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Файл:Алгоритмизация в инженерных задачах. Учебное пособие
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− ɟɫɥɢ ɡɧɚɱɟɧɢɟ ɫɨɜɩɚɞɚɟɬ ɫ ɜɵɪɚɠɟɧɢɟɦ_ɜɵɛɨɪɚ, ɬɨ ɭɩɪɚɜɥɟɧɢɟ ɩɟɪɟɞɚ-
ɟɬɫɹ ɧɚ ɨɩɟɪɚɬɨɪ, ɫɬɨɹɳɢɣ ɩɨɫɥɟ ɞɜɨɟɬɨɱɢɹ ɡɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɤɥɸɱɟɜɵɦ
ɫɥɨɜɨɦ case ɢ ɜɵɩɨɥɧɹɸɬɫɹ ɜɫɟ ɨɩɟɪɚɬɨɪɵ ɞɨ ɤɨɧɰɚ ɨɩɟɪɚɬɨɪɚ switch ɢɥɢ ɞɨ
ɨɩɟɪɚɬɨɪɚ break;
− ɟɫɥɢ ɧɟɬ ɧɢ ɨɞɧɨ ɫɨɜɩɚɞɟɧɢɹ, ɬɨ ɭɩɪɚɜɥɟɧɢɟ ɩɟɪɟɞɚɟɬɫɹ ɧɚ ɨɩɟɪɚɬɨɪ,
ɩɨɦɟɱɟɧɧɵɣ ɤɥɸɱɟɜɵɦ ɫɥɨɜɨɦ default, ɩɪɢ ɟɝɨ ɨɬɫɭɬɫɬɜɢɢ – ɧɚ ɫɥɟɞɭɸɳɢɣ ɩɨɫɥɟ switch ɨɩɟɪɚɬɨɪ.
Ɋɢɫ. 4. Ȼɥɨɤ-ɫɯɟɦɚ ɩɪɢɦɟɧɟɧɢɹ ɨɩɟɪɚɬɨɪɚ
switch/case
Ɉɩɟɪɚɬɨɪɵ ɰɢɤɥɨɜ
Ɉɩɟɪɚɬɨɪɵ ɰɢɤɥɚ ɩɪɢɦɟɧɹɸɬɫɹ ɞɥɹ ɨɪɝɚɧɢɡɚɰɢɢ ɦɧɨɝɨɤɪɚɬɧɨ ɩɨɜɬɨɪɹɸ-
ɳɢɯɫɹ ɜɵɱɢɫɥɟɧɢɣ.
Ʌɸɛɨɣ ɰɢɤɥ ɫɨɫɬɨɢɬ ɢɡ ɬɟɥɚ ɰɢɤɥɚ, ɬɨ ɟɫɬɶ ɬɟɯ ɨɩɟɪɚɬɨɪɨɜ, ɤɨɬɨɪɵɟ ɜɵɩɨɥɧɹɸɬɫɹ ɧɟɫɤɨɥɶɤɨ ɪɚɡ, ɧɚɱɚɥɶɧɵɯ ɭɫɬɚɧɨɜɨɤ, ɛɥɨɤɚ ɦɨɞɢɮɢɤɚɰɢɢ ɩɚɪɚɦɟɬɪɚ
ɰɢɤɥɚ ɢ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɹ ɜɵɯɨɞɚ ɢɡ ɰɢɤɥɚ, ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɪɚɡɦɟɳɚɬɶɫɹ ɥɢɛɨ
ɞɨ ɬɟɥɚ
ɰɢɤɥɚ (ɬɨɝɞɚ ɝɨɜɨɪɹɬ ɨ ɰɢɤɥɟ ɫ ɩɪɟɞɭɫɥɨɜɢɟɦ), ɥɢɛɨ ɩɨɫɥɟ ɬɟɥɚ ɰɢɤɥɚ
(ɰɢɤɥ ɫ ɩɨɫɬɭɫɥɨɜɢɟɦ).
ȼ ɬɟɨɪɢɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɪɚɡɥɢɱɚɸɬ ɞɜɚ ɜɢɞɚ ɰɢɤɥɨɜ:
1) ɚɪɢɮɦɟɬɢɱɟɫɤɢɟ;
2) ɢɬɟɪɚɰɢɨɧɧɵɟ;
Ⱥɪɢɮɦɟɬɢɱɟɫɤɢɟ ɢɥɢ ɫɱɟɬɧɵɟ ɰɢɤɥɵ – ɰɢɤɥɵ ɫ ɭɩɪɚɜɥɹɸɳɟɣ ɩɟɪɟɦɟɧɧɨɣ
(ɫɱɟɬɱɢɤɨɦ ɢɥɢ ɩɚɪɚɦɟɬɪɨɦ ɰɢɤɥɚ). ȼɵɩɨɥɧɹɟɬɫɹ ɢɡɜɟɫɬɧɨɟ ɱɢɫɥɨ ɪɚɡ.
ɂɬɟɪɚɰɢɨɧɧɵɟ – ɰɢɤɥɵ, ɤɨɬɨɪɵɟ ɜɵɩɨɥɧɹɸɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɢɫɬɢɧɧɨɫɬɢ
ɢɥɢ ɥɨɠɧɨɫɬɢ ɡɚɞɚɧɧɨɝɨ ɭɫɥɨɜɢɹ. ȼ ɢɬɟɪɚɰɢɨɧɧɵɯ ɰɢɤɥɚɯ ɢɡɜɟɫɬɧɨ ɭɫɥɨɜɢɟ
21
ɜɵɩɨɥɧɟɧɢɹ ɰɢɤɥɚ. ɂɬɟɪɚɰɢɨɧɧɵɦɢ ɰɢɤɥɚɦɢ ɹɜɥɹɸɬɫɹ ɰɢɤɥɵ ɫ ɩɪɟɞɭɫɥɨɜɢɟɦ ɢ
ɰɢɤɥɵ ɫ ɩɨɫɬɭɫɥɨɜɢɟɦ.
Ɉɞɢɧ ɩɪɨɯɨɞ ɰɢɤɥɚ ɧɚɡɵɜɚɟɬɫɹ ɢɬɟɪɚɰɢɟɣ. ɉɟɪɟɦɟɧɧɵɟ, ɩɪɢɧɭɞɢɬɟɥɶɧɨ
ɢɡɦɟɧɹɸɳɢɟɫɹ ɜ ɰɢɤɥɟ ɢ ɩɪɢɦɟɧɹɟɦɵɟ ɩɪɢ ɩɪɨɜɟɪɤɟ ɭɫɥɨɜɢɹ ɜɵɯɨɞɚ ɢɡ ɧɟɝɨ,
ɧɚɡɵɜɚɸɬɫɹ ɩɚɪɚɦɟɬɪɚɦɢ ɰɢɤɥɚ. ɐɟɥɨɱɢɫɥɟɧɧɵɟ ɩɚɪɚɦɟɬɪɵ ɰɢɤɥɚ, ɢɡɦɟɧɹɸɳɢɟɫɹ ɧɚ ɰɟɥɨɟ ɱɢɫɥɨ ɧɚ ɤɚɠɞɨɣ ɢɬɟɪɚɰɢɢ, ɧɚɡɵɜɚɸɬɫɹ ɫɱɟɬɱɢɤɚɦɢ ɰɢɤɥɚ.
ɇɟɥɶɡɹ ɩɟɪɟɞɚɜɚɬɶ ɭɩɪɚɜɥɟɧɢɟ
ɢɡɜɧɟ ɜɧɭɬɪɶ ɰɢɤɥɚ. ȼɵɯɨɞ ɢɡ ɰɢɤɥɚ ɜɨɡɦɨɠɟɧ ɤɚɤ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ ɜɵɯɨɞɚ, ɬɚɤ ɢ ɩɨ ɨɩɟɪɚɬɨɪɚɦ break, return
ɢɥɢ ɛɟɡɭɫɥɨɜɧɨɝɨ ɩɟɪɟɯɨɞɚ.
Ɉɩɟɪɚɬɨɪ ɰɢɤɥɚ while
ȼɵɪɚɠɟɧɢɟ ɨɩɪɟɞɟɥɹɟɬ ɭɫɥɨɜɢɟ ɩɨɜɬɨɪɟɧɢɹ ɬɟɥɚ ɰɢɤɥɚ, ɩɪɟɞɫɬɚɜɥɟɧɧɨɝɨ
ɩɪɨɫɬɵɦ ɢɥɢ ɫɨɫɬɚɜɧɵɦ ɨɩɟɪɚɬɨɪɨɦ. ȿɫɥɢ ɜɵɪɚɠɟɧɢɟ ɧɟ ɪɚɜɧɨ 0 (ɢɫɬɢɧɧɨ),
ɜɵɩɨɥɧɹɟɬɫɹ ɨɩɟɪɚɬɨɪ ɰɢɤɥɚ, ɩɨɫɥɟ ɱɟɝɨ ɨɩɹɬɶ ɜɵɱɢɫɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟ. ȿɫɥɢ
ɩɪɢ ɩɟɪɜɨɣ ɩɪɨɜɟɪɤɟ
ɜɵɪɚɠɟɧɢɟ ɪɚɜɧɨ 0, ɰɢɤɥ ɧɟ ɜɵɩɨɥɧɢɬɫɹ ɧɢ ɪɚɡɭ (ɪɢɫ. 5).
Ɍɢɩ ɜɵɪɚɠɟɧɢɹ ɞɨɥɠɟɧ ɛɵɬɶ ɚɪɢɮɦɟɬɢɱɟɫɤɢɦ ɢɥɢ ɩɪɢɜɨɞɢɦɵɦ ɤ ɧɟɦɭ.
Ɉɪɝɚɧɢɡɭɟɬ ɰɢɤɥ ɫ ɩɪɟɞɭɫɥɨɜɢɟɦ.
Ɉɛɳɢɣ ɜɢɞ ɨɩɟɪɚɬɨɪɚ [7]:
while (ɭɫɥɨɜɢɟ) {ɨɩɟɪɚɬɨɪɵ;}
ɍɫɥɨɜɢɟ – ɜɵɪɚɠɟɧɢɟ, ɤɨɬɨɪɨɟ ɩɪɢɧɢɦɚɟɬ ɥɨɝɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ true – ɢɫɬɢɧɚ (ɧɟ NULL) ɢɥɢ false – ɥɨɠɶ (NULL). ȼɵɩɨɥɧɟɧɢɟ ɨɩɟɪɚɬɨɪɚ ɩɨɜɬɨɪɹɟɬɫɹ
ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɡɧɚɱɟɧɢɟɦ ɭɫɥɨɜɢɹ ɹɜɥɹɟɬɫɹ true. ɍɫɥɨɜɢɟ ɜɵɱɢɫɥɹɟɬɫɹ
ɡɚɧɨɜɨ
ɩɟɪɟɞ ɤɚɠɞɨɣ ɢɬɟɪɚɰɢɟɣ, ɧɚɩɪɢɦɟɪ:
while (N > 1)
{
N = N / 10;
}
Ɋɢɫ. 5. Ȼɥɨɤ-ɫɯɟɦɚ ɩɪɢɦɟɧɟɧɢɹ
ɨɩɟɪɚɬɨɪɚ while/do
22
Ɉɩɟɪɚɬɨɪ ɰɢɤɥɚ do while
ɋɧɚɱɚɥɚ ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɨɫɬɨɣ ɢɥɢ ɫɨɫɬɚɜɧɨɣ ɨɩɟɪɚɬɨɪ, ɫɨɫɬɚɜɥɹɸɳɢɣ ɬɟɥɨ ɰɢɤɥɚ, ɚ ɡɚɬɟɦ ɜɵɱɢɫɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟ. ȿɫɥɢ ɨɧɨ ɧɟ ɪɚɜɧɨ 0 (ɢɫɬɢɧɧɨ), ɬɟɥɨ
ɰɢɤɥɚ ɜɵɩɨɥɧɹɟɬɫɹ ɟɳɟ ɪɚɡ, ɢ ɬɚɤ ɞɚɥɟɟ, ɩɨɤɚ ɜɵɪɚɠɟɧɢɟ ɧɟ ɫɬɚɧɟɬ ɪɚɜɧɵɦ ɧɭɥɸ ɢɥɢ ɜ ɬɟɥɟ ɰɢɤɥɚ ɧɟ ɛɭɞɟɬ ɜɵɩɨɥɧɟɧ ɤɚɤɨɣ-ɥɢɛɨ ɨɩɟɪɚɬɨɪ ɩɟɪɟɞɚɱɢ ɭɩɪɚɜɥɟɧɢɹ (ɪɢɫ. 6).
Ɍɢɩ ɜɵɪɚɠɟɧɢɹ ɞɨɥɠɟɧ ɛɵɬɶ ɚɪɢɮɦɟɬɢɱɟɫɤɢɦ ɢɥɢ ɩɪɢɜɨɞɢɦɵɦ
ɤ ɧɟɦɭ.
Ɉɪɝɚɧɢɡɭɟɬ ɰɢɤɥ ɫ ɩɨɫɬɭɫɥɨɜɢɟɦ.
Ɉɛɳɢɣ ɜɢɞ ɨɩɟɪɚɬɨɪɚ [7]:
do {ɨɩɟɪɚɬɨɪɵ;} while (ɭɫɥɨɜɢɟ);
ɍɫɥɨɜɢɟ – ɜɵɪɚɠɟɧɢɟ, ɤɨɬɨɪɨɟ ɩɪɢɧɢɦɚɟɬ ɥɨɝɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ true – ɢɫɬɢɧɚ (ɧɟ NULL) ɢɥɢ false – ɥɨɠɶ (NULL). ȼɵɩɨɥɧɟɧɢɟ ɨɩɟɪɚɬɨɪɚ ɩɨɜɬɨɪɹɟɬɫɹ
ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɡɧɚɱɟɧɢɟɦ ɭɫɥɨɜɢɹ ɹɜɥɹɟɬɫɹ true. ɍɫɥɨɜɢɟ ɜɵɱɢɫɥɹɟɬɫɹ ɡɚɧɨɜɨ
ɩɨɫɥɟ ɤɚɠɞɨɣ ɢɬɟɪɚɰɢɢ, ɧɚɩɪɢɦɟɪ:
do
{
N = N / 10;
}
while (N > 1)
Ɋɢɫ. 6. Ȼɥɨɤ-ɫɯɟɦɚ ɩɪɢɦɟɧɟɧɢɹ ɨɩɟɪɚɬɨɪɚ
do/while
Ɉɩɟɪɚɬɨɪ ɰɢɤɥɚ for
Ɉɪɝɚɧɢɡɭɟɬ ɰɢɤɥ ɫɨ ɫɱɟɬɱɢɤɨɦ. ɐɢɤɥ ɫ ɩɚɪɚɦɟɬɪɨɦ ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ
ɮɨɪɦɚɬ [7]:
for ( ɢɧɢɰɢɚɥɢɡɚɰɢɹ; ɜɵɪɚɠɟɧɢɟ; ɦɨɞɢɮɢɤɚɰɢɢ) ɨɩɟɪɚɬɨɪ;
ɂɧɢɰɢɚɥɢɡɚɰɢɹ ɩɪɢɦɟɧɹɟɬɫɹ ɞɥɹ ɨɛɴɹɜɥɟɧɢɹ ɢ ɩɪɢɫɜɨɟɧɢɹ ɧɚɱɚɥɶɧɵɯ
ɡɧɚɱɟɧɢɣ ɜɟɥɢɱɢɧɚɦ ɜ ɰɢɤɥɟ. ȼ ɷɬɨɣ ɱɚɫɬɢ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɧɟɫɤɨɥɶɤɨ ɨɩɟɪɚɬɨɪɨɜ, ɪɚɡɞɟɥɟɧɧɵɯ ɡɚɩɹɬɨɣ.
23
ȼɵɪɚɠɟɧɢɟ ɨɩɪɟɞɟɥɹɟɬ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɟɧɢɹ ɰɢɤɥɚ: ɟɫɥɢ ɨɧɨ ɧɟ ɪɚɜɧɨ 0
(ɢɫɬɢɧɧɨ), ɰɢɤɥ ɜɵɩɨɥɧɹɟɬɫɹ (ɪɢɫ. 7).
Ɇɨɞɢɮɢɤɚɰɢɢ ɜɵɩɨɥɧɹɸɬɫɹ ɩɨɫɥɟ ɤɚɠɞɨɣ ɢɬɟɪɚɰɢɢ ɰɢɤɥɚ ɢ ɫɥɭɠɚɬ
ɨɛɵɱɧɨ ɞɥɹ ɢɡɦɟɧɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɰɢɤɥɚ.
ɉɪɨɫɬɨɣ ɢɥɢ ɫɨɫɬɚɜɧɨɣ ɨɩɟɪɚɬɨɪ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɬɟɥɨ ɰɢɤɥɚ. Ʌɸɛɚɹ
ɢɡ ɱɚɫɬɟɣ ɨɩɟɪɚɬɨɪɚ for ɦɨɠɟɬ ɛɵɬɶ ɨɩɭɳɟɧɚ (ɧɨ ɬɨɱɤɢ ɫ ɡɚɩɹɬɨɣ ɧɟɨɛɯɨɞɢɦɨ
ɨɫɬɚɜɢɬɶ ɧɚ ɫɜɨɢɯ ɦɟɫɬɚɯ
!).
Ɉɛɳɢɣ ɜɢɞ ɨɩɟɪɚɬɨɪɚ [7]:
for (ɜɵɪɚɠɟɧɢɟ_1; ɜɵɪɚɠɟɧɢɟ_2; ɜɵɪɚɠɟɧɢɟ_3)
// ɡɚɝɨɥɨɜɨɤ ɰɢɤɥɚ
{ɨɩɟɪɚɬɨɪɵ;} // ɬɟɥɨ ɰɢɤɥɚ
Ɂɞɟɫɶ ɜɵɪɚɠɟɧɢɟ_1 – ɡɚɞɚɟɬ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɫɱɟɬɱɢɤɚ ɰɢɤɥɚ; ɜɵɪɚɠɟɧɢɟ_2 – ɭɫɥɨɜɢɟ ɰɢɤɥɚ (ɰɢɤɥ ɛɭɞɟɬ ɩɨɜɬɨɪɹɬɶɫɹ, ɩɨɤɚ ɭɫɥɨɜɢɟ ɢɫɬɢɧɧɨ); ɜɵɪɚɠɟɧɢɟ_3 – ɭɜɟɥɢɱɟɧɢɟ ɫɱɟɬɱɢɤɚ ɰɢɤɥɚ, ɧɚɩɪɢɦɟɪ:
for (i = 1; i < = 100; i = i + 1) sum = sum + i;
Ɋɢɫ. 7. Ȼɥɨɤ-ɫɯɟɦɚ ɩɪɢɦɟɧɟɧɢɹ ɨɩɟɪɚɬɨɪɚ for
1.7. Ɋɚɡɪɚɛɨɬɤɚ ɚɥɝɨɪɢɬɦɨɜ
Ɋɟɲɟɧɢɟ ɥɸɛɨɣ ɡɚɞɚɱɢ ɹɜɥɹɟɬɫɹ ɬɜɨɪɱɟɫɤɢɦ ɩɪɨɰɟɫɫɨɦ, ɤɨɬɨɪɵɣ ɫɨɫɬɨɢɬ
ɢɡ ɧɟɫɤɨɥɶɤɢɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɷɬɚɩɨɜ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɜ ɬɚɛɥ. 7 [24–26].
ɗɬɢ ɷɬɚɩɵ ɨɪɢɟɧɬɢɪɨɜɚɧɵ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɪɟɲɟɧɢɹ ɧɟ ɨɬɞɟɥɶɧɨ ɜɡɹɬɨɣ
(ɤɨɧɤɪɟɬɧɨɣ) ɡɚɞɚɱɢ, ɚ ɧɟɤɨɬɨɪɨɝɨ ɤɥɚɫɫɚ ɡɚɞɚɱ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɬɢɩɚ. ɗɬɚɩ ɩɨɫɬɪɨɟɧɢɹ ɚɥɝɨɪɢɬɦɨɜ, ɪɟɚɥɢɡɭɸɳɢɯ ɜɵɛɪɚɧɧɵɟ ɦɟɬɨɞɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ
, ɞɟɬɚɥɢɡɢɪɭɟɬ ɢ ɜɢɡɭɚɥɢɡɢɪɭɟɬ ɩɪɨɰɟɫɫ ɟɟ ɪɟɲɟɧɢɹ. Ⱥɥɝɨɪɢɬɦɢɡɚɰɢɹ ɩɨɡɜɨɥɹɟɬ ɭɠɟ
ɧɚ ɷɬɨɦ ɷɬɚɩɟ ɨɰɟɧɢɬɶ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɪɟɲɟɧɢɹ, ɭɬɨɱɧɢɬɶ ɦɟɬɨɞɵ ɪɟɲɟɧɢɹ ɞɥɹ
ɪɚɡɥɢɱɧɵɯ ɩɨɬɨɤɨɜ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢ ɜɵɹɜɢɬɶ ɧɟɤɨɬɨɪɵɟ ɨɲɢɛɤɢ.
24
ɭɤɬɭ
ɭ
Ɍɚɛɥɢɰɚ 7
ɗɬɚɩɵ ɚɥɝɨɪɢɬɦɢɡɚɰɢɢ ɡɚɞɚɱɢ
ɗɬɚɩ Ɂɚɞɚɱɢ
1. ɉɨɧɢɦɚɧɢɟ ɩɨɫɬɚɧɨɜɤɢ
ɢ ɬɪɟɛɨɜɚɧɢɣ ɢɫɯɨɞɧɨɣ ɡɚɞɚɱɢ,
ɨɩɪɟɞɟɥɟɧɢɟ ɩɪɟɞɦɟɬɧɨɣ ɨɛɥɚɫɬɢ, ɞɥɹ
Ⱥɧɚɥɢɡ ɩɨɫɬɚɧɨɜɤɢ ɡɚɞɚɱɢ
ɢ ɟɟ ɩɪɟɞɦɟɬɧɨɣ ɨɛɥɚɫɬɢ
ɤɨɬɨɪɨɣ ɩɨɫɬɚɜɥɟɧɚ ɡɚɞɚɱɚ
2. Ⱥɧɚɥɢɡ ɩɪɟɞɦɟɬɧɨɣ ɨɛɥɚɫɬɢ,
ɜɵɹɜɥɟɧɢɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ, ɤɨɬɨɪɵɟ
ɮɢɤɫɢɪɭɸɬ ɜɯɨɞɧɭɸ ɢ ɜɵɯɨɞɧɭɸ
ɢɧɮɨɪɦɚɰɢɸ (ɨɩɪɟɞɟɥɟɧɢɟ ɢɯ
ɫɬɪ
ɪɵ ɢ ɫɜɨɣɫɬɜ)
3. ȼɵɛɨɪ ɢ ɩɪɢɦɟɧɟɧɢɟ ɮɨɪɦɚɥɶɧɨɣ
ɫɢɫɬɟɦɵ ɞɥɹ ɨɩɢɫɚɧɢɹ ɦɨɞɟɥɢ
ɩɪɟɞɦɟɬɧɨɣ ɨɛɥɚɫɬɢ ɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ.
Ɏɨɪɦɚɥɶɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɪɟɲɟɧɢɹ
ɡɚɞɚɱɢ
4. Ɏɨɪɦɢɪɨɜɚɧɢɟ ɨɫɧɨɜɧɨɣ ɢɞɟɢ,
ɜɵɛɨɪ ɦɟɬɨɞɨɜ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ.
5. Ɉɩɪɟɞɟɥɟɧɢɟ ɬɟɯɧɨɥɨɝɢɣ, ɫɪɟɞɫɬɜ
ɢ ɢɫɩɨɥɧɢɬɟɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ,
ɩɨɫɬɪɨɟɧɢɟ ɚɥɝɨɪɢɬɦɨɜ, ɪɟɚɥɢɡɭɸɳɢɯ
ɜɵɛɪɚɧɧɵɟ ɦɟɬɨɞɵ
6. ɉɪɢɦɟɧɟɧɢɟ ɜɵɛɪɚɧɧɵɯ ɦɟɬɨɞɨɜ
ɉɪɚɤɬɢɱɟɫɤɨɟ ɪɟɲɟɧɢɟ
ɢ ɫɪɟɞɫɬɜ ɞɥɹ ɪɟɲɟɧɢɹ.
7. Ⱥɧɚɥɢɡ ɩɨɥ
ɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ
ɇɚɢɛɨɥɟɟ ɬɪɭɞɨɟɦɤɢɦ ɢ ɪɭɬɢɧɧɵɦ ɹɜɥɹɟɬɫɹ ɷɬɚɩ ɩɪɢɦɟɧɟɧɢɹ ɜɵɛɪɚɧɧɵɯ
ɦɟɬɨɞɨɜ ɢ ɫɪɟɞɫɬɜ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ. ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦ ɫɪɟɞɫɬɜɨɦ
ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɹɜɥɹɟɬɫɹ ɉɗȼɆ. ɉɪɢɦɟɧɟɧɢɟ ɜɵɛɪɚɧɧɵɯ ɦɟɬɨɞɨɜ ɢ ɚɥɝɨɪɢɬɦɨɜ ɞɥɹ ɪɟɲɟɧɢɹ ɧɚ ɉɗȼɆ ɜɤɥɸɱɚɟɬ ɞɚɥɶɧɟɣɲɭɸ ɞɟɬɚɥɢɡɚɰɢɸ ɟɟ ɪɟɲɟɧɢɹ
ɡɚ ɫɱɟɬ ɨɩɢɫɚɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɩɪɢɦɟɧɹɟɦɵɯ ɨɩɟɪɚɰɢɣ ɜ ɜɢɞɟ ɩɪɨɝɪɚɦɦɵ ɞɥɹ ɉɗȼɆ. ɗɬɨ
ɩɪɢɞɚɟɬ ɩɪɨɰɟɫɫɭ ɪɟɲɟɧɢɹ ɧɟ ɬɨɥɶɤɨ ɜɢɡɭɚɥɶɧɵɟ ɤɚɱɟɫɬɜɚ,
ɧɨ ɢ ɤɚɱɟɫɬɜɚ ɢɧɬɟɪɚɤɬɢɜɧɨɫɬɢ.
ɇɟ ɜɫɟ ɡɚɞɚɱɢ, ɪɟɲɚɟɦɵɟ ɫ ɩɨɦɨɳɶɸ ɉɗȼɆ, ɬɪɟɛɭɸɬ ɫɨɫɬɚɜɥɟɧɢɹ ɫɥɨɠɧɵɯ ɩɪɨɝɪɚɦɦ, ɧɚɩɪɢɦɟɪ, ɡɚɞɚɱɢ ɜɵɱɢɫɥɟɧɢɣ ɜ ɷɥɟɤɬɪɨɧɧɵɯ ɬɚɛɥɢɰɚɯ ɢɥɢ ɡɚɞɚɱɢ ɩɨɢɫɤɚ ɢ ɜɵɛɨɪɤɢ ɞɚɧɧɵɯ ɜ ɛɚɡɚɯ ɞɚɧɧɵɯ. Ɋɟɲɟɧɢɟ ɧɟɤɨɬɨɪɵɯ ɡɚɞɚɱ ɛɥɚɝɨɞɚɪɹ ɜɧɟɞɪɟɧɢɸ ɧɨɜɵɯ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɬɟɯɧɨɥɨɝɢɣ ɜɨɨɛɳɟ ɧɟ ɬɪɟɛɭɸɬ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɱɬɨ ɪɚɫɲɢɪɹɟɬ ɫɮɟɪɭ ɩɪɢɦɟɧɟɧɢɹ ɉɗȼɆ. Ɉɞɧɚɤɨ ɢ ɩɪɢ ɪɟɲɟɧɢɢ ɷɬɢɯ ɡɚɞɚɱ ɧɟɨɛɯɨɞɢɦɵ ɩɪɢɜɟɞɟɧɧɵɟ ɷɬɚɩɵ.
1.8. ɋɬɚɬɢɱɟɫɤɢɟ ɫɬɪɭɤɬɭɪɵ ɞɚɧɧɵɯ
Ⱦɚɧɧɵɟ ɜ ɋ++ ɦɨɝɭɬ ɯɪɚɧɢɬɶɫɹ ɜ ɫɬɚɬɢɱɟɫɤɢɯ ɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɫɬɪɭɤɬɭ-
ɪɚɯ.
25
ɋɬɪɭɤɬɭɪɚ ɞɚɧɧɵɯ – ɫɨɫɬɚɜɧɨɣ ɬɢɩ ɞɚɧɧɵɯ, ɜ ɤɨɬɨɪɵɣ ɦɨɝɭɬ ɜɯɨɞɢɬɶ
ɷɥɟɦɟɧɬɵ (ɩɨɥɹ) ɪɚɡɥɢɱɧɵɯ ɬɢɩɨɜ. ɋɨɜɨɤɭɩɧɨɫɬɶ ɩɨɥɟɣ ɫɬɪɭɤɬɭɪɵ ɞɥɹ ɨɞɧɨɣ
ɩɟɪɟɦɟɧɧɨɣ ɧɚɡɵɜɚɟɬɫɹ ɡɚɩɢɫɶɸ.
ɋɬɚɬɢɱɟɫɤɚɹ ɫɬɪɭɤɬɭɪɚ ɞɚɧɧɵɯ – ɫɨɜɨɤɭɩɧɨɫɬɶ ɮɢɤɫɢɪɨɜɚɧɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɩɟɪɟɦɟɧɧɵɯ ɩɨɫɬɨɹɧɧɨɣ ɪɚɡɦɟɪɧɨɫɬɢ ɫ ɧɟɢɡɦɟɧɧɵɦ ɯɚɪɚɤɬɟɪɨɦ ɫɜɹɡɟɣ
ɦɟɠɞɭ ɧɢɦɢ.
Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɫɬɪɭɤɬɭɪɵ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɬɟɦ, ɱɬɨ ɩɚɦɹɬɶ ɞɥɹ ɢɯ ɯɪɚɧɟɧɢɹ ɜɵɞɟɥɹɟɬɫɹ ɜɨ ɜɪɟɦɹ ɜɵɩɨɥɧɟɧɢɹ ɩɪɨɝɪɚɦɦɵ ɨɬɞɟɥɶɧɵɦɢ ɛɥɨɤɚɦɢ, ɤɨɬɨɪɵɟ ɫɜɹɡɚɧɵ ɦɟɠɞɭ ɫɨɛɨɣ ɩɪɢ ɩɨɦɨɳɢ ɭɤɚɡɚɬɟɥɟɣ (ɞɢɧɚɦɢɱɟɫɤɢɟ ɫɩɢɫɤɢ).
ɉɪɨɫɬɟɣɲɢɦ ɜɢɞɨɦ ɫɬɚɬɢɱɟɫɤɨɣ ɫɬɪɭɤɬɭɪɵ ɹɜɥɹɟɬɫɹ ɦɚɫɫɢɜ – ɢɦɟɧɨɜɚɧɧɚɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɹɱɟɟɤ ɩɚɦɹɬɢ, ɯɪɚɧɹɳɚɹ ɞɚɧɧɵɟ ɬɨɥɶɤɨ ɨɞɧɨɝɨ ɬɢɩɚ
[4, 6, 10, 25]:
int A[16] = { 5, -12, -12, 9, 10, 0, -9, -12, -1, 23, 65, 64, 11, 43, 39,
-15 };
Ɇɚɫɫɢɜɵ, ɫɨɫɬɨɹɳɢɟ ɬɨɥɶɤɨ ɢɡ ɷɥɟɦɟɧɬɨɜ ɬɢɩɚ char ɢ ɡɚɤɚɧɱɢɜɚɸɳɢɟɫɹ
ɧɭɥɟɜɵɦ ɬɟɪɦɢɧɚɬɨɪɨɦ (\0), ɧɚɡɵɜɚɸɬɫɹ ɫɬɪɨɤɚɦɢ:
char string[10] = {'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'f', '\0'};
ɋɬɪɭɤɬɭɪɵ, ɫɨɫɬɨɹɳɢɟ ɢɡ ɞɚɧɧɵɯ ɪɚɡɥɢɱɧɵɯ ɬɢɩɨɜ, ɨɛɴɹɜɥɹɸɬɫɹ ɫ ɩɨɦɨɳɶɸ ɫɥɨɜɚ struct:
struct Student {
int ID;
char SName[20];
};
ɋɥɨɜɨ Student – ɷɬɨ ɨɩɢɫɚɧɢɟ ɧɨɜɨɣ ɫɬɪɭɤɬɭɪɵ (ɧɨɜɨɝɨ ɤɨɦɩɥɟɤɫɧɨɝɨ ɬɢɩɚ ɞɚɧɧɵɯ) ɫ ɭɤɚɡɚɧɧɵɦɢ ɩɨɥɹɦɢ ID ɢ SName, ɩɚɦɹɬɶ ɩɨɞ ɧɟɟ ɩɪɢ ɷɬɨɦ ɧɟ
ɜɵɞɟɥɹɟɬ
-
ɫɹ. Ⱦɥɹ ɜɵɞɟɥɟɧɢɹ ɩɚɦɹɬɢ ɧɟɨɛɯɨɞɢɦɨ ɨɛɴɹɜɢɬɶ ɧɨɜɭɸ ɩɟɪɟɦɟɧɧɭɸ ɬɢɩɚ
ɫɬɪɭɤɬɭɪɵ Student, ɧɚɩɪɢɦɟɪ:
Student Ivanov;
ȿɫɥɢ ɩɪɢ ɨɛɴɹɜɥɟɧɢɢ ɫɬɪɭɤɬɭɪɵ ɨɬɫɭɬɫɬɜɭɟɬ ɢɦɹ ɬɢɩɚ ɞɚɧɧɵɯ, ɬɨ ɞɨɥɠɟɧ ɛɵɬɶ
ɭɤɚɡɚɧ ɫɩɢɫɨɤ ɩɟɪɟɦɟɧɧɵɯ:
struct {
int ID;
char SName[20];
} Ivanov, Petrov;
26
Ⱦɨɫɬɭɩ ɤ ɩɨɥɹɦ ɫɬɪɭɤɬɭɪɵ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɟɪɟɡ ɨɩɟɪɚɬɨɪ «.»:
Ivanov.ID = 12;
ɉɪɢɦɟɪ ɩɪɢɦɟɧɟɧɢɹ ɫɬɪɭɤɬɭɪɵ ɞɚɧɧɵɯ ɞɥɹ ɥɢɧɟɣɧɨɝɨ ɩɨɢɫɤɚ:
#include <stdio.h>
#include <vcl.h>
#pragma hdrstop
struct TStudent {
unsigned int ID;
char SName[20];
unsigned int Date;
char Group[10];
double Cost;
};
const N = 100;
typedef TStudent TDekanat[N];
typedef int TIndex[N];
// ɥɢɧɟɣɧɵɣ ɩɨɢɫɤ ɩɨ ɮɚɦɢɥɢɢ
void LS(TIndex &index, char *key, TDekanat &array, int n)
{
int i = 0;
for (int j = 0; j <n; j++)
if (StrPos(array[j].SName,key)! = NULL) {
index[i] = j;i++;}
index[i] = -1;
}
//--------------------------------------------------------------------------#pragma argsused
int main(int argc, char* argv[])
{
TDekanat Dekanat;
int d;
int n = 0;
while (1)
{
printf("Nomer deystviya( 0-Vyhod, 1- Vvod, 2-Vyvod, 3- Poisk ): ");
scanf("%d",&d);
printf("\n");
switch (d) {
case 0: return 0;
case 1:
27
printf("Vvedite ID SName Date Group Cost ):");
scanf("%u %s %u %s %lf",&Dekanat[n].ID, Dekanat[n].SName, &Dekanat[n].Date, Dekanat[n].Group, &Dekanat[n].Cost);
n++;
printf("\n");
break;
case 2:
printf("%6s %19s %8s %9s\n","ID", "SName", "Date",
"Group", "Cost" );
for (int i = 0; i <n; i++)
printf("%6u %19s %8u %9s %9/2f\n",
Dekanat[i].ID, Dekanat[i].SName, Dekanat[i].Date, Dekanat[i].Group, Dekanat[i].Cost);
printf("\n");
break;
case 3:
TIndex index;
char key[50];
printf("Stroka dlya poiska:");
scanf("%s",key);
LS(index, key, Dekanat, n);
if (index[0] = = -1)
printf("Nichego ne naydeno\n:");
else {
printf("%6s %19s %8s %9s\n","ID", "SName",
"Date", "Group", "Cost" );
for (int i = 0; index[i]! = -1; i++) {
int j = index[i];
printf("%6u %19s %8u %9s %9/2f\n",
Dekanat[i].ID, Dekanat[i].SName, Dekanat[i].Date, Dekanat[i].Group, Dekanat[i].Cost);
}
}
printf("\n");
break;
default:
printf("Nevernoe deystvie.\n");
printf("\n");
}
}
}
28
1.9. ɉɪɢɦɟɧɟɧɢɟ ɝɪɚɮɨɜ
Ɍɟɨɪɢɹ ɝɪɚɮɨɜ í ɨɛɥɚɫɬɶ ɞɢɫɤɪɟɬɧɨɣ ɦɚɬɟɦɚɬɢɤɢ, ɨɫɨɛɟɧɧɨɫɬɶɸ ɤɨɬɨɪɨɣ
ɹɜɥɹɟɬɫɹ ɝɪɚɮɢɱɟɫɤɚɹ ɢɧɬɟɪɩɪɟɬɚɰɢɹ ɩɪɢ ɢɡɭɱɟɧɢɢ ɫɜɨɣɫɬɜ ɤɨɧɟɱɧɵɯ ɦɧɨɠɟɫɬɜ
ɫ ɡɚɞɚɧɧɵɦɢ ɨɬɧɨɲɟɧɢɹɦɢ ɦɟɠɞɭ ɧɢɦɢ.
ɉɟɪɜɨɣ ɪɚɛɨɬɨɣ ɬɟɨɪɢɢ ɝɪɚɮɨɜ ɤɚɤ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɞɢɫɰɢɩɥɢɧɵ ɫɱɢɬɚɸɬ
ɫɬɚɬɶɸ ɗɣɥɟɪɚ, ɧɚɩɢɫɚɧɧɭɸ ɜ 1736 ɝɨɞɭ. ȼ ɫɬɚɬɶɟ ɪɚɫɫɦɚɬɪɢɜɚɥɚɫɶ ɡɚɞɚɱɚ ɨ Ʉɺɧɢɝɫɛɟɪɝɫɤɢɯ ɦɨɫɬɚɯ. ɗɣɥɟɪ ɩɨɤɚɡɚɥ, ɱɬɨ ɧɟɥɶɡɹ ɨɛɨɣɬɢ ɫɟɦɶ ɝɨɪɨɞɫɤɢɯ ɦɨɫɬɨɜ
ɢ ɜɟɪɧɭɬɶɫɹ ɜ ɢɫɯɨɞɧɭɸ ɬɨɱɤɭ, ɩɪɨɣɞɹ ɩɨ ɤɚɠɞɨɦɭ ɦɨɫɬɭ ɪɨɜɧɨ ɨɞɢɧ ɪɚɡ. Ⱦɨɥɝɨɟ ɜɪɟɦɹ ɷɬɨɬ ɪɟɡɭɥɶɬɚɬ ɨɫɬɚɜɚɥɫɹ ɟɞɢɧɫɬɜɟɧɧɵɦ ɪɟɡɭɥɶɬɚɬɨɦ ɬɟɨɪɢɢ ɝɪɚɮɨɜ.
ɋɥɟɞɭɸɳɢɣ ɢɦɩɭɥɶɫ ɬɟɨɪɢɹ ɝɪɚɮɨɜ ɩɨɥɭɱɢɥɚ ɬɨɥɶɤɨ ɜ ɫɟɪɟɞɢɧɟ XIX ɜɟɤɚ ɫ
ɪɚɡɜɢɬɢɟɦ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɨ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɫɟɬɹɦ, ɤɪɢɫɬɚɥɥɨɝɪɚɮɢɢ, ɨɪɝɚɧɢɱɟɫɤɨɣ ɯɢɦɢɢ ɢ ɞɪɭɝɢɦ ɧɚɭɤɚɦ.
ɋ ɝɪɚɮɚɦɢ, ɫɚɦɢ ɬɨɝɨ ɧɟ ɡɚɦɟɱɚɹ, ɦɵ ɫɬɚɥɤɢɜɚɟɦɫɹ ɩɨɫɬɨɹɧɧɨ.
Ɍɚɤ, ɝɪɚɮɨɦ ɹɜɥɹɟɬɫɹ ɫɯɟɦɚ ɥɢɧɢɣ ɦɟɬɪɨɩɨɥɢɬɟɧɚ. ɂɫɫɥɟɞɭɹ ɫɜɨɸ ɪɨɞɨɫɥɨɜɧɭɸ ɢ ɜɨɡɜɨɞɹ ɟɟ ɤ ɞɚɥɟɤɨɦɭ ɩɪɟɞɤɭ, ɦɵ ɫɬɪɨɢɦ ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɝɟɧɟɚɥɨɝɢɱɟɫɤɨɟ ɞɟɪɟɜɨ, ɤɨɬɨɪɨɟ ɬɚɤɠɟ ɹɜɥɹɟɬɫɹ ɝɪɚɮɨɦ.
Ɇɟɬɨɞɵ ɬɟɨɪɢɢ ɝɪɚɮɨɜ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɸɬɫɹ ɜ ɞɢɫɤɪɟɬɧɨɣ ɦɚɬɟɦɚɬɢɤɟ.
Ȼɟɡ ɧɢɯ ɧɟɜɨɡɦɨɠɧɨ ɨɛɨɣɬɢɫɶ ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɬɟɨɪɢɢ ɤɨɧɟɱɧɵɯ ɚɜɬɨɦɚɬɨɜ,
ɩɪɢ ɚɧɚɥɢɡɟ ɢ ɫɢɧɬɟɡɟ ɪɚɡɥɢɱɧɵɯ ɞɢɫɤɪɟɬɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɣ: ɮɭɧɤɰɢɨɧɚɥɶɧɵɯ ɛɥɨɤɨɜ ɤɨɦɩɶɸɬɟɪɨɜ, ɤɨɦɩɥɟɤɫɨɜ ɩɪɨɝɪɚɦɦ ɢ ɬ. ɞ. ɏɨɬɹ ɬɟɨɪɢɹ ɝɪɚɮɨɜ ɜɨɡɧɢɤɥɚ ɛɨɥɟɟ ɞɜɭɯɫɨɬ ɥɟɬ ɬɨɦɭ ɧɚɡɚɞ, ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɨɧɚ ɨɯɜɚɬɵɜɚɟɬ ɛɨɥɶɲɨɣ ɦɚɬɟɪɢɚɥ ɢ ɚɤɬɢɜɧɨ ɪɚɡɜɢɜɚɟɬɫɹ. ȼɫɥɟɞɫɬɜɢɟ ɷɬɨɝɨ ɬɟɪɦɢɧɨɥɨɝɢɹ ɜ ɬɟɨɪɢɢ
ɝɪɚɮɨɜ ɜɫɟ ɟɳɟ ɦɟɧɹɟɬɫɹ, ɜɨɡɧɢɤɚɸɬ ɧɨɜɵɟ ɩɨɧɹɬɢɹ ɢ ɦɟɬɨɞɵ.
Ƚɪɚɮɵ ɱɚɳɟ ɜɫɟɝɨ ɩɪɢɦɟɧɹɸɬɫɹ ɞɥɹ ɨɩɢɫɚɧɢɹ ɫɢɫɬɟɦɵ ɫɜɹɡɟɣ ɦɟɠɞɭ ɤɚɤɢɦɢ-ɥɢɛɨ ɨɛɴɟɤɬɚɦɢ, ɧɚɩɪɢɦɟɪ:
− ɫɟɬɢ ɚɜɬɨɦɨɛɢɥɶɧɵɯ ɞɨɪɨɝ;
− ɫɯɟɦɵ ɦɟɬɪɨ;
− ɤɨɦɩɶɸɬɟɪɧɵɟ ɫɟɬɢ;
− ɥɨɝɢɱɟɫɤɢɟ ɫɯɟɦɵ.
ɉɨɧɹɬɢɟ ɝɪɚɮɚ
Ƚɪɚɮ G – ɷɬɨ ɭɩɨɪɹɞɨɱɟɧɧɚɹ ɩɚɪɚ (V, E), ɝɞɟ V – ɧɟɩɭɫɬɨɟ ɦɧɨɠɟɫɬɜɨ
ɜɟɪɲɢɧ, E – ɦɧɨɠɟɫɬɜɨ ɩɚɪ ɷɥɟɦɟɧɬɨɜ ɦɧɨɠɟɫɬɜɚ V, ɧɚɡɵɜɚɟɦɨɟ ɦɧɨɠɟɫɬɜɨɦ
ɪɟɛɟɪ (ɞɭɝ) [2].
ɍɩɨɪɹɞɨɱɟɧɧɚɹ ɩɚɪɚ ɷɥɟɦɟɧɬɨɜ ɢɡ V ɧɚɡɵɜɚɟɬɫɹ ɞɭɝɨɣ. ȿɫɥɢ ɜɫɟ ɩɚɪɵ ɜ ȿ
ɭɩɨɪɹɞɨɱɟɧɵ, ɬɨ ɝɪɚɮ
ȿɫɥɢ ɞɭɝɚ E ɜɟɞɟɬ ɨɬ ɜɟɪɲɢɧɵ V
ɢɧɰɢɞɟɧɬɧɚ ɜɟɪɲɢɧɟ V
ɧɚɡɵɜɚɟɬɫɹ ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɦ (ɨɪɝɪɚɮɨɦ).
ɤ ɜɟɪɲɢɧɟ V2, ɬɨ ɝɨɜɨɪɹɬ, ɱɬɨ ɞɭɝɚ E
1
, ɚ ɜɟɪɲɢɧɚ V2 ɹɜɥɹɸɬɫɹ ɫɦɟɠɧɨɣ ɜɟɪɲɢɧɟ V1. ɉɪɢ
2
ɧɟɨɪɢɟɧɬɢɪɨɜɚɧɧɨɦ ɝɪɚɮɟ ɪɟɛɪɨ E ɹɜɥɹɟɬɫɹ ɢɧɰɢɞɟɧɬɧɨɣ ɨɛɟɢɦ ɜɟɪɲɢɧɚɦ V
ɢ V
, ɚ ɫɚɦɢ ɜɟɪɲɢɧɵ – ɜɡɚɢɦɧɨ ɫɦɟɠɧɵɦɢ.
2
ɉɭɬɶ – ɷɬɨ ɥɸɛɚɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜɟɪɲɢɧ ɨɪɝɪɚɮɚ ɬɚɤɚɹ, ɱɬɨ ɜ ɷɬɨɣ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɜɟɪɲɢɧɚ b ɦɨɠɟɬ ɫɥɟɞɨɜɚɬɶ ɡɚ ɜɟɪɲɢɧɨɣ a, ɬɨɥɶɤɨ ɟɫɥɢ
ɫɭɳɟɫɬɜɭɟɬ ɞɭɝɚ, ɫɥɟɞɭɸɳɚɹ ɢɡ a ɜ b. Ⱥɧɚɥɨɝɢɱɧɨ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɭɬɶ, ɫɨɫɬɨɹɳɢɣ ɢɡ ɞɭɝ.
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ɉɭɬɶ, ɧɚɱɢɧɚɸɳɢɣɫɹ ɢ ɡɚɤɚɧɱɢɜɚɸɳɢɣɫɹ ɜ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɜɟɪɲɢɧɟ,
ɧɚɡɵɜɚɟɬɫɹ ɰɢɤɥɨɦ. Ƚɪɚɮ, ɜ ɤɨɬɨɪɨɦ ɨɬɫɭɬɫɬɜɭɸɬ ɰɢɤɥɵ, ɧɚɡɵɜɚɟɬɫɹ ɚɰɢɤɥɢɱɟɫɤɢɦ.
ɉɟɬɥɹ – ɞɭɝɚ, ɫɨɟɞɢɧɹɸɳɚɹ ɧɟɤɨɬɨɪɭɸ ɜɟɪɲɢɧɭ ɫɚɦɚ ɫ ɫɨɛɨɣ.
Ɍɟɨɪɢɹ ɝɪɚɮɨɜ ɹɜɥɹɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɨɣ ɱɚɫɬɶɸ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɦɚɬɟɦɚɬɢɤɢ. ɋ ɩɨɦɨɳɶɸ ɷɬɨɣ ɬɟɨɪɢɢ ɪɟɲɚɸɬɫɹ ɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɡɚɞɚɱ ɢɡ ɪɚɡɥɢɱɧɵɯ
ɨɛɥɚɫɬɟɣ. Ƚɪɚɮ ɫɨɫɬɨɢɬ ɢɡ
ɦɧɨɠɟɫɬɜɚ ɜɟɪɲɢɧ ɢ ɦɧɨɠɟɫɬɜɚ ɪɟɛɟɪ, ɤɨɬɨɪɵɟ ɫɨɟɞɢɧɹɸɬ ɦɟɠɞɭ ɫɨɛɨɣ ɜɟɪɲɢɧɵ. ɋ ɬɨɱɤɢ ɡɪɟɧɢɹ ɬɟɨɪɢɢ ɝɪɚɮɨɜ ɧɟ ɢɦɟɟɬ ɡɧɚɱɟɧɢɹ, ɤɚɤɨɣ ɫɦɵɫɥ ɜɤɥɚɞɵɜɚɟɬɫɹ ɜ ɜɟɪɲɢɧɵ ɢ ɪɟɛɪɚ. ȼɟɪɲɢɧɚɦɢ ɦɨɝɭɬ ɛɵɬɶ
ɧɚɫɟɥɟɧɧɵɟ ɩɭɧɤɬɵ, ɚ ɪɟɛɪɚɦɢ ɞɨɪɨɝɢ, ɫɨɟɞɢɧɹɸɳɢɟ ɢɯ, ɢɥɢ ɜɟɪɲɢɧɚɦɢ ɹɜɥɹɬɶɫɹ ɩɨɞɩɪɨɝɪɚɦɦɵ, ɚ ɫɨɟɞɢɧɟɧɢɟ ɜɟɪɲɢɧ ɪɟɛɪɚɦɢ ɨɡɧɚɱɚɟɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ
ɩɨɞɩɪɨɝɪɚɦɦ. ɑɚɫɬɨ
ɢɦɟɟɬ ɡɧɚɱɟɧɢɟ ɧɚɩɪɚɜɥɟɧɢɟ ɞɭɝɢ ɜ ɝɪɚɮɟ.
Ɋɟɚɥɢɡɚɰɢɹ ɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ
ȼɵɛɨɪ ɫɬɪɭɤɬɭɪɵ ɞɚɧɧɵɯ ɞɥɹ ɯɪɚɧɟɧɢɹ ɝɪɚɮɚ ɜ ɩɚɦɹɬɢ ɢɦɟɟɬ ɩɪɢɧɰɢɩɢɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɪɢ ɪɚɡɪɚɛɨɬɤɟ ɷɮɮɟɤɬɢɜɧɵɯ ɚɥɝɨɪɢɬɦɨɜ. Ɋɚɫɫɦɨɬɪɢɦ ɞɜɚ
ɦɚɬɪɢɱɧɵɯ ɢ ɬɪɢ ɫɩɢɫɨɱɧɵɯ ɫɩɨɫɨɛɚ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɝɪɚɮɚ:
− ɦɚɬɪɢɰɚ ɫɦɟɠɧɨɫɬɢ;
− ɦɚɬɪɢɰɚ ɢɧɰɢɞɟɧɬɧɨɫɬɢ;
− ɫɩɢɫɤɢ ɫɦɟɠɧɵɯ;
− ɫɩɢɫɨɤ ɪɟɛɟɪ;
− ɫɩɢɫɤɢ ɜɟɪɲɢɧ ɢ
ɪɟɛɟɪ.
ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɢɡɥɨɠɟɧɢɢ ɪɚɫɫɦɨɬɪɢɦ ɝɪɚɮ (ɪɢɫ. 8), ɛɭɞɟɦ ɩɪɟɞɩɨɥɚɝɚɬɶ, ɱɬɨ ɜɟɪɲɢɧɵ ɝɪɚɮɚ ɨɛɨɡɧɚɱɟɧɵ ɫɢɦɜɨɥɶɧɨɣ ɫɬɪɨɤɨɣ ɢ ɜɫɟɝɨ ɢɯ n, ɚ ɪɟɛɟɪ
m. Ʉɚɠɞɨɦɭ ɪɟɛɪɭ ɢ ɤɚɠɞɨɣ ɜɟɪɲɢɧɟ ɫɨɩɨɫɬɚɜɥɟɧ ɜɟɫ – ɰɟɥɨɟ ɩɨɥɨɠɢɬɟɥɶɧɨɟ
ɱɢɫɥɨ. ȿɫɥɢ ɝɪɚɮ ɧɟ ɹɜɥɹɟɬɫɹ ɩɨɦɟɱɟɧɧɵɦ, ɬɨ ɫɱɢɬɚɟɬɫɹ, ɱɬɨ ɜɟɫ ɪɚɜɟɧ ɟɞɢɧɢɰɟ.
Ɋɢɫ. 8. ɂɫɯɨɞɧɵɣ ɝɪɚɮ
Ɇɚɬɪɢɰɚ ɫɦɟɠɧɨɫɬɢ ɷɬɨ ɞɜɭɦɟɪɧɵɣ ɦɚɫɫɢɜ ɪɚɡɦɟɪɨɦ n ɯ n, ɡɧɚɱɟɧɢɹ
ɷɥɟɦɟɧɬɨɜ ɤɨɬɨɪɨɝɨ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɫɦɟɠɧɨɫɬɶɸ ɜɟɪɲɢɧ ɝɪɚɮɚ. Ɂɧɚɱɟɧɢɸ
ɷɥɟɦɟɧɬɨɜ ɦɚɬɪɢɰɵ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɱɢɫɥɨ ɪɟɛɟɪ (ɜɟɫ), ɤɨɬɨɪɵɟ ɫɨɟɞɢɧɹɸɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɟɪɲɢɧɵ.
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