Протодьяконов Алгоритмы Data Science и их практическая реализация на Python 2022
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Ɉɮɨɪɦɥɟɧɢɟ ɂɡɞɚɬɟɥɶɫɬɜɨ ©ɂɧɮɪɚ ɂɧɠɟɧɟɪɢɹª |
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369 |
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380 |
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6
ǽǾdzDzǶǿǹǼǰǶdz
Ⱦɚɧɧɨɟ ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɩɪɟɞɩɨɥɚɝɚɟɬ ɨɛɭɱɟɧɢɟ ɫɬɭɞɟɧɬɨɜ ɬɟɯɧɢɱɟɫɤɢɯ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ ɢɹɜɥɹɟɬɫɹɩɪɨɮɢɥɶɧɵɦɞɥɹɫɬɭɞɟɧɬɨɜɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɬɟɯ ɧɨɥɨɝɢɣ ɧɚɜɵɤɚɦ ɢ ɦɟɬɨɞɢɤɚɦ ɪɚɛɨɬɵ ɫ ɫɥɨɠɧɵɦɢ ɦɨɞɟɥɹɦɢ ɦɚɲɢɧɧɨɝɨ ɢ ɝɥɭɛɨɤɨɝɨ ɨɛɭɱɟɧɢɹ
Ɉɬɥɢɱɢɬɟɥɶɧɨɣ ɱɟɪɬɨɣ ɩɨɫɨɛɢɹ ɨɬ ɞɪɭɝɢɯ ɫɯɨɠɢɯ ɤɭɪɫɨɜ ɨɛɭɱɟɧɢɹ ɢɫ ɤɭɫɫɬɜɟɧɧɨɦɭ ɢɧɬɟɥɥɟɤɬɭ ɨɧɥɚɣɧ ɩɥɨɳɚɞɤɢ ɢɧɬɟɪɧɟɬ ɤɭɪɫɵ ɹɜɥɹɟɬɫɹ ɩɥɚɜ ɧɨɫɬɶɜɨɡɪɚɫɬɚɧɢɹɫɥɨɠɧɨɫɬɢɢɰɟɥɨɫɬɧɨɫɬɶɥɨɝɢɤɢɩɨɜɟɫɬɜɨɜɚɧɢɹ ɋɥɨɠɧɨɫɬɶ ɜɯɨɞɧɨɝɨ ɩɨɪɨɝɚ ɤ ɢɡɭɱɟɧɢɸ ɚɥɝɨɪɢɬɦɨɜ ɢ ɦɨɞɟɥɟɣ ɦɚɲɢɧɧɨɝɨ ɝɥɭɛɨɤɨɝɨ ɨɛɭɱɟɧɢɹɹɜɥɹɟɬɫɹ ɦɢɧɢɦɚɥɶɧɨɣ ɢɡ ɜɫɟɯɜɨɡɦɨɠɧɵɯ ɬɨ ɟɫɬɶɞɚɠɟ ɧɟɩɨɞɝɨɬɨɜ ɥɟɧɧɵɣ ɫɬɭɞɟɧɬ ɦɨɠɟɬ ɧɚɱɚɬɶ ɨɛɭɱɟɧɢɸ ɩɨ ɧɚɫɬɨɹɳɟɦɭ ɭɱɟɛɧɨɦɭ ɩɨɫɨɛɢɸ ɢ ɩɥɚɜɧɨ ɭɩɪɨɱɧɹɬɶ ɫɜɨɢ ɧɚɜɵɤɢ ɞɨ ɭɪɨɜɧɹ -XQLRU 'DWD 6FLHQWLVWV.
ɋɨɫɬɚɜ ɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜɚɪɢɚɧɬɨɜ ɪɚɛɨɬ ɜ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɨɪɝɚ ɧɢɡɨɜɚɧɵ ɩɨ ɥɨɝɢɱɟɫɤɨɦɭ ɜɨɡɪɚɫɬɚɧɢɸ ɭɪɨɜɧɹ ɫɥɨɠɧɨɫɬɢ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɪɟɞɥɨɠɟɧɧɵɟ ɡɚɞɚɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɨɫɜɨɟɧɵ ɫɬɭɞɟɧɬɚɦɢ ɧɟ ɬɨɥɶɤɨ ɜ ɪɚɦɤɚɯ ɤɭɪɫɚ ɞɢɫɰɢɩɥɢɧɵ ɧɨ ɢ ɩɨ ɫɜɨɟɦɭ ɢɧɬɟɪɟɫɭ ɫɬɭɞɟɧɬɵ ɦɨɝɭɬ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɩɨɜɵɲɚɬɶ ɫɜɨɢ ɧɚɜɵɤɢ ɢ ɭɦɟɧɢɹ ɧɚ ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɡɚɞɚɧɢɹɯ ɧɟ ɡɚɬɪɚɱɢɜɚɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɜɪɟɦɹ ɧɚ ɩɨɢɫɤ ɡɚɞɚɧɢɣ ɢ ɧɚɛɨɪɨɜ ɞɚɧɧɵɯ ɜ ɫɟɬɢ ɂɧɬɟɪɧɟɬ
ɉɨɥɧɨɟ ɨɫɜɨɟɧɢɟ ɪɚɛɨɬ ɩɨ ɞɚɧɧɨɦɭ ɭɱɟɛɧɨɦɭ ɩɨɫɨɛɢɸ ɩɪɢ ɭɫɥɨɜɢɢ ɫɚ ɦɨɫɬɨɹɬɟɥɶɧɨɝɨɜɵɩɨɥɧɟɧɢɹɩɪɚɤɬɢɱɟɫɤɢɯɪɚɛɨɬ ɝɚɪɚɧɬɢɪɭɟɬɩɨɹɜɥɟɧɢɟɭɫɬɭ ɞɟɧɬɚ ɧɚɜɵɤɨɜ ɢ ɭɦɟɧɢɣ KDUG VNLOOV ɧɟɨɛɯɨɞɢɦɵɯ ɢ ɞɨɫɬɚɬɨɱɧɵɯ ɞɥɹ ɬɪɭɞɨ ɭɫɬɪɨɣɫɬɜɚ ɜ ɤɨɦɩɚɧɢɢ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɢ -XQLRU 'DWD 6FLHQWLVWV 'DWD $QDO\VW1.
1 ɋɨɝɥɚɫɧɨ ɪɟɚɥɶɧɵɦ ɞɚɧɧɵɦ ɚɧɤɟɬ ɨɞɧɨɝɨ ɢɡ ɤɪɭɩɧɟɣɲɢɯ ɜ ɊɎ ɩɨɢɫɤɨɜɵɯ ɫɟɪɜɢɫɨɜ ɪɚɛɨɬɵKWWSV VSE KK UX YDFDQFLHV GDWD DQDO\VW ɢ KWWSV VSE KK UX VHDUFK YDFDQF\"FOXVWHUV WUXH DUHD RUHGB FOXVWHUV WUXH HQDEOHBVQLSSHWV WUXH VDODU\ WH[W GDWD VFLHQWLVWV ɩɨ ɫɨɫɬɨɹɧɢɸ ɧɚ ɤɨɧɟɰ ɧɨɹɛɪɹ – ɧɚɱɚɥɨ ɞɟɤɚɛɪɹ ɝɨɞɚ
7
ȅȎȟȠȪ ǽǾǼȄdzǿǿ ǺǮȆǶǻǻǼDZǼ ǼǯȁȅdzǻǶȍ
ǵǮDzǮȅǶ ǺǮȆǶǻǻǼDZǼ ǼǯȁȅdzǻǶȍ
ɇɚɱɢɧɚɬɶɡɧɚɤɨɦɫɬɜɨɫɦɚɲɢɧɧɵɦɨɛɭɱɟɧɢɟɦɥɨɝɢɱɧɨɫɨɛɡɨɪɚɬɟɯɡɚɞɚɱɤɥɚɫɫɢɮɢɤɚɰɢɢ ɡɚɞɚɱ ɤɨɬɨɪɵɟ ɨɬɧɨɫɹɬɫɹ ɤ ɦɚɲɢɧɧɨɦɭ ɨɛɭɱɟɧɢɸ Ⱦɚɧɧɵɦ ɡɚɞɚɱɚɦ ɢ ɦɟɬɨɞɚɦ ɢɯ ɪɟɲɟɧɢɹ ɛɭɞɭɬ ɩɨɫɜɹɳɟɧɵ ɫɥɟɞɭɸɳɢɟ ɪɚɡɞɟɥɵ ɭɱɟɛ ɧɨɝɨ ɩɨɫɨɛɢɹ
Ʉɥɚɫɫɢɮɢɤɚɰɢɣ ɡɚɞɚɱ ɜ ɦɚɲɢɧɧɨɦ ɨɛɭɱɟɧɢɢ ɨɱɟɧɶ ɦɧɨɝɨ ɧɟɤɨɬɨɪɵɟ ɢɞɭɬ ɨɬ ɫɩɨɫɨɛɚ ɪɟɲɟɧɢɹ ɞɪɭɝɢɟ ɨɬ ɦɟɬɨɞɚ ɪɟɲɟɧɢɹ ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɩɪɢɦɟɦ ɡɚ ɨɫɧɨɜɭ ɫɚɦɭɸ ɨɛɳɭɸ ɢ ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɭɸ ɤɥɚɫɫɢɮɢɤɚɰɢɸ ɜɵɞɟɥɹɸɳɭɸ ɬɪɢ ɨɫɧɨɜɧɵɯ ɝɪɭɩɩɵ ɜ ɡɚɞɚɱɚɯ ɦɚɲɢɧɧɨɝɨ ɨɛɭɱɟɧɢɹ
1.Ɉɛɭɱɟɧɢɟ ɫ ɭɱɢɬɟɥɟɦ.
2.Ɉɛɭɱɟɧɢɟ ɛɟɡ ɭɱɢɬɟɥɹ.
3.Ɉɛɭɱɟɧɢɟ ɫ ɩɨɞɤɪɟɩɥɟɧɢɟɦ
ɇɚɱɧɟɦ ɫ ɩɟɪɜɨɣ ɝɪɭɩɩɵ ɡɚɞɚɱ Ɍɚɤɚɹ ɤɨɧɰɟɩɰɢɹ ɩɨɞɪɚɡɭɦɟɜɚɟɬ ɩɨɞ ɫɨ ɛɨɣ ɬɨɬ ɮɚɤɬ ɱɬɨ ɭ ɧɚɫ ɟɫɬɶ ɧɚ ɜɯɨɞɟ ɧɟɤɨɬɨɪɵɟ ɞɚɧɧɵɟ ɞɥɹ ɤɨɬɨɪɵɯ ɢɡɜɟɫɬɟɧ ɨɬɜɟɬ ɡɚɞɚɱɚɨɱɟɧɶɩɨɯɨɠɚɧɚɚɪɢɮɦɟɬɢɱɟɫɤɭɸ ɝɟɨɦɟɬɪɢɱɟɫɤɭɸɩɪɨɝɪɟɫɫɢɸ ɤɨɝɞɚ ɧɭɠɧɨ ɭɝɚɞɚɬɶ ɫɥɟɞɭɸɳɟɟ ɩɪɟɞɵɞɭɳɟɟ ɱɢɫɥɨ ɜ ɪɹɞɭ ɱɢɫɟɥ ɉɪɢ ɷɬɨɦɭ ɭ ɧɚɫ ɟɫɬɶ ɧɟɤɨɬɨɪɵɟ ɧɨɜɵɟ ɞɚɧɧɵɟ ɞɥɹ ɤɨɬɨɪɵɯ ɬɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɩɪɚɜɢɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɧɚɢɛɨɥɟɟ ɩɪɚɜɢɥɶɧɨɟ ɬɚɤ ɤɚɤ ɦɚɲɢɧɧɨɟ ɨɛɭɱɟɧɢɟ ɩɪɟɞɩɨɥɚɝɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɪɢ ɤɨɬɨɪɨɦ ɦɨɠɟɬ ɧɟ ɛɵɬɶ ɨɞɧɨɡɧɚɱɧɨ ɩɪɚɜɢɥɶɧɨɝɨ ɨɬɜɟɬɚ ɧɚ ɩɨɫɬɚɜɥɟɧɧɵɣ ɜɨɩɪɨɫ Ɍɨ ɟɫɬɶ ɫɭɳɟɫɬɜɭɟɬ ɧɟɤɨɬɨɪɵɣ ɧɚɛɨɪ ɨɬɜɟɬɨɜ ɤɚɠɞɵɣ ɢɡ ɤɨɬɨɪɵɯ ɩɨ ɫɜɨɟɦɭ ɛɥɢɡɨɤ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɧɨ ɫɤɨɪɟɟ ɜɫɟɝɨ ɩɪɚɜɢɥɶɧɵɦ ɧɟ ɹɜɥɹɟɬɫɹ ɜɫɟɝɞɚ ɫɭɳɟɫɬɜɭɟɬ ɨɩɪɟɞɟɥɟɧɧɚɹ ɫɬɚɬɢɫɬɢɱɟɫɤɚɹ ɨɲɢɛɤɚ
Ɉɛɭɱɟɧɢɟ ɫ ɭɱɢɬɟɥɟɦ – ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɨɣ ɤɥɚɫɫ ɡɚɞɚɱ ɜ ɦɚɲɢɧɧɨɦ ɨɛɭ ɱɟɧɢɢ ɬɚɤ ɤɚɤ ɩɪɟɞɩɨɥɚɝɚɟɬ ɱɬɨɭ ɧɚɫ ɭɠɟ ɟɫɬɶ ɫɨɛɪɚɧɧɵɟ ɞɚɧɧɵɟ ɧɚ ɷɬɢ ɞɚɧ ɧɵɟ ɟɫɬɶ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬɵ ɢ ɩɨ ɚɧɚɥɨɝɢɱɧɵɦ ɞɚɧɧɵɦ ɧɚɦ ɧɭɠɧɨ ɩɪɟɞɫɤɚ ɡɚɬɶ ɨɬɜɟɬ ɤɨɬɨɪɵɣ ɛɭɞɟɬ ɩɨɯɨɠ ɧɚ ɩɪɚɜɢɥɶɧɵɣ ɢ ɦɚɤɫɢɦɚɥɶɧɨ ɛɥɢɡɨɤ ɤ ɩɪɚ ɜɢɥɶɧɨɦɭ ɜɨ ɜɫɹɤɨɦ ɫɥɭɱɚɟ ɦɵ ɫɦɨɠɟɦ ɨɰɟɧɢɬɶ ɧɚɫɤɨɥɶɤɨ ɩɪɟɞɫɤɚɡɵɜɚɟɦɵɣ
8
ɨɬɜɟɬ ɛɥɢɡɨɤ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ȼ ɨɛɭɱɟɧɢɢ ɫ ɭɱɢɬɟɥɟɦ ɜɵɞɟɥɹɸɬ ɞɜɟ ɨɫɧɨɜɧɵɟ ɡɚɞɚɱɢ
xɡɚɞɚɱɚ ɪɟɝɪɟɫɫɢɢ
xɡɚɞɚɱɚ ɤɥɚɫɫɢɮɢɤɚɰɢɢ
ɉɨ ɫɭɬɢ ɨɧɢ ɞɨɫɬɚɬɨɱɧɨ ɩɨɯɨɠɢ ɞɪɭɝ ɧɚ ɞɪɭɝɚ ɬɨɥɶɤɨ ɜ ɡɚɞɚɱɢ ɪɟɝɪɟɫ ɫɢɢ ɦɵ ɩɪɟɞɫɤɚɡɵɜɚɟɦ ɱɢɫɥɨɜɨɟ ɡɧɚɱɟɧɢɟ ɚ ɜ ɡɚɞɚɱɢ ɤɥɚɫɫɢɮɢɤɚɰɢɢ ɨɬɜɟɬ ɩɪɟɞɫɬɚɜɥɟɧ ɜ ɜɢɞɟ ɪɚɧɝɚ ɢɥɢ ɤɚɬɟɝɨɪɢɢ ɩɨ ɮɚɤɬɭ – ɧɟɱɢɫɥɨɜɨɟ ɡɧɚɱɟɧɢɟ Ɂɚ ɞɚɱɢ ɪɟɲɚɸɬɫɹ ɨɞɧɢɦɢ ɢ ɬɟɦɢ ɠɟ ɚɥɝɨɪɢɬɦɚɦɢ ɧɨ ɩɪɢɧɹɬɨ ɢɯ ɪɚɡɞɟɥɹɬɶ ɢ ɝɨ ɜɨɪɢɬɶ ɱɬɨ ɟɫɥɢ ɩɪɟɞɫɤɚɡɵɜɚɟɬɫɹ ɱɢɫɥɨɜɨɟ ɡɧɚɱɟɧɢɟ – ɬɨ ɷɬɨ ɬɨɱɧɨ ɡɚɞɚɱɚ ɪɟ ɝɪɟɫɫɢɢ ɭ ɧɟɺ ɫɜɨɣ ɧɚɛɨɪ ɦɟɬɨɞɨɜ – ɥɢɧɟɣɧɚɹ ɪɟɝɪɟɫɫɢɹ ɧɟɥɢɧɟɣɧɚɹ ɪɟɝɪɟɫ ɫɢɹ ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ ɩɪɟɞɫɤɚɡɚɧɢɟ ɪɚɧɝɨɜ ɢ ɤɥɚɫɫɨɜ ɨɬɧɨɫɢɬɫɹ ɤ ɡɚɞɚɱɟ ɤɥɚɫɫɢ ɮɢɤɚɰɢɢ ɭ ɧɟɺ ɫɭɳɟɫɬɜɭɟɬ ɞɪɭɝɨɣ ɧɚɛɨɪ ɚɥɝɨɪɢɬɦɨɜ – ɦɟɬɨɞ ɛɥɢɠɚɣɲɢɯ ɫɨ ɫɟɞɟɣ ɦɧɨɠɟɫɬɜɟɧɧɚɹ ɤɥɚɫɫɢɮɢɤɚɰɢɹ
Ɉɛɭɱɟɧɢɟɛɟɡɭɱɢɬɟɥɹ– ɜɬɨɪɚɹɝɪɭɩɩɚɡɚɞɚɱ– ɝɨɜɨɪɢɬ ɱɬɨɭɧɚɫɧɟɬɩɪɚ ɜɢɥɶɧɨɝɨ ɨɬɜɟɬɚ ɋɭɳɟɫɬɜɭɸɬ ɞɚɧɧɵɟ ɧɨ ɨɬɜɟɬɚ ɧɚ ɧɢɯ ɧɟɬ ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜɨɡɧɢɤɚɟɬ ɪɹɞ ɡɚɞɚɱ ɜ ɫɜɹɡɢ ɫ ɬɟɦ ɱɬɨ ɭ ɧɚɫ ɧɟɬ ɨɬɜɟɬɚ ɧɚ ɞɚɧɧɵɟ
ɉɟɪɜɚɹ ɩɨɞɡɚɞɚɱɚ – ɡɚɞɚɱɚ ɤɥɚɫɬɟɪɢɡɚɰɢɢ ȼ ɧɟɣ ɩɨ ɨɩɪɟɞɟɥɺɧɧɵɦ ɩɚɪɚ ɦɟɬɪɚɦ ɧɚɩɪɢɦɟɪ ɤɨɥɢɱɟɫɬɜɨ ɤɥɚɫɬɟɪɨɜ ɧɟɨɛɯɨɞɢɦɨ ɩɪɟɞɫɤɚɡɚɬɶ ɤɚɤɢɦ ɨɛ ɪɚɡɨɦ ɞɚɧɧɵɟ ɪɚɫɩɪɟɞɟɥɟɧɵ ɦɟɠɞɭ ɫɨɛɨɣ ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɪɚɡɧɟɫɬɢ ɞɚɧɧɵɟ ɩɨ ɤɥɚɫɬɟɪɚɦ ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɫɪɟɞɧɟɦ ɭɞɚɥɟɧɢɢ ɨɬ ɰɟɧɬɪɚ ɤɥɚɫɬɟɪɚ ɧɚ ɤɨɥɢɱɟ ɫɬɜɟ ɤɥɚɫɬɟɪɨɜ ɢ ɞɪɭɝɢɯ ɩɪɢɡɧɚɤɨɜ ɬɟɦ ɫɚɦɵɦ ɪɟɲɢɜ ɡɚɞɚɱɭ ɤɥɚɫɬɟɪɢɡɚɰɢɢ ɬɚɤɢɦ ɨɛɪɚɡɨɦ
Ʉɪɨɦɟ ɬɨɝɨ ɝɪɭɩɩɚ ɡɚɞɚɱ ɨɛɭɱɟɧɢɹ ɛɟɡ ɭɱɢɬɟɥɹ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɦɟɬɨɞɵ ɩɨɧɢɠɟɧɢɹ ɪɚɡɦɟɪɧɨɫɬɢ ɤɨɝɞɚ ɫɭɳɟɫɬɜɭɟɬ ɨɝɪɨɦɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɩɪɢɡɧɚɤɨɜ ɢ ɧɚɦ ɬɪɟɛɭɟɬɫɹ ɭɦɟɧɶɲɢɬɶ ɢɯ ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɱɬɨɛɵ ɩɨɬɨɦ ɩɪɢɦɟɧɢɬɶ ɡɚɞɚɱɭ ɤɥɚɫɬɟɪɢɡɚɰɢɢ ɢɥɢ ɡɚɞɚɱɭ ɨɛɭɱɟɧɢɹ ɫ ɭɱɢɬɟɥɟɦ ɱɬɨɛɵ ɧɚ ɪɚɡɧɵɯ ɩɚɪɚɦɟɬɪɚɯ ɨɩɪɟɞɟɥɢɬɶɤɚɤɢɟɩɚɪɚɦɟɬɪɵɜɚɠɧɵɢ ɫɧɢɡɢɜɪɚɡɦɟɪɧɨɫɬɶ ɪɟɲɢɬɶɡɚɞɚɱɭɨɛɭ ɱɟɧɢɹ ɫ ɭɱɢɬɟɥɟɦ ɉɪɢ ɛɨɥɶɲɨɣ ɪɚɡɦɟɪɧɨɫɬɢ ɪɟɲɢɬɶ ɡɚɞɚɱɭ ɫ ɭɱɢɬɟɥɟɦ ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɵɦ ɛɟɡ ɫɟɪɶɟɡɧɨɝɨ ɚɩɩɚɪɚɬɧɨɝɨ ɨɛɟɫɩɟɱɟɧɢɹ
Ɍɚɤɠɟ ɤ ɤɥɚɫɫɭ ɡɚɞɚɱ ɨɛɭɱɟɧɢɹ ɛɟɡ ɭɱɢɬɟɥɹ ɨɬɧɨɫɢɬɫɹ ɤɥɚɫɫ ɡɚɞɚɱɩɨ ɜɵ ɹɜɥɟɧɢɢ ɚɧɨɦɚɥɢɣ Ɉɧɢ ɩɨɯɨɠɢ ɧɚ ɤɥɚɫɬɟɪɢɡɚɰɢɸ ɝɞɟ ɟɫɬɶ ɜɫɟ ɞɚɧɧɵɟ ɢ ɞɨ ɩɨɥɧɢɬɟɥɶɧɨ ɦɨɝɭɬ ɛɵɬɶ ɟɳɺ ɤɚɤɢɟ ɬɨ Ɉɛɪɚɳɚɟɦ ɨɫɨɛɨɟ ɜɧɢɦɚɧɢɟ ɧɚ ɬɨ ɱɬɨ
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