Лекции 1-4 (2 семестр)

ɉɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ ɬɢɩɨɜɵɯ ɚɥɝɨɪɢɬɦɨɜ

ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɰɢɤɥɚ

ȼɵɱɢɫɥɟɧɢɟ ɫɭɦɦɵ ɡɧɚɱɟɧɢɣ ɧɟɤɨɬɨɪɨɣ ɮɭɧɤɰɢɢ ɭ f(x) ɫɜɨɞɢɬɫɹ ɤ ɟɟ ɧɚɤɨɩɥɟɧɢɸ ɜ ɰɢɤɥɟ ɜ ɜɢɞɟ ɡɧɚɱɟɧɢɹ ɩɟɪɟɦɟɧɧɨɣ:

ɉɪɢ ɤɚɠɞɨɣ ɢɬɟɪɚɰɢɢ ɡɧɚɱɟɧɢɟ S ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɧɚ ɨɱɟɪɟɞɧɨɣ ɱɥɟɧ ɫɭɦɦɵ ɉɪɢ ɷɬɨɦ ɜɧɨɜɶ ɧɚɣɞɟɧɧɨɟ ɫɥɚɝɚɟɦɨɟ ɩɪɢɛɚɜɥɹɟɬɫɹ ɤ ɫɭɦɦɟ ɜɫɟɯ ɩɪɟɞɵɞɭɳɢɯ, ɬɟ ɜ ɰɢɤɥɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɵɱɢɫɥɹɸɬɫɹ ɜɫɟ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɫɭɦɦɵ

S1 = S0+y1 = y1 S2 = S1+y2 =y1+y2

S3 = S2+y3 = y1+y2+y3

Ɏɨɪɦɭɥɚ ɞɥɹ ɧɚɤɨɩɥɟɧɢɹ ɫɭɦɦɵ

Ɍɚɤ, ɧɚɞɨɛɧɨɫɬɢ ɯɪɚɧɢɬɶɬ ɜ ɩɚɦɹɬɢ ɗȼɆ ɜɫɟ ɫɥɚɝɚɟɦɵɟ ɢ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɫɭɦɦɵ ɬɨ ɢɯ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɩɪɨɫɬɵɦɢ ɩɟɪɟɦɟɧɧɵɦɢ ɚ ɧɟ ɩɟɪɟɦɟɧɧɵɦɢ ɫ ɢɧɞɟɤɫɚɦɢ

ɇɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɫɭɦɦɦɵɵ ɡɚɞɚɟɬɫɹ ɩɟɪɟɞ ɰɢɤɥɨɦ ɪɚɜɧɵɦ ɧɭɥɸ:

ɉɪɨɢɡɜɟɞɟɧɢɟ ɜɵɱɢɫɥɹɟɬɫɹ ɚɧɚɥɨɝɢɱɧɨ ɫɭɦɦɟ ɩɨ ɮɨɪɦɭɥɟ

- ɮɨɪɦɭɥɚ ɞɥɹ ɧɚɤɨɩɥɟɧɢɹ ɩɪɨɢɡɜɟɞɟɧɢɹɡ

ɇɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɪɨɢɡɜɟɞɟɧɢɹ ɡɚɞɚɟɬɫɹ ɞɨ ɰɢɤɥɚ ɪɚɜɧɵɦ

ɋɭɳɟɫɬɜɭɟɬ ɞɜɚ ɬɢɩɚ ɡɚɞɚɱ:

ɑɢɫɥɨ ɱɥɟɧɨɜ ɪɹɞɚ ɢɡɜɟɫɬɧɨ, ɢɫɩɨɥɶɡɭɟɬɫɹ ɰɢɤɥ ɫ ɩɚɪɚɦɟɬɪɨɦ;

ɑɢɫɥɨ ɱɥɟɧɨɜ ɪɹɞɚ ɡɚɪɚɧɟɟ ɧɟ ɡɚɞɚɧɨ, ɚ ɡɚɞɚɧɚ ɬɨɱɧɨɫɬɶ ɜɵɱɢɫɥɟɧɢɹ ɤɚɠɞɨɝɨ ɱɥɟɧɚ ɪɹɞɚ ȿ, ɝɞɟ ȿ – ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɱɢɫɥɨ.

Ɂɚɞɚɱɢ ɜɬɨɪɨɝɨ ɬɢɩɚ ɹɜɥɹɸɬɫɹ ɬɢɩɢɱɧɵɦɢ ɡɚɞɚɱɚɦɢ, ɢɫɩɨɥɶɡɭɸɳɢɦɢ ɢɬɟɪɚɰɢɨɧɧɵɣ ɩɪɨɰɟɫɫ ɫ ɧɟɢɡɜɟɫɬɧɵɦ ɱɢɫɥɨɦ ɩɨɜɬɨɪɟɧɢɣ, ɬ.ɤ. ɡɚɪɚɧɟɟ ɧɟ ɢɡɜɟɫɬɧɨ ɩɪɢ ɤɚɤɨɦ ɱɥɟɧɟ ɪɹɞɚ ɛɭɞɟɬ ɞɨɫɬɢɝɧɭɬ ɬɪɟɛɭɟɦɚɹ ɬɨɱɧɨɫɬɶ.

ȼɵɯɨɞ ɢɡ ɰɢɤɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ _ɭ_ȿ, ɝɞɟ ɭ – ɡɧɚɱɟɧɢɟ ɬɟɤɭɳɟɝɨ ɱɥɟɧɚ ɪɹɞɚ

ȼɵɱɢɫɥɟɧɢɟ ɫɭɦɦɵ ɱɥɟɧɨɜ ɪɹɞɚ ɨɪɝɚɧɢɡɭɟɬɫɹ ɬɚɤɠɟ ɤɚɤ ɜɵɱɢɫɥɟɧɢɟ ɫɭɦɦɵ ɡɧɚɱɟɧɢɣ ɮɭɧɤɰɢɢ

ɋɨɫɬɚɜɢɬɶ ɩɪɨɝɪɚɦɦɭ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɫɭɦɦɵ ɛɟɫɤɨɧɟɱɧɨɝɨ ɪɹɞɚ:

Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɧɚɢɛɨɥɶɲɟɝɨ ɢɥɢ ɧɚɢɦɟɧɶɲɟɝɨ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɭ f(ɯ) ɧɟɨɛɯɨɞɢɦɨ ɨɪɝɚɧɢɡɨɜɚɬɶ ɰɢɤɥ, ɜ ɤɨɬɨɪɨɦ ɜɵɱɢɫɥɹɟɬɫɹ ɬɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢɩɪɢ ɪɚɡɥɢɱɧɵɯ ɯ ɢ ɫɪɚɜɧɢɜɚɟɬɫɹ ɫ ɧɚɢɛɨɥɶɲɟɦ ɢɥɢ ɧɚɢɦɟɧɶɲɢɦ ɢɡ ɜɫɟɯ ɩɪɟɞɵɞɭɳɢɯ ɡɧɚɱɟɧɢɣ ɮɭɧɤɰɢɣ.

ȿɫɥɢ ɬɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ ɛɭɞɟɬ ɧɚɩɪɢɦɟɪ ɛɨɥɶɲɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɢɡ ɩɪɟɞɵɞɭɳɢɯ ɬɨ ɨɧɨ ɫɱɢɬɚɟɬɫɹ ɧɨɜɵɦ ɦɚɤɫɢɦɭɦɨɦ, ɢɧɚɱɟ ɦɚɤɫɢɦɭɦ ɨɫɬɚɟɬɫɹ ɛɟɡ ɢɡɦɟɧɟɧɢɣ.

Ⱥɥɝɨɪɢɬɦ

Ɂɚɞɚɟɬɫɹ ɧɚɱɚɥɶɧɨɟ ɧɚɢɛɨɥɶɲɟɟ ɡɧɚɱɟɧɢɟ

ymax;

ȼɵɱɢɫɥɹɟɬɫɹ y1 = f(x1) ɢ ɫɪɚɜɧɢɜɚɟɬɫɹ ɫ ymax. ȿɫɥɢɷɬɚɩ; y1 > ymax, ɬɨ ymax = y1, ɢɧɚɱɟ ɫɥɟɞɭɸɳɢɣ

ȼɵɱɢɫɥɟɧɢɟ y2 = f(x2) ɢ ɟɫɥɢ y2 > ymax, ɬɨ ymax = y2, ɢɧɚɱɟ ɫɥɟɞɭɸɳɢɣ ɷɬɚɩ ɢ ɬɞ

Ɉɛɳɚɹ ɮɨɪɦɭɥɚ ɧɚɯɨɠɞɟɧɢɹ ɧɚɢɛɨɥɶɲɟɝɨ ɢ ɧɚɢɦɟɧɶɲɟɝɨ ɡɧɚɱɟɧɢɣ

ɹɞ ɜɵɩɨɥɧɢɥɨɫɶ ɭɫɥɨɜɢɟ y1>ymax. ymin ɡɚɞɚɟɬɫɹ ɩɨɪɹɞɤɚ 1010, ɱɬɨɛɵ ɜɵɩɨɥɧɢɥɨɫɶ ɭɫɥɨɜɢɟ y1< ymin.

ɉɪɢ ɧɚɯɨɠɞɟɧɢɢ max ɢ min ɪɟɱɶ ɢɞɟɬ ɧɟ ɨ ɦɚɤɫɢɦɭɦɟ ɢɥɢ ɦɢɧɢɦɭɦɟ ɮɭɧɤɰɢɢ ɚ ɨ ɧɚɢɛɨɥɶɲɟɦ ɢɥɢ ɧɚɢɦɟɧɶɲɟɦ ɢɡ ɜɵɱɢɫɥɟɧɧɵɯ ɡɧɚɱɟɧɢɣ

ȀȖȝȩ ȒȎțțȩȣ

Ɍɢɩ ɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ – ɷɬɨ ɦɧɨɠɟɫɬɜɨ ɞɥɹ ɤɨɬɨɪɨɝɨ ɨɝɨɜɨɪɟɧ ɧɟɤɨɬɨɪɵɯ ɧɚɛɨɪ ɨɩɟɪɚɰɢɣ ɧɚɞ ɷɥɟɦɟɧɬɚɦɢ ɋɚɦɢ ɷɥɟɦɟɧɬɵ ɦɧɨɠɟɫɬɜɚ ɧɚɡɵɜɚɸɬɫɹ ɨɛɴɟɤɬɚɦɢ ɢɥɢ ɡɧɚɱɟɧɢɹɦɢ ɞɚɧɧɨɝɨ ɬɢɩɚ

Ɍɢɩɵ real ɢ integer – ɷɬɨ ɱɢɫɥɨɜɵɟ ɦɧɨɠɟɫɬɜɚ ȼɦɟɫɬɟ ɫ ɧɢɦɢ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɚɪɢɮɦɟɬɢɱɟɫɤɢɟ ɨɩɟɪɚɰɢɢ ɢ ɨɩɟɪɚɰɢɢ ɫɪɚɜɧɟɧɢɹ

Ɍɢɩ char – ɷɬɨ ɦɧɨɠɟɫɬɜɨ ɫɢɦɜɨɥɨɜ ɜɦɟɫɬɟ ɫ ɧɢɦ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɨɩɟɪɚɰɢɢ ɫɪɚɜɧɟɧɢɹ

ɗɬɢ ɬɪɢ ɬɢɩɚ ɹɜɥɹɸɬɫɹ ɫɬɚɧɞɚɪɬɧɵɦɢ ɬɢɩɚɦɢ ɉɚɫɤɚɥɹ

ȼ ɉɚɫɤɚɥɟ ɢɦɟɸɬɫɹ ɫɪɟɞɫɬɜɚ, ɩɨɡɜɨɥɹɸɳɢɟ ɨɩɪɟɞɟɥɹɬɶ, ɢɫɯɨɞɹ ɢɡ ɢɦɟɸɳɢɯɫɹ ɬɢɩɨɜ, ɧɨɜɵɟ ɧɟɫɬɚɧɞɚɪɬɧɵɟ ɬɢɩɵ, ɧɚɡɵɜɚɟɦɵɟ ɫɬɪɭɤɬɭɪɢɪɨɜɚɧɧɵɦɢ ɬɢɩɚɦɢ ɞɚɧɧɵɯ

ȼ ɹɡɵɤɟ ɉɚɫɤɚɥɶ ɫɭɳɟɫɬɜɭɸɬ ɫɥɟɞɭɸɳɢɟ ɫɬɪɭɤɬɭɪɢɪɨɜɚɧɧɵɟ ɬɢɩɵ:

ɬɢɩ-ɦɚɫɫɢɜ;

ɬɢɩ-ɡɚɩɢɫɶ;

ɬɢɩ-ɦɧɨɠɟɫɬɜɨ;

ɬɢɩ-ɮɚɣɥ .

ȼ ɉɚɫɤɚɥɟ ɢɦɟɟɬɫɹ ɟɳɟ ɞɜɚ ɫɬɪɭɤɬɭɪɢɪɨɜɚɧɧɵɯ ɬɢɩɚ – ɬɢɩɫɬɪɨɤɚ String ɢ ɬɢɩ-ɫɬɪɨɤɚ PChar, ɤɨɬɨɪɵɟ ɹɜɥɹɸɬɫɹ ɪɚɡɧɨɜɢɞɧɨɫɬɹɦɢ ɦɚɫɫɢɜɚ

Ɍɢɩ-ɦɚɫɫɢɜ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɮɢɤɫɢɪɨɜɚɧɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɭɩɨɪɹɞɨɱɟɧɧɵɯ ɨɞɧɨɬɢɩɧɵɯ ɤɨɦɩɨɧɟɧɬɨɜ, ɫɧɚɛɠɟɧɧɵɯ ɢɧɞɟɤɫɚɦɢ

ɍɩɨɪɹɞɨɱɟɧɧɨɫɬɶ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɷɥɟɦɟɧɬɵ ɦɚɫɫɢɜɚ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɹɱɟɣɤɚɯ ɩɚɦɹɬɢ əɱɟɣɤɚ – ɷɬɨ ɷɥɟɦɟɧɬ ɦɚɫɫɢɜɚ, ɚ ɧɨɦɟɪ ɹɱɟɣɤɢ – ɷɬɨ ɢɧɞɟɤɫ ɷɥɟɦɟɧɬɚ ɦɚɫɫɢɜɚ

A 1 4

2

9

3

3

4

5

5

7

6

1

Ɇɚɫɫɢɜ ɦɨɠɟɬ ɛɵɬɶ ɨɞɧɨɦɟɪɧɵɦ ɢ ɦɧɨɝɨɦɟɪɧɵɦ

ɑɬɨɛɵ ɩɨɥɭɱɢɬɶ ɞɨɫɬɭɩ ɤ ɧɭɠɧɨɣ ɹɱɟɣɤɟ, ɧɟɨɛɯɨɞɢɦɨ ɭɤɚɡɚɬɶ ɢɦɹ ɦɚɫɫɢɜɚ ɢ ɧɨɦɟɪ ɷɬɨɣ ɹɱɟɣɤɢ – ɢɧɞɟɤɫ ɦɚɫɫɢɜɚ, ɤɨɬɨɪɵɣ

ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɤɜɚɞɪɚɬɧɵɯ ɫɤɨɛɤɚɯ ɩɨɫɥɟ ɢɦɟɧɢ ɦɚɫɫɢɜɚ Ⱥ> @.

ɂɦɹ ɦɚɫɫɢɜɚ ɨɛɪɚɡɭɟɬɫɹ ɬɚɤ ɠɟ, ɤɚɤ ɢ ɢɦɹ ɩɪɨɫɬɨɣ ɩɟɪɟɦɟɧɧɨɣ Ɉɩɢɫɚɧɢɟ ɦɚɫɫɢɜɚ

VAR A: ARRAY [N1..M1] OF T; - ȜȒțȜȚȓȞțȩȗ;

VAR B: ARRAY [N1..M1, N2..M2] OF T; – ȒȐȡȚȓȞțȩȗ;

VAR C: ARRAY [N1..M1, N2..M2,N3..M3] OF T; – ɬɪɟɯȚȓȞțȩȗ.

Ɂɞɟɫɶ:

Ⱥ, ȼ, C – ɢɦɹ ɦɚɫɫɢɜɚ;

N1, N2, N3, M1, M2, M3 – ɧɢɠɧɢɣ ɢ ɜɟɪɯɧɢɣ ɩɪɟɞɟɥɵ ɢɡɦɟɧɟɧɢɹ ɢɧɞɟɤɫɨɜ ɦɚɫɫɢɜɚ;

Ɍ – ɬɢɩ ɦɚɫɫɢɜɚ.

ȼ ɞɜɭɦɟɪɧɨɦ ɦɚɫɫɢɜɟ ɩɨɥɨɠɟɧɢɟ ɤɚɠɞɨɝɨ ɷɥɟɦɟɧɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɜɭɦɹ ɢɧɞɟɤɫɚɦɢ ɪɚɡɞɟɥɟɧɧɵɦɢ ɡɚɩɹɬɨɣ ɝɞɟ ɩɟɪɜɵɣ ɢɧɞɟɤɫ – ɷɬɨ ɧɨɦɟɪ

ɫɬɪɨɤɢ ɜɬɨɪɨɣ – ɧɨɦɟɪ ɫɬɨɥɛɰɚ B[1,2] ȼ ɬɪɟɯɦɟɪɧɨɦ ɦɚɫɫɢɜɟ -

C[1,2,3]

ɉɪɟɞɟɥɵ ɢɡɦɟɧɟɧɢɹ ɢɧɞɟɤɫɨɜ ɦɚɫɫɢɜɚ ɦɨɠɧɨ ɡɚɞɚɜɚɬɶ ɜ ɨɩɢɫɚɧɢɢ ɤɨɧɫɬɚɧɬɚɦɢ ɰɟɥɨɝɨ ɬɢɩɚ ɢɥɢ ɱɟɪɟɡ ɢɦɟɧɚ ɤɨɧɫɬɚɧɬ

Var A: array [1..50] of real;

Const N=50; Var A: array [1..N] of real;

Ɋɚɡɦɟɪɧɨɫɬɶ ɦɚɫɫɢɜɚ ɦɨɠɟɬ ɛɵɬɶ ɥɸɛɨɣ, ɷɥɟɦɟɧɬɵ ɦɚɫɫɢɜɚ ɦɨɝɭɬ ɛɵɬɶ ɥɸɛɨɝɨ ɬɢɩɚ

Ɉɞɧɨɦɭ ɦɚɫɫɢɜɭ ɦɨɠɧɨ ɩɪɢɫɜɨɢɬɶ ɡɧɚɱɟɧɢɟ ɞɪɭɝɨɝɨ ɦɚɫɫɢɜɚ, ɧɨ ɬɨɥɶɤɨ ɢɞɟɧɬɢɱɧɨɝɨ ɬɢɩɚ ɇɚɩɪɢɦɟɪ ɡɚɞɚɧɵ ɦɚɫɫɢɜɵ

Var A, B: array [1..5] of integer; C: array [1..5] of integer;

ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɞɨɩɭɫɬɢɦ ɫɥɟɞɭɸɳɢɣ ɨɩɟɪɚɬɨɪ: Ⱥ ȼ; ɫ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, ɨɩɟɪɚɬɨɪ ɋ Ⱥ; ɧɟɞɨɩɭɫɬɢɦ, ɬɚɤ ɤɚɤ ɦɚɫɫɢɜɵ Ⱥ ɢ ɋ ɧɟ ɢɞɟɧɬɢɱɧɵɯ ɬɢɩɨɜ, ɯɨɬɹ ɨɧɢ ɢ ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɭɸ ɫɬɪɭɤɬɭɪɭ, ɫɨɞɟɪɠɚɬ ɪɚɡɧɵɟ ɷɥɟɦɟɧɬɵ

Ɉɩɢɫɚɧɢɟ ɦɚɫɫɢɜɚ ɤɚɤ ɫɬɪɭɤɬɭɪɢɪɨɜɚɧɧɨɝɨ ɬɢɩɚ ɞɚɧɧɵɯ

Const N=50;

Type MAS: ARRAY [1..N] of real; Var A,B: MAS;

ȼɜɨɞɢɬɶ ɢ ɜɵɜɨɞɢɬɶ ɦɚɫɫɢɜɵ ɦɨɠɧɨ ɬɨɥɶɤɨ ɩɨɷɥɟɦɟɧɬɧɨ, ɩɨɷɬɨɦɭ ɞɥɹ ɷɬɨɝɨ ɧɭɠɧɨ ɫɨɫɬɚɜɢɬɶ ɩɪɨɝɪɚɦɦɭ, ɨɛɟɫɩɟɱɢɜɚɸɳɭɸ ɢɡɦɟɧɟɧɢɟ ɟɝɨ ɢɧɞɟɤɫɨɜ ɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ ɡɚɩɨɥɧɟɧɢɟ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ ɞɚɧɧɵɦɢ

ɫ ɤɥɚɜɢɚɬɭɪɵ

Writeln (’vvedite elemeti Ⱥ’); FOR I: = 1 to N do

Read(A[I]); ɢɥɢ readln(a[i]);

1<ɩɪɨɛɟɥ>2<ɩɪɨɛɟɥ>3<Enter>

ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɞɚɬɱɢɤɚ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ

For I:= 1 to N do

A [I]:=Random; - ɷɥɟɦɟɧɬɵ ɦɚɫɫɢɜɚ ɱɢɫɥɚɦɢ Ai ȯ (0;1)

For I: = 1 to N do

A [I]: = Random(x); - ɷɥɟɦɟɧɬɵ ɦɚɫɫɢɜɚ ɛɭɞɭɬ ɱɢɫɥɚɦɢ Ai ȯ (0; x-1).

Ȑ ȟȠȜșȏȓȤ:

For I: = 1 to N do

Writeln(A[I]); ȖșȖ Writeln(‘A[‘,I,’]=‘,A[I]);

1 A[1]=1

Ȑ ȟȠȞȜȘȡ:

For I: = 1 to N do Write(A [I],‘’:2);

1<ǽȞȜȏȓș><ǽȞȜȏȓș>2<ǸȡȞȟȜȞ>

ȼɜɨɞ ɦɚɬɪɢɰɵ ɦɨɠɧɨ ɨɫɭɳɟɫɬɜɥɹɬɶ ɩɨ ɫɬɪɨɤɚɦ ɢɥɢ ɩɨ ɫɬɨɥɛɰɚɦ, ɬɨ ɟɫɬɶ ɡɞɟɫɶ ɧɟɨɛɯɨɞɢɦɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɥɨɠɟɧɧɵɟ ɰɢɤɥɵ

ȼ ɰɢɤɥ, ɧɚɡɵɜɚɟɦɵɣ ɜɧɟɲɧɢɦ, ɦɨɝɭɬ ɜɯɨɞɢɬɶ ɨɞɢɧ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɰɢɤɥɨɜ, ɧɚɡɵɜɚɟɦɵɯ ɜɧɭɬɪɟɧɧɢɦɢ

Ɉɪɝɚɧɢɡɚɰɢɹ ɤɚɤ ɜɧɟɲɧɟɝɨ, ɬɚɤ ɢ ɜɧɭɬɪɟɧɧɟɝɨ ɰɢɤɥɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɨ ɬɟɦ ɠɟ ɩɪɚɜɢɥɚɦ, ɱɬɨ ɢ ɩɪɨɫɬɨɝɨ ɰɢɤɥɚ, ɧɨ ɩɚɪɚɦɟɬɪɵ ɜɧɟɲɧɟɝɨ ɢ ɜɧɭɬɪɟɧɧɟɝɨ ɰɢɤɥɨɜ ɪɚɡɧɵɟ ɢ ɢɡɦɟɧɹɸɬɫɹ ɧɟ ɨɞɧɨɜɪɟɦɟɧɧɨ, ɬɨ ɟɫɬɶ ɩɪɢ ɨɞɧɨɦ ɢɡɦɟɧɟɧɢɢ ɩɚɪɚɦɟɬɪɚ ɜɧɟɲɧɟɝɨ ɰɢɤɥɚ, ɩɚɪɚɦɟɬɪ ɜɧɭɬɪɟɧɧɟɝɨ ɰɢɤɥɚ ɩɪɢɧɢɦɚɟɬ ɩɨɨɱɟɪɟɞɧɨ ɜɫɟ ɫɜɨɢ ɡɧɚɱɟɧɢɹ

ɂɫɯɨɞɹ ɢɡ ɷɬɨɝɨ, ɞɥɹ ɜɜɨɞɚ ɦɚɬɪɢɰɵ ɧɟɨɛɯɨɞɢɦɨ ɨɪɝɚɧɢɡɨɜɚɬɶ ɜɧɟɲɧɢɣ ɰɢɤɥ ɩɨ ɧɨɦɟɪɭ ɫɬɪɨɤɢ ɢ ɜɧɭɬɪɟɧɧɢɣ – ɩɨ ɧɨɦɟɪɭ ɫɬɨɥɛɰɚ

Ⱦɨɩɭɫɬɢɦɵɟ ɜɥɨɠɟɧɧɵɟ ɰɢɤɥɵ

							ȼ
	ȼ	ȼ	ȼ		ȼɧ	ȼɧ	ɧ
ȼ	ɧ	ɧ	ɧ	ȼ	ɭɬ	ɭɬ	ɟ	ȼ
ɧ	ɭ	ɭ	ɭ	ɧ	ɪɟ	ɪɟ	ɲ	ɧ
ɟ	ɬ	ɬ	ɬ	ɟ	ɧɧ	ɧɧ	ɧ	ɭ
ɲ	ɪ	ɪ	ɪ	ɲ	ɢɣ	ɢɣ	ɢ	ɬ
ɧ	ɟ	ɟ	ɟ	ɧ			ɣ	ɪ
	ɧ	ɧ	ɧ					ɟ
ɢ				ɢ
	ɧ	ɧ	ɧ					ɧ
ɣ				ɣ
	ɢ	ɢ	ɢ		ȼɧɭ			ɧ
	ɣ	ɣ	ɣ		ɬɪɟɧ			ɢ
					ɧɢɣ			ɣ

ȼɜɨɞ ɫ ɤɥɚɜɢɚɬɭɪɵ

Writeln(‘Vvedite elementi matrix A(N*M)’) For I:= 1 to N do

For J:= 1 to M do

Read(A [I, J]); ɢɥɢ ReadLn(A [I, J]);

ȼɜɨɞ ɫ ɩɨɦɨɳɶɸ ɞɚɬɱɢɤɚ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ

For I:= 1 to N do For J:= 1 to M do

A [I, J]):=Random; ɢɥɢ A [I, J]: = Random(x);

ȼ ɜɢɞɟ ɦɚɬɪɢɰɵ

For I: = 1 to N do

Begin

For J: = 1 to M do

Write (A [I, J], ’’: 2); Writeln;

End;

ȼ ɫɬɨɥɛɟɰ
For I:= 1 to N do
For J:= 1 to M do
Writeln(A [I, J]);	ɢɥɢ Writeln(‘A[‘,I,’,’,J,’]=‘,A[I, J]);
1	A[1,1]=1

1

I=1..N

J=1..M

A[I, J]

2

ɉɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ ɬɢɩɨɜɵɯ ɚɥɝɨɪɢɬɦɨɜ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɨɞɧɨɦɟɪɧɵɯ ɦɚɫɫɢɜɨɜ

ɮɪɚɝɦɟɧɬɵ ɩɪɨɝɪɚɦɦ

Ⱦɚɧɵ ɞɜɚ ɨɞɧɨɦɟɪɧɵɯ ɦɚɫɫɢɜɚ Ⱥ ɢ ȼ ɨɞɢɧɚɤɨɜɨɣ ɪɚɡɦɟɪɧɨɫɬɢ N

ɧɟɨɛɯɨɞɢɦɨ ɩɨɥɭɱɢɬɶ ɬɪɟɬɢɣ ɦɚɫɫɢɜ , ɤɚɠɞɵɣ ɷɥɟɦɟɧɬ ɤɨɬɨɪɨɝɨ ɜɵɱɢɫɥɹɟɬɫɹɫɹ ɩɨ ɮɨɪɦɭɥɟ

For i:=1 to N do

C[i]:=a[i]+b[i]; ɢɥɢC[i]:=a[i]*b[i];

Ɍɪɟɛɭɟɬɫɹ ɭɞɚɥɢɬɶ k-ɵɣ ɷɥɟɦɟɧɬ ɢɡ ɨɞɧɨɦɟɪɧɨɝɨ ɦɚɫɫɢɜɚ

ɥɢ ɚ k-ɨɣ ɩɨɡɢɰɢɢ, ɦɨɠɧɨ ɫɞɜɢɧɭɜ ɜɟɫɶ ©ɯɜɨɫɬª ɦɚɫɫɢɜɚ, ɧɚɱɢɧɚɹ ɫ k+1 ɷɥɟɦɟɧɬɚ, ɧɚ ɨɞɧɭ ɩɨɡɢɰɢɸ ɜɥɟɜɨ

For I:=1 to N do S:=S+a[i]; ɢɥɢp:=p*a[i];

ɉɪɢ ɷɬɨɦ ɪɚɡɦɟɪɧɨɫɬɶ ɦɚɫɫɢɜɚ ɭɦɟɧɶɲɚɟɬɫɹ ɧɚ

Ɇɚɫɫɢɜ Ⱥ 1	3	2	7 3	5	4	8	5	9
ɩɨɥɭɱɚɟɦ 1	3	2	7 3	8	4	9

ɭɞɚɥɹɟɦ Ⱥ[3]=5

5

9

Ɍɨ ɟɫɬɶ ɩɪɨɢɡɜɨɞɢɦ ɩɪɢɫɜɚɢɜɚɧɢɟ ɩɪɟɞɵɞɭɳɟɦɭ ɷɥɟɦɟɧɬɭ ɦɚɫɫɢɜɚ ɩɨɫɥɟɞɭɸɳɟɝɨ

ɧɚɱɢɧɚɹ ɫ k-ɝɨ

For i:=k to n-1 do

A[i]:=a[i+1];

ɉɟɪɟɞ ɜɤɥɸɱɟɧɢɟɦ ɷɥɟɦɟɧɬɚ ȼ ɜ k-ɭɸ ɩɨɡɢɰɢɸ ɨɞɧɨɦɟɪɧɨɝɨ ɦɚɫɫɢɜɚ Ⱥ ɧɟɨɛɯɨɞɢɦɨ ɪɚɡɞɜɢɧɭɬɶ ɦɚɫɫɢɜ, ɬɨ ɟɫɬɶ ɩɟɪɟɦɟɫɬɢɬɶ ©ɯɜɨɫɬª ɦɚɫɫɢɜɚ, ɧɚɱɢɧɚɹ k-ɝɨ ɷɥɟɦɟɧɬɚ ɧɚ ɨɞɧɭ ɩɨɡɢɰɢɸ ɜɩɪɚɜɨ ɇɚɩɪɢɦɟɪ, k=3 ɡɧɚɱɟɧɢɟ ɪɚɜɧɨ .

1

3

2

7

3

5

4

8

5

9

1

3

2

7 3

0

4

5 5

8

6

9

ɉɟɪɟɦɟɳɚɬɶ ɷɥɟɦɟɧɬɵ ɦɚɫɫɢɜɚ ɧɭɠɧɨ ɧɚɱɢɧɚɬɶ ɫ

ɩɨɫɥɟɞɧɟɝɨ ɷɥɟɦɟɧɬɚ, ɢɧɚɱɟ ɜɟɫɶ ©ɯɜɨɫɬª ɦɚɫɫɢɜɚ ɛɭɞɟɬ ɡɚɩɨɥɧɟɧ ɷɥɟɦɟɧɬɨɦ Ⱥ[k]. Ɂɚɬɟɦ k-ɦɭ ɷɥɟɦɟɧɬɭ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɡɧɚɱɟɧɢɟ ȼ ɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɡɦɟɪɧɨɫɬɶ ɦɚɫɫɢɜɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɧɚ

For i:=N downto k do A[i+1]:=a[i]; A[k]:=B;

ɇɟɨɛɯɨɞɢɦɨ ɩɨɦɟɧɹɬɶ ɦɟɫɬɚɦɢ ɷɥɟɦɟɧɬ ɢɦɟɸɳɢɣ ɧɨɦɟɪ l ɢ ɷɥɟɦɟɧɬ ɫ ɧɨɦɟɪɨɦ k.

ɗɬɚ ɩɟɪɟɫɬɚɧɨɜɤɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ ɩɟɪɟɦɟɧɧɨɣ Ɋ, ɜ ɤɨɬɨɪɭɸ ɜɪɟɦɟɧɧɨ ɩɨɦɟɳɚɸɬ ɨɞɢɧ ɢɡ ɷɬɢɯ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ.

P:=a[k];

A[k]:=a[l];

A[l]:=p;

ɉɭɫɬɶ ɬɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɦɢɧɢɦɚɥɶɧɵɣ ɷɥɟɦɟɧɬ ɜ ɦɚɫɫɢɜɟ Ⱥ ɢ ɟɝɨ ɡɧɚɱɟɧɢɟ ɩɨɦɟɫɬɢɬɶ ɜ ɩɟɪɟɦɟɧɧɭɸ A_min, ɚ ɟɝɨ ɢɧɞɟɤɫ – ɜ ɩɟɪɟɦɟɧɧɭɸ I_min.

Ⱦɥɹ ɩɨɢɫɤɚ ɦɢɧɢɦɚɥɶɧɨɝɨ ɷɥɟɦɟɧɬɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɥɝɨɪɢɬɦ ɧɚɯɨɠɞɟɧɢɹ ɧɚɢɦɟɧɶɲɟɝɨ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ, ɧɨ ɫ ɬɨɣ ɪɚɡɧɢɰɟɣ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɦɚɫɫɢɜɚ ɜɫɟ ɟɝɨ ɷɥɟɦɟɧɬɵ ɧɚɯɨɞɹɬɫɹ ɜ ɩɚɦɹɬɢ ɗȼɆ, ɩɨɷɬɨɦɭ, ɞɨɫɬɚɬɨɱɧɨ ɢɡɦɟɧɢɬɶ ɢɧɞɟɤɫ ɧɚ .

A_min:=a[1]; I_min:=1;

For i:=2 to n do

If a[i]<a_min then begin A_min:=a[i]; I_min:=I;

End;

I_min:=1;

For i:=2 to n do

If a[i]<a[I_min] then I_min:=I;

ɇɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɫɤɨɥɶɤɨ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ Ⱥ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɧɟɤɨɬɨɪɨɦɭ ɭɫɥɨɜɢɸ, ɧɚɩɪɢɦɟɪ .

Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɟɨɛɯɨɞɢɦɨ ɨɪɝɚɧɢɡɨɜɚɬɶ ɰɢɤɥɢ ɩɨ i ɢ ɞɥɹɞ ɤɚɠɞɨɝɨ ɡɧɚɱɟɧɢɹ i ɩɪɨɜɟɪɹɬɶ ɞɚɧɧɨɟ ɭɫɥɨɜɢɟ ȿɫɥɢ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɹɟɬɫɹ, ɬɨ ɤ ɫɱɟɬɱɢɤɭ ɱɢɫɥɚ ɷɥɟɦɟɧɬɨɜ, ɧɚɩɪɢɦɟɪ ɩɟɪɟɦɟɧɧɨɣ k, ɩɪɢɛɚɜɥɹɟɬɫɹ 1 ɂɧɚɱɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɟɪɟɯɨɞ ɤ ɫɥɟɞɭɸɳɟɦɭ ɷɥɟɦɟɧɬɭ ɦɚɫɫɢɜɚ.

k:=0;

For I:= 1 to N do

If A[I]=0 Then k:=k+1; ɢɥɢ If A[I]=0 Then Inc(k);

S: = 0;

For I:=1 to N do

If A[I]>0 Then S:=S+A[I];

ɇɟɨɛɯɨɞɢɦɨ ɨɪɝɚɧɢɡɨɜɚɬɶ ɰɢɤɥ ɩɨ I, ɢ ɞɥɹ ɤɚɠɞɨɝɨ ɡɧɚɱɟɧɢɹ ɢɧɞɟɤɫɚ i ɜɵɩɨɥɧɢɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɩɪɢɫɜɚɢɜɚɧɢɹ Ɋɚɡɦɟɪɧɨɫɬɶ ɦɚɫɫɢɜɚ ɋ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɜ 2 ɪɚɡɚ

For I:=1 to N do Begin

C[2*I-1]:=A[I];

C[2*I]: =B[I]; End;

	Ɂɚɞɚɧɵ ɞɜɚ ɨɞɧɨɦɟɪɧɵɯ ɦɚɫɫɢɜɚ		ɇɟɨɛɯɨɞɢɦɨ ɢɡ ɞɚɧɧɨɝɨ ɨɞɧɨɦɟɪɧɨɝɨ ɦɚɫɫɢɜɚ
	ɇɟɨɛɯɨɞɢɦɨ ɩɨɥɭɱɢɬɶ ɦɚɫɫɢɜ	ɝɞɟ	ɜɵɛɪɚɬɶ ɷɥɟɦɟɧɬɵ ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɧɟɤɨɬɨɪɨɦɭ
			ɭɫɥɨɜɢɸ ɧɚɩɪɢɦɟɪ ai>0 ɢ ɫɮɨɪɦɢɪɨɜɚɬɶ ɢɡ ɧɢɯ
			ɨɞɧɨɦɟɪɧɵɯ ɦɚɫɫɢɜ .

Ɉɫɨɛɟɧɧɨɫɬɶɸ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɹɜɥɹɟɬɫɹɬ ɬɨ, ɱɬɨ ɢɧɞɟɤɫɚ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɨɜ Ⱥ ɢ ȼ ɢɡɦɟɧɹɸɬɫɹ ɧɟ ɨɞɧɨɜɪɟɦɟɧɧɨ, ɬɨ ɟɫɬɶ ɧɟ ɫɨɜɩɚɞɚɸɬ, ɬɚɤ ɤɚɤ ɧɟ ɜɫɟ ɷɥɟɦɟɧɬɵ ɦɚɫɫɢɜɚ Ⱥ ɛɭɞɭɬ ɜɤɥɸɱɟɧɵ ɜ ɦɚɫɫɢɜ ȼ.