɵɯɨɞɨɜ. ɉɪɢ ɷɬɨɦ
ɤɚɠɞɵɣ ɜɵɯɨɞ ɞɨɥɠɟɧ ɫɨɩɪɨɜɨɠɞɚɬɶɫɹ ɡɧɚɱɟɧɢɹɦɢ ɭɫɥɨɜɢɣ, ɱɬɨɛɵ ɭɤɚɡɚɬɶ ɥɨɝɢɱɟɫɤɢɣ ɩɭɬɶ, ɤɨɬɨɪɵɣ ɨɧ ɩɪɟɞɫɬɚɜɥɹɟɬ.
ȼ ɛɨɥɶɲɢɯ ɤɨɥɥɟɤɬɢɜɚɯ ɩɪɨɝɪɚɦɦɢɫɬɨɜ ɩɪɢ ɪɚɡɪɚɛɨɬɤɟ ɫɥɨɠɧɵɯ ɩɪɨɟɤ-
ɬɨɜ ɪɚɛɨɬɚɸɬ ɫɨ ɫɩɟɰɢɚɥɶɧɵɦɢ ɩɪɨɝɪɚɦɦɧɵɦɢ ɫɪɟɞɫɬɜɚɦɢ ɞɥɹ ɚɜɬɨɦɚɬɢɡɢɪɨ-
-
9
ɜɚɧɧɨɝɨ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɚɥɝɨɪɢɬɦɨɜ ɢ ɩɪɨɝɪɚɦɦ. ɋɭɳɟɫɬɜɭɟɬ ɢ ɫɜɨɛɨɞɧɨɟ ɉɈ,
ɩɨɡɜɨɥɹɸɳɟɟ ɭɩɪɨɫɬɢɬɶ ɫɨɫɬɚɜɥɟɧɢɟ ɛɥɨɤ-ɫɯɟɦ ɚɥɝɨɪɢɬɦɨɜ (Draw.io, Dia, AFCE
ɪɟɞɚɤɬɨɪ ɛɥɨɤ-ɫɯɟɦ, Edraw MAX ɢ ɞɪ.).
1.2. ɉɨɧɹɬɢɟ ɬɢɩɚ ɞɚɧɧɵɯ
Ⱦɥɹ ɯɪɚɧɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ ɜ ɋ++ ɩɪɢɦɟɧɹɸɬɫɹ ɩɟɪɟɦɟɧɧɵɟ. ɉɟɪɟɦɟɧɧɚɹ
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɹɱɟɣɤɭ ɜ ɩɚɦɹɬɢ ɗȼɆ, ɜ ɤɨɬɨɪɨɣ ɯɪɚɧɢɬɫɹ ɡɧɚɱɟɧɢɟ. ɉɚɦɹɬɶ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɪɹɞ ɹɱɟɟɤ, ɤɨɬɨɪɵɟ ɩɪɨɧɭɦɟɪɨɜɚɧɵ
(
ɚɞɪɟɫɚ ɩɚɦɹɬɢ).
Ʉɨɦɩɢɥɹɬɨɪɭ ɩɪɨɝɪɚɦɦɵ ɧɟɨɛɯɨɞɢɦɨ ɡɚɪɚɧɟɟ ɩɪɟɞɨɫɬɚɜɢɬɶ ɢɧɮɨɪɦɚɰɢɸ
ɨ ɬɢɩɟ ɩɟɪɟɦɟɧɧɨɣ, ɱɬɨɛɵ ɨɧ ɦɨɝ ɡɚɪɟɡɟɪɜɢɪɨɜɚɬɶ ɞɥɹ ɧɟɟ ɦɟɫɬɨ.
Ȼɚɡɨɜɵɟ ɬɢɩɵ ɞɚɧɧɵɯ
Ɉɫɧɨɜɧɚɹ ɰɟɥɶ ɥɸɛɨɣ ɩɪɨɝɪɚɦɦɵ ɫɨɫɬɨɢɬ ɜ ɨɛɪɚɛɨɬɤɟ ɞɚɧɧɵɯ.
Ⱦɚɧɧɵɟ ɪɚɡɥɢɱɧɨɝɨ ɬɢɩɚ ɯɪɚɧɹɬɫɹ ɢ ɨɛɪɚɛɚɬɵɜɚɸɬɫɹ ɩɨ-ɪɚɡɧɨɦɭ. ȼ ɥɸɛɨɦ ɚɥɝɨɪɢɬɦɢɱɟɫɤɨɦ ɹɡɵɤɟ ɤɚɠɞɚɹ ɤɨɧɫɬɚɧɬɚ, ɩɟɪɟɦɟɧɧɚɹ, ɪɟɡɭɥɶɬɚɬ ɜɵɱɢɫɥɟɧɢɹ ɜɵɪɚɠɟɧɢɹ
ɢɥɢ
ɮɭɧɤɰɢɢ ɞɨɥɠɧɵ ɢɦɟɬɶ ɨɩɪɟɞɟɥɺɧɧɵɣ ɬɢɩ.
Ɍɢɩ ɞɚɧɧɵɯ ɨɩɪɟɞɟɥɹɟɬ:
− ɜɧɭɬɪɟɧɧɟɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɞɚɧɧɵɯ ɜ ɩɚɦɹɬɢ ɤɨɦɩɶɸɬɟɪɚ;
− ɦɧɨɠɟɫɬɜɨ ɡɧɚɱɟɧɢɣ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɪɢɧɢɦɚɬɶ ɜɟɥɢɱɢɧɵ ɷɬɨɝɨ ɬɢɩɚ;
− ɨɩɟɪɚɰɢɢ ɢ ɮɭɧɤɰɢɢ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɩɪɢɦɟɧɹɬɶ ɤ ɩɟɪɟɦɟɧɧɵɦ ɷɬɨɝɨ
ɬɢɩɚ.
əɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɋ++ ɩɨɞɞɟɪɠɢɜɚɟɬ ɫɥɟɞɭɸɳɢɟ ɬɢɩɵ ɞɚɧɧɵɯ
(ɪɢɫ. 1):
− ɛɚɡɨɜɵɟ ɬɢɩɵ (ɨɫɧɨɜɧɵɟ), ɤɨɬɨɪɵɟ ɩɪɟɞɫɬɚɜɥɟɧɵ
ɫɬɚɧɞɚɪɬɨɦ ɹɡɵɤɚ,
ɭɤɚɡɵɜɚɸɬɫɹ ɡɚɪɟɡɟɪɜɢɪɨɜɚɧɧɵɦɢ ɤɥɸɱɟɜɵɦɢ ɫɥɨɜɚɦɢ. Ȼɚɡɨɜɵɟ ɬɢɩɵ ɞɚɧɧɵɯ
ɫɨɡɞɚɸɬ ɨɫɧɨɜɭ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɬɢɩɨɜ;
− ɩɪɨɢɡɜɨɞɧɵɟ ɬɢɩɵ ɡɚɞɚɸɬɫɹ ɩɨɥɶɡɨɜɚɬɟɥɟɦ, ɢ ɩɟɪɟɦɟɧɧɵɟ ɷɬɢɯ ɬɢɩɨɜ
ɫɨɡɞɚɸɬɫɹ ɤɚɤ ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɛɚɡɨɜɵɯ ɬɢɩɨɜ, ɬɚɤ ɢ ɬɢɩɨɜ ɤɥɚɫɫɨɜ. ɉɪɨɢɡɜɨɞɧɵɟ ɬɢɩɵ ɞɚɧɧɵɯ ɛɵɜɚɸɬ ɩɪɨɫɬɵɟ ɢ ɫɨɫɬɚɜɧɵɟ (ɚɛɫɬɪɚɤɬɧɵɟ). Ⱥɛɫɬɪɚɤɬɧɵɣ
ɬɢɩ ɞɚɧɧɵɯ – ɷɬɨ ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɞɚɧɧɵɯ ɫ ɫɨɜɨɤɭɩɧɨɫɬɶɸ ɨɩɟɪɚɬɨɪɨɜ,
ɨɩɪɟɞɟɥɟɧɧɵɯ ɩɨɥɶɡɨɜɚɬɟɥɟɦ ɷɬɨɣ ɦɨɞɟɥɢ;
− ɬɢɩɵ ɤɥɚɫɫɚ ɩɪɢɦɟɧɹɸɬɫɹ ɜ ɨɛɴɟɤɬɧɨ-ɨɪɢɟɧɬɢɪɨɜɚɧɧɨɦ ɩɪɨɝɪɚɦɦɢɪɨ-
ɜɚɧɢɢ, ɷɤɡɟɦɩɥɹɪɵ ɷɬɢɯ ɬɢɩɨɜ ɧɚɡɵɜɚɸɬɫɹ ɨɛɴɟɤɬɚɦɢ. Ʉɥɚɫɫ ɹɜɥɹɟɬɫɹ ɱɚɫɬɧɵɦ
ɫɥɭɱɚɟɦ ɚɛɫɬɪɚɤɬɧɨɝɨ ɬɢɩɚ ɞɚɧɧɵɯ [24, 25].
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