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# Критерии ИН11 1422012

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```ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
1
Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ
C1
Ɍɪɟɛɨɜɚɥɨɫɶ ɧɚɩɢɫɚɬɶ ɩɪɨɝɪɚɦɦɭ, ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɤɨɬɨɪɨɣ ɫ ɤɥɚɜɢɚɬɭɪɵ
ɫɱɢɬɵɜɚɟɬɫɹ ɤɨɨɪɞɢɧɚɬɚ ɬɨɱɤɢ ɧɚ ɩɪɹɦɨɣ (x – ɞɟɣɫɬɜɢɬɟɥɶɧɨɟ ɱɢɫɥɨ) ɢ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɷɬɨɣ ɬɨɱɤɢ ɨɞɧɨɦɭ ɢɡ ɜɵɞɟɥɟɧɧɵɯ ɨɬɪɟɡɤɨɜ
(ɜɤɥɸɱɚɹ ɝɪɚɧɢɰɵ). ɉɪɨɝɪɚɦɦɢɫɬ ɬɨɪɨɩɢɥɫɹ ɢ ɧɚɩɢɫɚɥ ɩɪɨɝɪɚɦɦɭ
ɧɟɩɪɚɜɢɥɶɧɨ.
Ȼɟɣɫɢɤ
ɉɚɫɤɚɥɶ
ɋɢ
INPUT x
IF x>=-7 OR x<=1 THEN
IF x>=-5 AND x<=5 THEN
IF x>=-1 AND x<=7 THEN
PRINT "ɩɪɢɧɚɞɥɟɠɢɬ"
ELSE
PRINT "ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ"
END IF
END IF
END IF
END
var x: real;
begin
readln(x);
if (x>=-7) or (x<=1) then
if (x>=-5) and (x<=5) then
if (x>=-1) and (x<=7) then
write('ɩɪɢɧɚɞɥɟɠɢɬ')
else
write('ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ')
end.
#include <stdio.h>
void main(){
float x;
scanf("%f",&x);
if (x>=-7 || x<=1)
if (x>=-5 && x<=5)
if (x>=-1 && x<=7)
printf("ɩɪɢɧɚɞɥɟɠɢɬ");
else
printf("ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ");
}
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru 2
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ɚɥɝ
ɧɚɱ
Ⱥɥɝɨɪɢɬɦɢɱɟɫɤɢɣ
ɹɡɵɤ
ɤɨɧ
ɜɟɳ x
ɜɜɨɞ x
ɟɫɥɢ x>=-7 ɢɥɢ x<=1 ɬɨ
ɟɫɥɢ x>=-5 ɢ x<=5 ɬɨ
ɟɫɥɢ x>=-1 ɢ x<=7 ɬɨ
ɜɵɜɨɞ 'ɩɪɢɧɚɞɥɟɠɢɬ'
ɢɧɚɱɟ
ɜɵɜɨɞ 'ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ'
ɜɫɟ
ɜɫɟ
ɜɫɟ
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɵɩɨɥɧɢɬɟ ɫɥɟɞɭɸɳɟɟ.
1. ɉɟɪɟɪɢɫɭɣɬɟ ɢ ɡɚɩɨɥɧɢɬɟ ɬɚɛɥɢɰɭ, ɤɨɬɨɪɚɹ ɩɨɤɚɡɵɜɚɟɬ, ɤɚɤ ɪɚɛɨɬɚɟɬ
ɩɪɨɝɪɚɦɦɚ ɩɪɢ ɚɪɝɭɦɟɧɬɟ, ɩɪɢɧɚɞɥɟɠɚɳɟɦ ɪɚɡɥɢɱɧɵɦ ɨɛɥɚɫɬɹɦ (A, B, C, D,
E, F, G). Ɍɨɱɤɢ, ɥɟɠɚɳɢɟ ɧɚ ɝɪɚɧɢɰɚɯ ɨɛɥɚɫɬɟɣ, ɨɬɞɟɥɶɧɨ ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɬɶ.
ɍɫɥɨɜɢɟ 1 ɍɫɥɨɜɢɟ 2 ɍɫɥɨɜɢɟ 3
Ɉɛɥɚɫɬɶ
ɉɪɨɝɪɚɦɦɚ
ɨɛɪɚɛɚɬɵɜɚɟɬɫɹ
Ɉɛɥɚɫɬɶ (x>= –7 ɢɥɢ (x>= –5 ɢ (x>= –1 ɢ
ɜɵɜɟɞɟɬ
ɜɟɪɧɨ
x<=1)
x<=5)
x<=7)
A
B
C
D
E
F
G
ȼ ɫɬɨɥɛɰɚɯ ɭɫɥɨɜɢɣ ɭɤɚɠɢɬɟ «ɞɚ», ɟɫɥɢ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɢɬɫɹ, «ɧɟɬ», ɟɫɥɢ
ɭɫɥɨɜɢɟ ɧɟ ɜɵɩɨɥɧɢɬɫɹ, «—» (ɩɪɨɱɟɪɤ), ɟɫɥɢ ɭɫɥɨɜɢɟ ɧɟ ɛɭɞɟɬ ɩɪɨɜɟɪɹɬɶɫɹ,
«ɧɟ ɢɡɜ.», ɟɫɥɢ ɩɪɨɝɪɚɦɦɚ ɜɟɞɺɬ ɫɟɛɹ ɩɨ-ɪɚɡɧɨɦɭ ɞɥɹ ɪɚɡɧɵɯ ɡɧɚɱɟɧɢɣ,
ɩɪɢɧɚɞɥɟɠɚɳɢɯ ɞɚɧɧɨɣ ɨɛɥɚɫɬɢ.
ȼ ɫɬɨɥɛɰɟ «ɉɪɨɝɪɚɦɦɚ ɜɵɜɟɞɟɬ» ɭɤɚɠɢɬɟ, ɱɬɨ ɩɪɨɝɪɚɦɦɚ ɜɵɜɟɞɟɬ ɧɚ ɷɤɪɚɧ.
ȿɫɥɢ ɩɪɨɝɪɚɦɦɚ ɧɢɱɟɝɨ ɧɟ ɜɵɜɨɞɢɬ, ɧɚɩɢɲɢɬɟ «—» (ɩɪɨɱɟɪɤ). ȿɫɥɢ ɞɥɹ
ɪɚɡɧɵɯ ɡɧɚɱɟɧɢɣ, ɩɪɢɧɚɞɥɟɠɚɳɢɯ ɨɛɥɚɫɬɢ, ɛɭɞɭɬ ɜɵɜɟɞɟɧɵ ɪɚɡɧɵɟ ɬɟɤɫɬɵ,
ɧɚɩɢɲɢɬɟ «ɧɟ ɢɡɜ.». ȼ ɩɨɫɥɟɞɧɟɦ ɫɬɨɥɛɰɟ ɭɤɚɠɢɬɟ «ɞɚ» ɢɥɢ «ɧɟɬ».
2. ɍɤɚɠɢɬɟ, ɤɚɤ ɧɭɠɧɨ ɞɨɪɚɛɨɬɚɬɶ ɩɪɨɝɪɚɦɦɭ, ɱɬɨɛɵ ɧɟ ɛɵɥɨ ɫɥɭɱɚɟɜ ɟɺ
ɧɟɩɪɚɜɢɥɶɧɨɣ ɪɚɛɨɬɵ. (ɗɬɨ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɧɟɫɤɨɥɶɤɢɦɢ ɫɩɨɫɨɛɚɦɢ,
ɞɨɫɬɚɬɨɱɧɨ ɭɤɚɡɚɬɶ ɥɸɛɨɣ ɫɩɨɫɨɛ ɞɨɪɚɛɨɬɤɢ ɢɫɯɨɞɧɨɣ ɩɪɨɝɪɚɦɦɵ.)
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ɗɥɟɦɟɧɬɵ ɨɬɜɟɬɚ:
ɉɪɚɜɢɥɶɧɨ ɡɚɩɨɥɧɟɧɧɚɹ ɬɚɛɥɢɰɚ:
ɍɫɥɨɜɢɟ 1
ɍɫɥɨɜɢɟ 2
Ɉɛɥɚɫɬɶ (x>= –7 ɢɥɢ (x>= –5 ɢ
x<=1)
x<=5)
A
Ⱦɚ
ɇɟɬ
B
Ⱦɚ
ɇɟɬ
C
Ⱦɚ
Ⱦɚ
D
Ⱦɚ
Ⱦɚ
E
Ⱦɚ
Ⱦɚ
F
Ⱦɚ
ɇɟɬ
G
Ⱦɚ
ɇɟɬ
ɍɫɥɨɜɢɟ 3
ɉɪɨɝɪɚɦɦɚ
(x>= –1 ɢ
ɜɵɜɟɞɟɬ
x<=7)
–
–
–
–
ɇɟɬ
ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ
Ⱦɚ
ɩɪɢɧɚɞɥɟɠɢɬ
Ⱦɚ
ɩɪɢɧɚɞɥɟɠɢɬ
–
–
–
–
3
Ɉɛɥɚɫɬɶ
ɨɛɪɚɛɚɬɵɜɚɟɬɫɹ
ɜɟɪɧɨ
ɇɟɬ
ɇɟɬ
Ⱦɚ
Ⱦɚ
ɇɟɬ
ɇɟɬ
ɇɟɬ
ȼɨɡɦɨɠɧɵ ɪɚɡɥɢɱɧɵɟ ɫɩɨɫɨɛɵ ɞɨɪɚɛɨɬɤɢ ɩɪɨɝɪɚɦɦɵ. ɇɢɠɟ ɩɪɢɜɟɞɟɧɵ ɪɚɡɥɢɱɧɵɟ
ɩɪɚɜɢɥɶɧɵɟ ɪɟɲɟɧɢɹ, ɡɚɩɢɫɚɧɧɵɟ ɧɚ ɪɚɡɧɵɯ ɹɡɵɤɚɯ. Ⱦɚɧɧɵɟ ɪɟɲɟɧɢɹ ɧɟ ɩɪɢɜɹɡɚɧɵ ɤ
ɹɡɵɤɚɦ: ɥɸɛɭɸ ɢɡ ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɧɢɯ ɢɞɟɣ ɦɨɠɧɨ ɩɪɢɦɟɧɢɬɶ, ɢɫɩɨɥɶɡɭɹ ɥɸɛɨɣ ɹɡɵɤ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ.
ɉɪɢɦɟɪ ɧɚ ɚɥɝɨɪɢɬɦɢɱɟɫɤɨɦ ɹɡɵɤɟ
ɟɫɥɢ -7<=x<=-5 ɢɥɢ -1<=x<=1 ɢɥɢ 5<=x<=7 ɬɨ
ɜɵɜɨɞ 'ɩɪɢɧɚɞɥɟɠɢɬ'
ɢɧɚɱɟ
ɜɵɜɨɞ 'ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ'
ɜɫɟ
ɉɪɢɦɟɪ ɧɚ ɉɚɫɤɚɥɟ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ! ȼ ɡɚɞɚɱɟ ɬɪɟɛɭɟɬɫɹ ɜɵɩɨɥɧɢɬɶ ɬɪɢ ɞɟɣɫɬɜɢɹ.
1. Ɂɚɩɨɥɧɢɬɶ ɬɚɛɥɢɰɭ.
2. ɂɫɩɪɚɜɢɬɶ ɨɲɢɛɤɭ ɜ ɭɫɥɨɜɧɨɦ ɨɩɟɪɚɬɨɪɟ.
3. ɂɫɩɪɚɜɢɬɶ ɨɲɢɛɤɭ, ɫɜɹɡɚɧɧɭɸ ɫ ɧɟɩɪɚɜɢɥɶɧɵɦ ɧɚɛɨɪɨɦ ɭɫɥɨɜɢɣ.
Ȼɚɥɥɵ ɡɚ ɞɚɧɧɨɟ ɡɚɞɚɧɢɟ ɧɚɱɢɫɥɹɸɬɫɹ ɤɚɤ ɫɭɦɦɚ ɛɚɥɥɨɜ ɡɚ ɜɟɪɧɨɟ ɜɵɩɨɥɧɟɧɢɟ ɤɚɠɞɨɝɨ
ɞɟɣɫɬɜɢɹ.
Ɋɚɫɫɦɨɬɪɢɦ ɨɬɞɟɥɶɧɨ ɤɚɠɞɨɟ ɞɟɣɫɬɜɢɟ.
1. Ⱦɟɣɫɬɜɢɟ ɩɨ ɡɚɩɨɥɧɟɧɢɸ ɬɚɛɥɢɰɵ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɜ ɬɚɛɥɢɰɟ ɧɟɬ
ɨɲɢɛɨɤ ɢɥɢ ɨɲɢɛɤɢ ɩɪɢɫɭɬɫɬɜɭɸɬ ɬɨɥɶɤɨ ɜ ɨɞɧɨɣ ɫɬɪɨɤɟ.
2. ɇɟɩɪɚɜɢɥɶɧɨɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɭɫɥɨɜɧɨɝɨ ɨɩɟɪɚɬɨɪɚ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɩɪɢ
ɧɟɜɵɩɨɥɧɟɧɢɢ ɩɟɪɜɨɝɨ ɢɥɢ ɜɬɨɪɨɝɨ ɭɫɥɨɜɢɹ ɩɪɨɝɪɚɦɦɚ ɧɟ ɜɵɞɚɜɚɥɚ ɧɢɱɟɝɨ
(ɨɬɫɭɬɫɬɜɭɸɬ ɫɥɭɱɚɢ ELSE). ɂɫɩɪɚɜɥɟɧɢɟɦ ɷɬɨɣ ɨɲɢɛɤɢ ɦɨɠɟɬ ɛɵɬɶ ɥɢɛɨ ɞɨɛɚɜɥɟɧɢɟ
ɫɥɭɱɚɹ ELSE ɤ ɤɚɠɞɨɦɭ ɭɫɥɨɜɢɸ IF, ɥɢɛɨ ɨɛɴɟɞɢɧɟɧɢɟ ɜɫɟɯ ɭɫɥɨɜɢɣ IF ɜ ɨɞɧɨ ɩɪɢ
ɩɨɦɨɳɢ ɤɨɧɴɸɧɤɰɢɢ.
ȼ ɫɥɨɠɧɵɯ ɫɥɭɱɚɹɯ ɷɬɨ ɞɟɣɫɬɜɢɟ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɩɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ
ɨɞɧɨ ɢɡ ɞɜɭɯ ɫɨɨɛɳɟɧɢɣ: «ɩɪɢɧɚɞɥɟɠɢɬ» ɢɥɢ «ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ» – ɞɥɹ ɥɸɛɵɯ ɱɢɫɟɥ x,
ɩɪɢ ɷɬɨɦ ɩɪɨɝɪɚɦɦɚ ɧɟ ɫɬɚɥɚ ɪɚɛɨɬɚɬɶ ɯɭɠɟ, ɱɟɦ ɪɚɧɶɲɟ, ɬ. ɟ. ɞɥɹ ɜɫɟɯ ɬɨɱɟɤ, ɞɥɹ
ɤɨɬɨɪɵɯ ɩɪɨɝɪɚɦɦɚ ɪɚɧɟɟ ɜɵɞɚɜɚɥɚ ɜɟɪɧɵɣ ɨɬɜɟɬ, ɞɨɪɚɛɨɬɚɧɧɚɹ ɩɪɨɝɪɚɦɦɚ ɬɚɤɠɟ
ɞɨɥɠɧɚ ɜɵɞɚɜɚɬɶ ɜɟɪɧɵɣ ɨɬɜɟɬ.
3. ɉɪɢɜɟɞɺɧɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ ɧɟ ɨɩɢɫɵɜɚɸɬ ɬɪɟɛɭɟɦɵɟ ɨɛɥɚɫɬɢ. ɉɟɪɜɨɟ ɭɫɥɨɜɢɟ ɜɟɪɧɨ
ɞɥɹ ɥɸɛɵɯ x, ɬɨ ɟɫɬɶ ɧɟ ɩɨɡɜɨɥɹɟɬ ɩɪɢɧɹɬɶ ɧɢɤɚɤɢɯ ɪɟɲɟɧɢɣ, ɜɬɨɪɨɟ ɢ ɬɪɟɬɶɟ ɧɟ
ɡɚɯɜɚɬɵɜɚɸɬ ɨɛɥɚɫɬɢ B ɢ F ɢ ɧɟ ɩɨɡɜɨɥɹɸɬ ɨɬɞɟɥɢɬɶ ɞɪɭɝ ɨɬ ɞɪɭɝɚ ɨɛɥɚɫɬɢ D ɢ E.
ɂɫɩɪɚɜɥɟɧɢɟɦ ɷɬɨɣ ɨɲɢɛɤɢ ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɛɢɟɧɢɟ ɨɛɥɚɫɬɢ ɧɚ ɱɚɫɬɢ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɟ
ɞɢɡɴɸɧɤɰɢɢ ɥɢɛɨ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɤɨɦɛɢɧɚɰɢɢ ɤɚɫɤɚɞɧɵɯ ɭɫɥɨɜɢɣ. ɇɟɫɤɨɥɶɤɨ
ɩɪɢɦɟɪɨɜ ɪɚɡɥɢɱɧɵɯ ɜɟɪɧɵɯ ɪɟɲɟɧɢɣ ɩɪɢɜɟɞɟɧɵ ɜɵɲɟ.
ȼ ɫɥɨɠɧɵɯ ɫɥɭɱɚɹɯ ɷɬɨ ɞɟɣɫɬɜɢɟ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɜɟɪɧɨ ɨɩɪɟɞɟɥɟɧɵ
ɡɚɲɬɪɢɯɨɜɚɧɧɵɟ ɨɛɥɚɫɬɢ, ɬ. ɟ. ɩɪɨɝɪɚɦɦɚ ɜɵɜɨɞɢɬ ɫɨɨɛɳɟɧɢɟ «ɩɪɢɧɚɞɥɟɠɢɬ» ɞɥɹ ɜɫɟɯ
ɬɨɱɟɤ ɡɚɤɪɚɲɟɧɧɵɯ ɨɛɥɚɫɬɟɣ ɢ ɬɨɥɶɤɨ ɞɥɹ ɧɢɯ, ɞɥɹ ɬɨɱɟɤ ɜɧɟ ɡɚɲɬɪɢɯɨɜɚɧɧɵɯ
ɨɛɥɚɫɬɟɣ ɩɪɨɝɪɚɦɦɚ ɜɵɜɨɞɢɬ «ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ» ɢɥɢ ɧɟ ɜɵɜɨɞɢɬ ɧɢɱɟɝɨ.
if (abs(x)<=1) or (5<=abs(x)) and (abs(x)<=7) then
write('ɩɪɢɧɚɞɥɟɠɢɬ')
else
write('ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ');
ɉɪɢɦɟɪ ɧɚ Ȼɟɣɫɢɤɟ:
T = ABS(ABS(x)-3)
IF 2<=T AND T<=4 THEN
PRINT "ɩɪɢɧɚɞɥɟɠɢɬ"
ELSE
PRINT "ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ"
END IF
ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɞɨɪɚɛɨɬɤɢ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
4
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
5
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɟɧɵ ɨɛɚ ɩɭɧɤɬɚ ɡɚɞɚɧɢɹ. ȼɟɪɧɨ ɡɚɩɨɥɧɟɧɚ ɬɚɛɥɢɰɚ,
ɢɫɩɪɚɜɥɟɧɵ ɞɜɟ ɨɲɢɛɤɢ. ɉɪɨɝɪɚɦɦɚ ɞɥɹ ɜɫɟɯ ɱɢɫɟɥ x ɜɟɪɧɨ ɨɩɪɟɞɟɥɹɟɬ
ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɬɨɱɤɢ ɡɚɤɪɚɲɟɧɧɨɣ ɨɛɥɚɫɬɢ. ȼ ɪɚɛɨɬɟ (ɜɨ ɮɪɚɝɦɟɧɬɚɯ
3
ɩɪɨɝɪɚɦɦ) ɞɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬɞɟɥɶɧɵɯ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ ɨɲɢɛɨɤ, ɧɟ
ɢɫɤɚɠɚɸɳɢɯ ɡɚɦɵɫɥɚ ɚɜɬɨɪɚ ɪɟɲɟɧɢɹ.
1. ɉɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɟɧɵ ɞɜɚ ɞɟɣɫɬɜɢɹ ɢɡ ɬɪɺɯ (ɢɫɩɪɚɜɥɟɧɵ ɨɛɟ ɨɲɢɛɤɢ, ɧɨ
ɜ ɩɟɪɜɨɦ ɩɭɧɤɬɟ ɡɚɞɚɧɢɹ ɧɟ ɩɪɢɜɟɞɟɧɚ ɬɚɛɥɢɰɚ (ɥɢɛɨ ɬɚɛɥɢɰɚ ɫɨɞɟɪɠɢɬ
ɨɲɢɛɤɢ ɜ ɞɜɭɯ ɢ ɛɨɥɟɟ ɫɬɪɨɤɚɯ), ɥɢɛɨ ɩɪɢɜɟɞɟɧɚ ɬɚɛɥɢɰɚ (ɤɨɬɨɪɚɹ ɫɨɞɟɪɠɢɬ
ɨɲɢɛɤɢ ɧɟ ɛɨɥɟɟ ɱɟɦ ɜ ɨɞɧɨɣ ɫɬɪɨɤɟ), ɧɨ ɢɫɩɪɚɜɥɟɧɚ ɬɨɥɶɤɨ ɨɞɧɚ ɨɲɢɛɤɚ
ɩɪɨɝɪɚɦɦɵ).
ɉɪɢ ɧɚɩɢɫɚɧɢɢ ɨɩɟɪɚɰɢɣ ɫɪɚɜɧɟɧɢɹ ɞɨɩɭɫɤɚɟɬɫɹ ɨɞɧɨ ɧɟɩɪɚɜɢɥɶɧɨɟ
2
ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɫɬɪɨɝɢɯ/ɧɟɫɬɪɨɝɢɯ ɧɟɪɚɜɟɧɫɬɜ (ɫɱɢɬɚɟɬɫɹ ɧɟɫɭɳɟɫɬɜɟɧɧɨɣ
ɨɲɢɛɤɨɣ, ɩɨɝɪɟɲɧɨɫɬɶɸ ɡɚɩɢɫɢ). ɇɚɩɪɢɦɟɪ, ɜɦɟɫɬɨ «x>=5» ɢɫɩɨɥɶɡɭɟɬɫɹ
«x>5».
2. ɂɥɢ ɜɵɩɨɥɧɟɧɵ ɜɫɟ ɬɪɢ ɞɟɣɫɬɜɢɹ, ɧɨ ɩɪɢ ɷɬɨɦ ɜ ɥɨɝɢɱɟɫɤɨɦ ɜɵɪɚɠɟɧɢɢ
ɧɟɜɟɪɧɨ ɭɱɬɟɧɵ ɩɪɢɨɪɢɬɟɬɵ ɥɨɝɢɱɟɫɤɢɯ ɨɩɟɪɚɰɢɣ (ɧɟ ɪɚɫɫɬɚɜɥɟɧɵ ɢɥɢ
ɧɟɩɪɚɜɢɥɶɧɨ ɪɚɫɫɬɚɜɥɟɧɵ ɫɤɨɛɤɢ ɜ ɜɵɪɚɠɟɧɢɹɯ).
ɉɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɟɧɨ ɬɨɥɶɤɨ ɨɞɧɨ ɞɟɣɫɬɜɢɟ ɢɡ ɬɪɺɯ, ɬɨ ɟɫɬɶ ɥɢɛɨ ɬɨɥɶɤɨ
ɩɪɢɜɟɞɟɧɚ ɬɚɛɥɢɰɚ, ɤɨɬɨɪɚɹ ɫɨɞɟɪɠɢɬ ɨɲɢɛɤɢ ɜ ɧɟ ɛɨɥɟɟ ɱɟɦ ɨɞɧɨɣ ɫɬɪɨɤɟ,
ɥɢɛɨ ɬɚɛɥɢɰɚ ɧɟ ɩɪɢɜɟɞɟɧɚ (ɢɥɢ ɩɪɢɜɟɞɟɧɚ ɢ ɫɨɞɟɪɠɢɬ ɨɲɢɛɤɢ ɛɨɥɟɟ ɱɟɦ
1
ɜ ɨɞɧɨɣ ɫɬɪɨɤɟ), ɧɨ ɢɫɩɪɚɜɥɟɧɚ ɨɞɧɚ ɨɲɢɛɤɚ ɩɪɨɝɪɚɦɦɵ. ɉɪɢ ɨɰɟɧɢɜɚɧɢɢ
ɷɬɨɝɨ ɡɚɞɚɧɢɹ ɧɚ 1 ɛɚɥɥ ɞɨɩɭɫɤɚɟɬɫɹ ɧɟ ɭɱɢɬɵɜɚɬɶ ɤɨɪɪɟɤɬɧɨɫɬɶ ɪɚɛɨɬɵ
ɩɪɨɝɪɚɦɦ ɧɚ ɬɨɱɤɚɯ ɝɪɚɧɢɰ ɨɛɥɚɫɬɟɣ (ɜɦɟɫɬɨ ɧɟɫɬɪɨɝɢɯ ɧɟɪɚɜɟɧɫɬɜ
ɜ ɪɟɲɟɧɢɢ ɛɵɥɢ ɢɫɩɨɥɶɡɨɜɚɧɵ ɫɬɪɨɝɢɟ ɧɟɪɚɜɟɧɫɬɜɚ ɢɥɢ ɧɚɨɛɨɪɨɬ).
ȼɫɟ ɩɭɧɤɬɵ ɡɚɞɚɧɢɹ ɜɵɩɨɥɧɟɧɵ ɧɟɜɟɪɧɨ (ɬɚɛɥɢɰɚ ɚɧɚɥɢɡɚ ɩɪɚɜɢɥɶɧɨɫɬɢ
0
ɚɥɝɨɪɢɬɦɚ ɧɟ ɩɪɢɜɟɞɟɧɚ ɥɢɛɨ ɫɨɞɟɪɠɢɬ ɨɲɢɛɤɢ ɜ ɞɜɭɯ ɢ ɛɨɥɟɟ ɫɬɪɨɤɚɯ,
ɩɪɨɝɪɚɦɦɚ ɧɟ ɩɪɢɜɟɞɟɧɚ, ɥɢɛɨ ɧɢ ɨɞɧɚ ɢɡ ɞɜɭɯ ɨɲɢɛɨɤ ɧɟ ɢɫɩɪɚɜɥɟɧɚ).
3
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
C2
Ⱦɚɧ ɦɚɫɫɢɜ, ɫɨɞɟɪɠɚɳɢɣ 70 ɰɟɥɵɯ ɱɢɫɟɥ. Ɉɩɢɲɢɬɟ ɧɚ ɨɞɧɨɦ ɢɡ ɹɡɵɤɨɜ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɚɥɝɨɪɢɬɦ, ɩɨɡɜɨɥɹɸɳɢɣ ɧɚɣɬɢ ɢ ɜɵɜɟɫɬɢ ɧɚɢɦɟɧɶɲɟɟ
ɫɨɞɟɪɠɚɳɟɟɫɹ ɜ ɦɚɫɫɢɜɟ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɱɢɫɥɨ, ɞɟɫɹɬɢɱɧɚɹ ɡɚɩɢɫɶ ɤɨɬɨɪɨɝɨ
ɨɤɚɧɱɢɜɚɟɬɫɹ ɰɢɮɪɨɣ 7. Ƚɚɪɚɧɬɢɪɭɟɬɫɹ, ɱɬɨ ɜ ɦɚɫɫɢɜɟ ɟɫɬɶ ɯɨɬɹ ɛɵ ɨɞɢɧ
ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɷɥɟɦɟɧɬ, ɞɟɫɹɬɢɱɧɚɹ ɡɚɩɢɫɶ ɤɨɬɨɪɨɝɨ ɨɤɚɧɱɢɜɚɟɬɫɹ ɰɢɮɪɨɣ 7.
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɨɛɴɹɜɥɟɧɵ ɬɚɤ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɢɠɟ. Ɂɚɩɪɟɳɚɟɬɫɹ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɟɪɟɦɟɧɧɵɟ, ɧɟ ɨɩɢɫɚɧɧɵɟ ɧɢɠɟ, ɧɨ ɪɚɡɪɟɲɚɟɬɫɹ ɧɟ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɱɚɫɬɶ ɢɡ ɧɢɯ.
const
N=70;
var
a: array [1..N] of integer;
i, j, m: integer;
ɉɚɫɤɚɥɶ
begin
for i:=1 to N do
readln(a[i]);
…
end.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
Ȼɟɣɫɢɤ
N=70
DIM A(N) AS INTEGER
DIM I, J, M AS INTEGER
FOR I = 1 TO N
INPUT A(I)
NEXT I
…
END
ɋɢ
#include <stdio.h>
#define N 70
void main(){
int a[N];
int i, j, m;
for (i=0; i<N; i++)
scanf("%d", &a[i]);
…
}
ɚɥɝ
ɧɚɱ
Ⱥɥɝɨɪɢɬɦɢɱɟɫɤɢɣ
ɹɡɵɤ
ɤɨɧ
ɰɟɥ N=70
ɰɟɥɬɚɛ a[1:N]
ɰɟɥ i, j, m
ɧɰ ɞɥɹ i ɨɬ 1 ɞɨ N
ɜɜɨɞ a[i]
ɤɰ
…
ȼ ɤɚɱɟɫɬɜɟ ɨɬɜɟɬɚ ȼɚɦ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɜɟɫɬɢ ɮɪɚɝɦɟɧɬ ɩɪɨɝɪɚɦɦɵ, ɤɨɬɨɪɵɣ
ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɧɚ ɦɟɫɬɟ ɦɧɨɝɨɬɨɱɢɹ. ȼɵ ɦɨɠɟɬɟ ɡɚɩɢɫɚɬɶ ɪɟɲɟɧɢɟ ɬɚɤɠɟ
ɧɚ ɞɪɭɝɨɦ ɹɡɵɤɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ (ɭɤɚɠɢɬɟ ɧɚɡɜɚɧɢɟ ɢ ɢɫɩɨɥɶɡɭɟɦɭɸ
ɜɟɪɫɢɸ ɹɡɵɤɚ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɧɚɩɪɢɦɟɪ Free Pascal 2.4) ɢɥɢ ɜ ɜɢɞɟ ɛɥɨɤɫɯɟɦɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ȼɵ ɞɨɥɠɧɵ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɟ ɠɟ ɫɚɦɵɟ ɢɫɯɨɞɧɵɟ
ɞɚɧɧɵɟ ɢ ɩɟɪɟɦɟɧɧɵɟ, ɤɚɤɢɟ ɛɵɥɢ ɩɪɟɞɥɨɠɟɧɵ ɜ ɭɫɥɨɜɢɢ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
6
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
7
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
ȼ ɡɚɞɚɱɟ ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɦɢɧɢɦɚɥɶɧɵɣ ɫɪɟɞɢ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ
ɡɚɞɚɧɧɨɦɭ ɜ ɭɫɥɨɜɢɢ ɨɝɪɚɧɢɱɟɧɢɸ. ɉɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɬɚɧɞɚɪɬɧɨɣ ɡɚɞɚɱɟɣ ɩɨɢɫɤɚ
ɦɢɧɢɦɚɥɶɧɨɝɨ ɫɪɟɞɢ ɜɫɟɯ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ ɞɨɩɨɥɧɢɬɟɥɶɧɚɹ ɫɥɨɠɧɨɫɬɶ ɞɚɧɧɨɣ
ɡɚɞɚɱɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɧɟɥɶɡɹ ɛɪɚɬɶ ɜ ɤɚɱɟɫɬɜɟ ɩɟɪɜɨɝɨ ɡɧɚɱɟɧɢɹ ɦɢɧɢɦɭɦɚ
ɩɟɪɜɵɣ ɷɥɟɦɟɧɬ ɦɚɫɫɢɜɚ, ɬɚɤ ɤɚɤ ɷɬɨɬ ɷɥɟɦɟɧɬ ɦɨɠɟɬ ɧɟ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɡɚɞɚɧɧɵɦ
ɨɝɪɚɧɢɱɟɧɢɹɦ. ɇɟɥɶɡɹ ɬɚɤɠɟ ɩɪɢɧɹɬɶ ɜ ɤɚɱɟɫɬɜɟ ɩɟɪɜɨɝɨ ɡɧɚɱɟɧɢɹ ɛɨɥɶɲɨɟ ɱɢɫɥɨ,
ɡɚɜɟɞɨɦɨ ɩɪɟɜɨɫɯɨɞɹɳɟɟ ɜɫɟ ɜɨɡɦɨɠɧɵɟ ɡɧɚɱɟɧɢɹ ɞɚɧɧɵɯ, ɬɚɤ ɤɚɤ ɜ ɭɫɥɨɜɢɢ ɧɟ ɭɤɚɡɚɧ
ɞɢɚɩɚɡɨɧ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ.
ɇɢɠɟ
ɩɪɟɞɫɬɚɜɥɟɧɵ
ɧɟɫɤɨɥɶɤɨ
ɜɨɡɦɨɠɧɵɯ
ɫɩɨɫɨɛɨɜ
ɪɟɲɟɧɢɹ
ɡɚɞɚɱɢ,
ɩɪɨɢɥɥɸɫɬɪɢɪɨɜɚɧɧɵɟ ɮɪɚɝɦɟɧɬɚɦɢ ɩɪɨɝɪɚɦɦ ɧɚ ɪɚɡɧɵɯ ɹɡɵɤɚɯ. ɋɩɨɫɨɛɵ ɪɟɲɟɧɢɹ ɧɟ
ɩɪɢɜɹɡɚɧɵ ɤ ɹɡɵɤɚɦ: ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɫɩɨɫɨɛɨɜ ɦɨɠɟɬ ɛɵɬɶ ɪɟɚɥɢɡɨɜɚɧ ɧɚ ɥɸɛɨɦ
ɞɨɩɭɫɬɢɦɨɦ ɹɡɵɤɟ.
ɋɩɨɫɨɛ 1.
ȼ ɤɚɱɟɫɬɜɟ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɦɢɧɢɦɭɦɚ ɩɪɢɧɢɦɚɟɬɫɹ ɡɧɚɱɟɧɢɟ, ɡɚɜɟɞɨɦɨ ɧɟ
ɩɨɞɯɨɞɹɳɟɟ ɩɨɞ ɡɚɞɚɧɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ, ɧɚɩɪɢɦɟɪ 0.
ɉɪɢɦɟɪ ɩɪɨɝɪɚɦɦɵ ɧɚ ɉɚɫɤɚɥɟ
m:=0;
for i:=1 to N do begin
if (a[i]>0) and (a[i] mod 10=7) and ((m=0) or (a[i]<m))
then m := a[i];
end;
writeln(m);
ɋɩɨɫɨɛ 2.
ȼɦɟɫɬɨ ɩɪɨɜɟɪɤɢ ɫɩɟɰɢɚɥɶɧɨɝɨ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɬɞɟɥɶɧɚɹ
ɩɟɪɟɦɟɧɧɚɹ, ɩɨɤɚɡɵɜɚɸɳɚɹ, ɛɵɥ ɥɢ ɭɠɟ ɧɚɣɞɟɧ ɯɨɬɹ ɛɵ ɨɞɢɧ ɩɨɞɯɨɞɹɳɢɣ ɩɨɞ
ɨɝɪɚɧɢɱɟɧɢɹ ɷɥɟɦɟɧɬ. Ⱦɥɹ ɷɬɨɣ ɩɟɪɟɦɟɧɧɨɣ ɫɥɟɞɨɜɚɥɨ ɛɵ ɢɫɩɨɥɶɡɨɜɚɬɶ ɥɨɝɢɱɟɫɤɢɣ
ɬɢɩ, ɧɨ ɜ ɭɫɥɨɜɢɢ ɪɚɡɪɟɲɟɧɵ ɬɨɥɶɤɨ ɰɟɥɵɟ ɩɟɪɟɦɟɧɧɵɟ, ɩɨɷɬɨɦɭ ɥɨɝɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ
ɦɨɞɟɥɢɪɭɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɰɟɥɨɝɨ.
ɉɪɢɦɟɪ ɩɪɨɝɪɚɦɦɵ ɧɚ Ȼɟɣɫɢɤɟ
M = 0: J = 0
FOR I = 1 TO N
IF A(I)>0 AND A(i) MOD 10 = 7 AND (J = 0 OR A(I) < M) THEN
M = A(I)
J = 1
END IF
NEXT I
PRINT M
ɋɩɨɫɨɛ 3.
ɋɧɚɱɚɥɚ ɜ ɦɚɫɫɢɜɟ ɢɳɟɬɫɹ ɩɟɪɜɵɣ ɷɥɟɦɟɧɬ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɨɝɪɚɧɢɱɟɧɢɹɦ. Ɂɚɬɟɦ
ɜ ɨɫɬɚɜɲɟɣɫɹ ɱɚɫɬɢ ɦɚɫɫɢɜɚ ɢɳɟɬɫɹ ɩɨɞɯɨɞɹɳɢɣ ɧɚɢɦɟɧɶɲɢɣ ɷɥɟɦɟɧɬ. ɗɬɨɬ ɫɩɨɫɨɛ
ɩɪɢɜɨɞɢɬ ɤ ɛɨɥɟɟ ɞɥɢɧɧɨɣ (ɬɪɟɛɭɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɜɚ ɰɢɤɥɚ), ɧɨ ɧɟ ɦɟɧɟɟ
ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɟ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɉɪɢɦɟɪ ɩɪɨɝɪɚɦɦɵ ɧɚ ɚɥɝɨɪɢɬɦɢɱɟɫɤɨɦ ɹɡɵɤɟ
i:=1
ɧɰ ɩɨɤɚ ɧɟ (a[i]>0 ɢ mod(a[i],10)=7)
i := i+1
ɤɰ
m := a[i]
ɧɰ ɞɥɹ i ɨɬ i+1 ɞɨ N
ɟɫɥɢ a[i]>0 ɢ mod(a[i],10)=7 ɢ a[i]<m
ɬɨ m:=a[i]
ɜɫɟ
ɤɰ
ɜɵɜɨɞ m
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɟɞɥɨɠɟɧ ɩɪɚɜɢɥɶɧɵɣ ɚɥɝɨɪɢɬɦ, ɜɵɞɚɸɳɢɣ ɜɟɪɧɨɟ ɡɧɚɱɟɧɢɟ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɡɚɩɢɫɶ ɚɥɝɨɪɢɬɦɚ ɧɚ ɞɪɭɝɨɦ ɹɡɵɤɟ, ɢɫɩɨɥɶɡɭɸɳɚɹ ɚɧɚɥɨɝɢɱɧɵɟ
ɩɟɪɟɦɟɧɧɵɟ. ȼ ɫɥɭɱɚɟ ɟɫɥɢ ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɢɫɩɨɥɶɡɭɟɬ
ɬɢɩɢɡɢɪɨɜɚɧɧɵɟ ɩɟɪɟɦɟɧɧɵɟ, ɨɩɢɫɚɧɢɹ ɩɟɪɟɦɟɧɧɵɯ ɞɨɥɠɧɵ ɛɵɬɶ
ɚɧɚɥɨɝɢɱɧɵ ɨɩɢɫɚɧɢɹɦ ɩɟɪɟɦɟɧɧɵɯ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɦ ɹɡɵɤɟ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ
2
ɧɟɬɢɩɢɡɢɪɨɜɚɧɧɵɯ ɢɥɢ ɧɟɨɛɴɹɜɥɟɧɧɵɯ ɩɟɪɟɦɟɧɧɵɯ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ
ɜ ɫɥɭɱɚɟ, ɟɫɥɢ ɷɬɨ ɞɨɩɭɫɤɚɟɬɫɹ ɹɡɵɤɨɦ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɩɪɢ ɷɬɨɦ
ɤɨɥɢɱɟɫɬɜɨ ɩɟɪɟɦɟɧɧɵɯ ɢ ɢɯ ɢɞɟɧɬɢɮɢɤɚɬɨɪɵ ɞɨɥɠɧɵ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ
ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ. ȼ ɚɥɝɨɪɢɬɦɟ, ɡɚɩɢɫɚɧɧɨɦ ɧɚ ɹɡɵɤɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ,
ɞɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬɞɟɥɶɧɵɯ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ ɨɲɢɛɨɤ, ɧɟ ɢɫɤɚɠɚɸɳɢɯ
ɡɚɦɵɫɥɚ ɚɜɬɨɪɚ ɩɪɨɝɪɚɦɦɵ.
ȼ ɥɸɛɨɦ ɜɚɪɢɚɧɬɟ ɪɟɲɟɧɢɹ ɦɨɠɟɬ ɩɪɢɫɭɬɫɬɜɨɜɚɬɶ ɧɟ ɛɨɥɟɟ ɨɞɧɨɣ ɨɲɢɛɤɢ ɢɡ
ɱɢɫɥɚ ɫɥɟɞɭɸɳɢɯ:
1) ɇɟ ɢɧɢɰɢɚɥɢɡɢɪɭɟɬɫɹ ɢɥɢ ɧɟɜɟɪɧɨ ɢɧɢɰɢɚɥɢɡɢɪɭɟɬɫɹ ɩɟɪɟɦɟɧɧɚɹ m.
ȼ ɱɚɫɬɧɨɫɬɢ, ɧɟɥɶɡɹ ɢɧɢɰɢɚɥɢɡɢɪɨɜɚɬɶ ɷɬɭ ɩɟɪɟɦɟɧɧɭɸ ɩɟɪɜɵɦ ɷɥɟɦɟɧɬɨɦ
ɦɚɫɫɢɜɚ. ɇɟɥɶɡɹ ɬɚɤɠɟ ɢɧɢɰɢɚɥɢɡɢɪɨɜɚɬɶ ɟɺ ɤɚɤɢɦ-ɬɨ ɨɱɟɧɶ ɛɨɥɶɲɢɦ
ɡɧɚɱɟɧɢɟɦ (ɧɚɩɪɢɦɟɪ, maxInt ɜ ɉɚɫɤɚɥɟ)
2) ɇɟɜɟɪɧɨ ɩɪɨɜɟɪɹɟɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨɫɬɶ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ
3) ɇɟɜɟɪɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɫɥɟɞɧɹɹ ɰɢɮɪɚ ɞɟɫɹɬɢɱɧɨɣ ɡɚɩɢɫɢ ɱɢɫɥɚ
4) ȼ ɫɥɨɠɧɨɦ ɥɨɝɢɱɟɫɤɨɦ ɭɫɥɨɜɢɢ ɩɪɨɫɬɵɟ ɩɪɨɜɟɪɤɢ ɜɟɪɧɵ, ɧɨ ɭɫɥɨɜɢɟ
1
ɜ ɰɟɥɨɦ ɩɨɫɬɪɨɟɧɨ ɧɟɜɟɪɧɨ (ɧɚɩɪɢɦɟɪ, ɩɟɪɟɩɭɬɚɧɵ ɨɩɟɪɚɰɢɢ ɂ ɢ ɂɅɂ,
ɧɟɜɟɪɧɨ ɪɚɫɫɬɚɜɥɟɧɵ ɫɤɨɛɤɢ ɜ ɥɨɝɢɱɟɫɤɨɦ ɜɵɪɚɠɟɧɢɢ).
5) ȼɦɟɫɬɨ ɡɧɚɱɟɧɢɹ ɷɥɟɦɟɧɬɚ ɩɪɨɜɟɪɹɟɬɫɹ ɟɝɨ ɢɧɞɟɤɫ.
6) Ɉɬɫɭɬɫɬɜɭɟɬ ɜɵɜɨɞ ɨɬɜɟɬɚ.
7)
ɂɫɩɨɥɶɡɭɟɬɫɹ ɩɟɪɟɦɟɧɧɚɹ, ɧɟ ɨɛɴɹɜɥɟɧɧɚɹ ɜ ɪɚɡɞɟɥɟ ɨɩɢɫɚɧɢɹ
ɩɟɪɟɦɟɧɧɵɯ.
8) ɇɟ ɭɤɚɡɚɧɨ ɢɥɢ ɧɟɜɟɪɧɨ ɭɤɚɡɚɧɨ ɭɫɥɨɜɢɟ ɡɚɜɟɪɲɟɧɢɹ ɰɢɤɥɚ.
9) ɂɧɞɟɤɫɧɚɹ ɩɟɪɟɦɟɧɧɚɹ ɜ ɰɢɤɥɟ ɧɟ ɦɟɧɹɟɬɫɹ (ɧɚɩɪɢɦɟɪ, ɜ ɰɢɤɥɟ while)
ɢɥɢ ɦɟɧɹɟɬɫɹ ɧɟɜɟɪɧɨ.
Ɉɲɢɛɨɤ, ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜ ɩ. 1–9, ɞɜɟ ɢɥɢ ɛɨɥɶɲɟ, ɢɥɢ ɚɥɝɨɪɢɬɦ
0
ɫɮɨɪɦɭɥɢɪɨɜɚɧ ɧɟɜɟɪɧɨ.
2
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
8
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
C3
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
9
Ⱦɜɚ ɢɝɪɨɤɚ, ɉɚɲɚ ɢ ȼɨɜɚ, ɢɝɪɚɸɬ ɜ ɫɥɟɞɭɸɳɭɸ ɢɝɪɭ. ɉɟɪɟɞ ɢɝɪɨɤɚɦɢ ɥɟɠɢɬ
ɤɭɱɚ ɤɚɦɧɟɣ. ɂɝɪɨɤɢ ɯɨɞɹɬ ɩɨ ɨɱɟɪɟɞɢ, ɩɟɪɜɵɣ ɯɨɞ ɞɟɥɚɟɬ ɉɚɲɚ. Ɂɚ ɨɞɢɧ ɯɨɞ
ɢɝɪɨɤ ɦɨɠɟɬ ɞɨɛɚɜɢɬɶ ɜ ɤɭɱɭ 1 ɤɚɦɟɧɶ ɢɥɢ 10 ɤɚɦɧɟɣ. ɇɚɩɪɢɦɟɪ, ɢɦɟɹ ɤɭɱɭ
ɢɡ 7 ɤɚɦɧɟɣ, ɡɚ ɨɞɢɧ ɯɨɞ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɤɭɱɭ ɢɡ 8 ɢɥɢ 17 ɤɚɦɧɟɣ. ɍ ɤɚɠɞɨɝɨ
ɢɝɪɨɤɚ, ɱɬɨɛɵ ɞɟɥɚɬɶ ɯɨɞɵ, ɟɫɬɶ ɧɟɨɝɪɚɧɢɱɟɧɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ.
ɂɝɪɚ ɡɚɜɟɪɲɚɟɬɫɹ ɜ ɬɨɬ ɦɨɦɟɧɬ, ɤɨɝɞɚ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ ɜ ɤɭɱɟ ɫɬɚɧɨɜɢɬɫɹ
ɧɟ ɦɟɧɟɟ 31. ɉɨɛɟɞɢɬɟɥɟɦ ɫɱɢɬɚɟɬɫɹ ɢɝɪɨɤ, ɫɞɟɥɚɜɲɢɣ ɩɨɫɥɟɞɧɢɣ ɯɨɞ, ɬɨ ɟɫɬɶ
ɩɟɪɜɵɦ ɩɨɥɭɱɢɜɲɢɣ ɤɭɱɭ, ɜ ɤɨɬɨɪɨɣ ɛɭɞɟɬ 31 ɢɥɢ ɛɨɥɶɲɟ ɤɚɦɧɟɣ.
ȼ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜ ɤɭɱɟ ɛɵɥɨ S ɤɚɦɧɟɣ, 1 S30.
Ȼɭɞɟɦ ɝɨɜɨɪɢɬɶ, ɱɬɨ ɢɝɪɨɤ ɢɦɟɟɬ ɜɵɢɝɪɵɲɧɭɸ ɫɬɪɚɬɟɝɢɸ, ɟɫɥɢ ɨɧ ɦɨɠɟɬ
ɜɵɢɝɪɚɬɶ ɩɪɢ ɥɸɛɵɯ ɯɨɞɚɯ ɩɪɨɬɢɜɧɢɤɚ. Ɉɩɢɫɚɬɶ ɫɬɪɚɬɟɝɢɸ ɢɝɪɨɤɚ – ɡɧɚɱɢɬ
ɨɩɢɫɚɬɶ, ɤɚɤɨɣ ɯɨɞ ɨɧ ɞɨɥɠɟɧ ɫɞɟɥɚɬɶ ɜ ɥɸɛɨɣ ɫɢɬɭɚɰɢɢ, ɤɨɬɨɪɚɹ ɟɦɭ ɦɨɠɟɬ
ɜɫɬɪɟɬɢɬɶɫɹ ɩɪɢ ɪɚɡɥɢɱɧɨɣ ɢɝɪɟ ɩɪɨɬɢɜɧɢɤɚ.
ȼɵɩɨɥɧɢɬɟ ɫɥɟɞɭɸɳɢɟ ɡɚɞɚɧɢɹ. ȼɨ ɜɫɟɯ ɫɥɭɱɚɹɯ ɨɛɨɫɧɨɜɵɜɚɣɬɟ ɫɜɨɣ ɨɬɜɟɬ.
1. ɚ) ɍɤɚɠɢɬɟ ɜɫɟ ɬɚɤɢɟ ɡɧɚɱɟɧɢɹ ɱɢɫɥɚ S, ɩɪɢ ɤɨɬɨɪɵɯ ɉɚɲɚ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ
ɜ ɨɞɢɧ ɯɨɞ. Ɉɛɨɫɧɭɣɬɟ, ɱɬɨ ɧɚɣɞɟɧɵ ɜɫɟ ɧɭɠɧɵɟ ɡɧɚɱɟɧɢɹ S, ɢ ɭɤɚɠɢɬɟ
ɜɵɢɝɪɵɜɚɸɳɢɟ ɯɨɞɵ.
ɛ) ɍɤɚɠɢɬɟ ɬɚɤɨɟ ɡɧɚɱɟɧɢɟ S, ɩɪɢ ɤɨɬɨɪɨɦ ɉɚɲɚ ɧɟ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɡɚ ɨɞɢɧ
ɯɨɞ, ɧɨ ɩɪɢ ɥɸɛɨɦ ɯɨɞɟ ɉɚɲɢ ȼɨɜɚ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɫɜɨɢɦ ɩɟɪɜɵɦ ɯɨɞɨɦ.
Ɉɩɢɲɢɬɟ ɜɵɢɝɪɵɲɧɭɸ ɫɬɪɚɬɟɝɢɸ ȼɨɜɵ.
2. ɍɤɚɠɢɬɟ ɞɜɚ ɡɧɚɱɟɧɢɹ S, ɩɪɢ ɤɨɬɨɪɵɯ ɭ ɉɚɲɢ ɟɫɬɶ ɜɵɢɝɪɵɲɧɚɹ ɫɬɪɚɬɟɝɢɹ,
ɩɪɢɱɺɦ ɉɚɲɚ ɧɟ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɡɚ ɨɞɢɧ ɯɨɞ, ɧɨ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɫɜɨɢɦ
ɜɬɨɪɵɦ ɯɨɞɨɦ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɬɨɝɨ, ɤɚɤ ɛɭɞɟɬ ɯɨɞɢɬɶ ȼɨɜɚ. Ⱦɥɹ ɭɤɚɡɚɧɧɵɯ
ɡɧɚɱɟɧɢɣ S ɨɩɢɲɢɬɟ ɜɵɢɝɪɵɲɧɭɸ ɫɬɪɚɬɟɝɢɸ ɉɚɲɢ.
3. ɍɤɚɠɢɬɟ ɡɧɚɱɟɧɢɟ S, ɩɪɢ ɤɨɬɨɪɨɦ ɭ ȼɨɜɵ ɟɫɬɶ ɜɵɢɝɪɵɲɧɚɹ ɫɬɪɚɬɟɝɢɹ,
ɩɨɡɜɨɥɹɸɳɚɹ ɟɦɭ ɜɵɢɝɪɚɬɶ ɩɟɪɜɵɦ ɢɥɢ ɜɬɨɪɵɦ ɯɨɞɨɦ ɩɪɢ ɥɸɛɨɣ ɢɝɪɟ ɉɚɲɢ,
ɨɞɧɚɤɨ ɭ ȼɨɜɵ ɧɟɬ ɫɬɪɚɬɟɝɢɢ, ɤɨɬɨɪɚɹ ɩɨɡɜɨɥɢɬ ɟɦɭ ɝɚɪɚɧɬɢɪɨɜɚɧɧɨ ɜɵɢɝɪɚɬɶ
ɩɟɪɜɵɦ ɯɨɞɨɦ. Ⱦɥɹ ɭɤɚɡɚɧɧɨɝɨ ɡɧɚɱɟɧɢɹ S ɨɩɢɲɢɬɟ ɜɵɢɝɪɵɲɧɭɸ ɫɬɪɚɬɟɝɢɸ
ȼɨɜɵ. ɉɨɫɬɪɨɣɬɟ ɞɟɪɟɜɨ ɜɫɟɯ ɩɚɪɬɢɣ, ɜɨɡɦɨɠɧɵɯ ɩɪɢ ɷɬɨɣ ɜɵɢɝɪɵɲɧɨɣ
ɫɬɪɚɬɟɝɢɢ ȼɨɜɵ (ɜ ɜɢɞɟ ɪɢɫɭɧɤɚ ɢɥɢ ɬɚɛɥɢɰɵ). ɇɚ ɪɟɛɪɚɯ ɞɟɪɟɜɚ ɭɤɚɡɵɜɚɣɬɟ,
ɤɬɨ ɞɟɥɚɟɬ ɯɨɞ, ɜ ɭɡɥɚɯ – ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ ɜ ɤɭɱɟ.
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
1. ɚ) ɉɚɲɚ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɩɟɪɜɵɦ ɯɨɞɨɦ, ɟɫɥɢ S =21, …, 30. ȼɨ ɜɫɟɯ ɫɥɭɱɚɹɯ ɦɨɠɧɨ
ɞɨɛɚɜɢɬɶ ɜ ɤɭɱɭ 10 ɤɚɦɧɟɣ. ɉɪɢ ɦɟɧɶɲɢɯ ɡɧɚɱɟɧɢɹɯ S ɡɚ ɨɞɢɧ ɯɨɞ ɧɟɥɶɡɹ ɩɨɥɭɱɢɬɶ
ɤɭɱɭ, ɜ ɤɨɬɨɪɨɣ ɛɨɥɶɲɟ 30 ɤɚɦɧɟɣ.
ɛ) ȼɨɜɚ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɩɟɪɜɵɦ ɯɨɞɨɦ (ɤɚɤ ɛɵ ɧɢ ɢɝɪɚɥ ɉɚɲɚ), ɟɫɥɢ ɢɫɯɨɞɧɨ ɜ ɤɭɱɟ
ɛɭɞɟɬ S=20 ɤɚɦɧɟɣ. Ɍɨɝɞɚ ɩɨɫɥɟ ɩɟɪɜɨɝɨ ɯɨɞɚ ɉɚɲɢ ɜ ɤɭɱɟ ɛɭɞɟɬ 21 ɤɚɦɟɧɶ ɢɥɢ 30
ɤɚɦɧɟɣ. ȼ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ȼɨɜɚ ɦɨɠɟɬ ɞɨɛɚɜɢɬɶ ɜ ɤɭɱɭ 10 ɤɚɦɧɟɣ ɢ ɜɵɢɝɪɚɬɶ ɩɟɪɜɵɦ
ɯɨɞɨɦ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
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2. ȼɨɡɦɨɠɧɵɟ ɡɧɚɱɟɧɢɹ S: 10 ɢ 19. ȼ ɷɬɢɯ ɫɥɭɱɚɹɯ ɉɚɲɚ, ɨɱɟɜɢɞɧɨ, ɧɟ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ
ɩɟɪɜɵɦ ɯɨɞɨɦ. Ɉɞɧɚɤɨ ɨɧ ɦɨɠɟɬ ɩɨɥɭɱɢɬɶ ɤɭɱɭ ɢɡ 20 ɤɚɦɧɟɣ. ɗɬɚ ɩɨɡɢɰɢɹ ɪɚɡɨɛɪɚɧɚ ɜ
ɩ. 1ɛ. ȼ ɧɟɣ ɢɝɪɨɤ, ɤɨɬɨɪɵɣ ɛɭɞɟɬ ɯɨɞɢɬɶ (ɬɟɩɟɪɶ ɷɬɨ ȼɨɜɚ), ɜɵɢɝɪɚɬɶ ɧɟ ɦɨɠɟɬ, ɚ ɟɝɨ
ɩɪɨɬɢɜɧɢɤ (ɬɨ ɟɫɬɶ ɉɚɲɚ) ɫɥɟɞɭɸɳɢɦ ɯɨɞɨɦ ɜɵɢɝɪɚɟɬ.
3. ȼɨɡɦɨɠɧɨɟ ɡɧɚɱɟɧɢɟ S: 18. ɉɨɫɥɟ ɩɟɪɜɨɝɨ ɯɨɞɚ ɉɚɲɢ ɜ ɤɭɱɟ ɛɭɞɟɬ 19 ɢɥɢ 28 ɤɚɦɧɟɣ.
ȿɫɥɢ ɜ ɤɭɱɟ ɫɬɚɧɟɬ 28 ɤɚɦɧɟɣ, ȼɨɜɚ ɞɨɛɚɜɢɬ ɜ ɤɭɱɭ 10 ɤɚɦɧɟɣ ɢ ɜɵɢɝɪɚɟɬ ɩɟɪɜɵɦ
ɯɨɞɨɦ. ɋɢɬɭɚɰɢɹ, ɤɨɝɞɚ ɜ ɤɭɱɟ 19 ɤɚɦɧɟɣ, ɪɚɡɨɛɪɚɧɚ ɜ ɩ. 2. ȼ ɷɬɨɣ ɫɢɬɭɚɰɢɢ ɢɝɪɨɤ,
ɤɨɬɨɪɵɣ ɛɭɞɟɬ ɯɨɞɢɬɶ (ɬɟɩɟɪɶ ɷɬɨ ȼɨɜɚ), ɜɵɢɝɪɵɜɚɟɬ ɫɜɨɢɦ ɜɬɨɪɵɦ ɯɨɞɨɦ.
ȼ ɬɚɛɥɢɰɟ ɢɡɨɛɪɚɠɟɧɨ ɞɟɪɟɜɨ ɜɨɡɦɨɠɧɵɯ ɩɚɪɬɢɣ ɩɪɢ ɨɩɢɫɚɧɧɨɣ ɫɬɪɚɬɟɝɢɢ ȼɨɜɵ.
Ɂɚɤɥɸɱɢɬɟɥɶɧɵɟ ɩɨɡɢɰɢɢ (ɜ ɧɢɯ ɜɵɢɝɪɵɜɚɟɬ ȼɨɜɚ) ɩɨɞɱɺɪɤɧɭɬɵ. ɇɚ ɪɢɫɭɧɤɟ ɷɬɨ ɠɟ
ɞɟɪɟɜɨ ɢɡɨɛɪɚɠɟɧɨ ɜ ɝɪɚɮɢɱɟɫɤɨɦ ɜɢɞɟ (ɨɛɚ ɫɩɨɫɨɛɚ ɢɡɨɛɪɚɠɟɧɢɹ ɞɟɪɟɜɚ ɞɨɩɭɫɬɢɦɵ).
ɉɨɥɨɠɟɧɢɹ ɩɨɫɥɟ ɨɱɟɪɟɞɧɵɯ ɯɨɞɨɜ
1-ɣ ɯɨɞ ɉɚɲɢ 1-ɣ ɯɨɞ ȼɨɜɵ 2-ɣ ɯɨɞ ɉɚɲɢ 2-ɣ ɯɨɞ ȼɨɜɵ
ɂɫɯɨɞɧɚɹ (ɪɚɡɨɛɪɚɧɵ ɜɫɟ (ɬɨɥɶɤɨ ɯɨɞ ɩɨ (ɪɚɡɨɛɪɚɧɵ ɜɫɟ (ɬɨɥɶɤɨ ɯɨɞ ɩɨ
ɩɨɡɢɰɢɹ
ɯɨɞɵ)
ɫɬɪɚɬɟɝɢɢ)
ɯɨɞɵ)
ɫɬɪɚɬɟɝɢɢ)
20+1=21
21+10=31
18+1 =19
19+1=20
18
20+10=30
30+10=40
18+10=28
28+10=38
Ɋɢɫ. 1. Ⱦɟɪɟɜɨ ɜɫɟɯ ɩɚɪɬɢɣ, ɜɨɡɦɨɠɧɵɯ ɩɪɢ ȼɨɜɢɧɨɣ ɫɬɪɚɬɟɝɢɢ.
Ɂɧɚɤɨɦ >> ɨɛɨɡɧɚɱɟɧɵ ɩɨɡɢɰɢɢ, ɜ ɤɨɬɨɪɵɯ ɩɚɪɬɢɹ ɡɚɤɚɧɱɢɜɚɟɬɫɹ
ȼ ɡɚɞɚɱɟ ɨɬ ɭɱɟɧɢɤɚ ɬɪɟɛɭɟɬɫɹ ɜɵɩɨɥɧɢɬɶ 3 ɡɚɞɚɧɢɹ. ɂɯ ɬɪɭɞɧɨɫɬɶ ɜɨɡɪɚɫɬɚɟɬ.
Ʉɨɥɢɱɟɫɬɜɨ ɛɚɥɥɨɜ ɜ ɰɟɥɨɦ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɨɥɢɱɟɫɬɜɭ ɜɵɩɨɥɧɟɧɧɵɯ ɡɚɞɚɧɢɣ
(ɩɨɞɪɨɛɧɟɟ ɫɦ. ɧɢɠɟ).
Ɉɲɢɛɤɚ ɜ ɪɟɲɟɧɢɢ, ɧɟ ɢɫɤɚɠɚɸɳɚɹ ɨɫɧɨɜɧɨɝɨ ɡɚɦɵɫɥɚ, ɧɚɩɪɢɦɟɪ ɚɪɢɮɦɟɬɢɱɟɫɤɚɹ
ɨɲɢɛɤɚ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɤɨɥɢɱɟɫɬɜɚ ɤɚɦɧɟɣ ɜ ɡɚɤɥɸɱɢɬɟɥɶɧɨɣ ɩɨɡɢɰɢɢ ɩɪɢ ɨɰɟɧɤɟ
ɪɟɲɟɧɢɹ ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
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ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɜɵɩɨɥɧɟɧɵ ɨɛɚ ɩɭɧɤɬɚ ɚ) ɢ ɛ). ɉɭɧɤɬ ɚ)
ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɵ ɜɫɟ ɩɨɡɢɰɢɢ, ɜ ɤɨɬɨɪɵɯ ɉɚɲɚ
ɜɵɢɝɪɵɜɚɟɬ ɩɟɪɜɵɦ ɯɨɞɨɦ, ɢ ɭɤɚɡɚɧɨ, ɤɚɤɢɦ ɞɨɥɠɟɧ ɛɵɬɶ ɩɟɪɜɵɣ ɯɨɞ. ɉɭɧɤɬ ɛ)
ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɚ ɩɨɡɢɰɢɹ, ɜ ɤɨɬɨɪɨɣ ȼɨɜɚ ɜɵɢɝɪɵɜɚɟɬ
ɩɟɪɜɵɦ ɯɨɞɨɦ, ɢ ɨɩɢɫɚɧɚ ɫɬɪɚɬɟɝɢɹ ȼɨɜɵ, ɬ. ɟ. ɩɨɤɚɡɚɧɨ, ɤɚɤ ȼɨɜɚ ɦɨɠɟɬ ɩɨɥɭɱɢɬɶ
ɤɭɱɭ, ɜ ɤɨɬɨɪɨɣ ɫɨɞɟɪɠɢɬɫɹ ɧɭɠɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ, ɩɪɢ ɥɸɛɨɦ ɯɨɞɟ ɉɚɲɢ.
ɉɭɧɤɬ ɚ) ɩɟɪɜɨɝɨ ɡɚɞɚɧɢɹ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ ɱɚɫɬɢɱɧɨ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɵ
ɜɫɟ ɩɨɡɢɰɢɢ, ɜ ɤɨɬɨɪɵɯ ɉɚɲɚ ɜɵɢɝɪɵɜɚɟɬ ɩɟɪɜɵɦ ɯɨɞɨɦ. ɉɭɧɤɬ ɛ) ɩɟɪɜɨɝɨ ɡɚɞɚɧɢɹ
ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ ɱɚɫɬɢɱɧɨ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɚ ɩɨɡɢɰɢɹ, ɜ ɤɨɬɨɪɨɣ ȼɨɜɚ
ɜɵɢɝɪɵɜɚɟɬ ɩɟɪɜɵɦ ɯɨɞɨɦ ɢ ɹɜɧɨ ɫɤɚɡɚɧɨ, ɱɬɨ ɩɪɢ ɥɸɛɨɦ ɯɨɞɟ ɉɚɲɢ ȼɨɜɚ ɦɨɠɟɬ
ɩɨɥɭɱɢɬɶ ɤɭɱɭ, ɤɨɬɨɪɚɹ ɫɨɞɟɪɠɢɬ ɧɭɠɧɨɟ ɞɥɹ ɜɵɢɝɪɵɲɚ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ.
ȼɬɨɪɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɵ ɨɛɟ ɩɨɡɢɰɢɢ, ɜɵɢɝɪɵɲɧɵɟ ɞɥɹ
ɉɚɲɢ, ɢ ɨɩɢɫɚɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɫɬɪɚɬɟɝɢɹ ɉɚɲɢ – ɬɚɤ, ɤɚɤ ɷɬɨ ɧɚɩɢɫɚɧɨ ɜ ɩɪɢɦɟɪɟ
ɪɟɲɟɧɢɹ, ɢɥɢ ɞɪɭɝɢɦ ɫɩɨɫɨɛɨɦ, ɧɚɩɪɢɦɟɪ ɫ ɩɨɦɨɳɶɸ ɞɟɪɟɜɚ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɩɚɪɬɢɣ.
Ɍɪɟɬɶɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɚ ɩɨɡɢɰɢɹ, ɜɵɢɝɪɵɲɧɚɹ ɞɥɹ ȼɨɜɵ, ɢ
ɩɨɫɬɪɨɟɧɨ ɞɟɪɟɜɨ ɜɫɟɯ ɩɚɪɬɢɣ, ɜɨɡɦɨɠɧɵɯ ɩɪɢ ȼɨɜɢɧɨɣ ɫɬɪɚɬɟɝɢɢ. Ⱦɨɥɠɧɨ ɛɵɬɶ ɹɜɧɨ
ɫɤɚɡɚɧɨ, ɱɬɨ ɜ ɷɬɨɦ ɞɟɪɟɜɟ ɜ ɤɚɠɞɨɣ ɩɨɡɢɰɢɢ, ɝɞɟ ɞɨɥɠɟɧ ɯɨɞɢɬɶ ɉɚɲɚ, ɪɚɡɨɛɪɚɧɵ ɜɫɟ
ɜɨɡɦɨɠɧɵɟ ɯɨɞɵ, ɚ ɞɥɹ ɩɨɡɢɰɢɣ, ɝɞɟ ɞɨɥɠɟɧ ɯɨɞɢɬɶ ȼɨɜɚ, – ɬɨɥɶɤɨ ɯɨɞ,
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɫɬɪɚɬɟɝɢɢ, ɤɨɬɨɪɭɸ ɜɵɛɪɚɥ ȼɨɜɚ.
ȼɨ ɜɫɟɯ ɫɥɭɱɚɹɯ ɫɬɪɚɬɟɝɢɢ ɦɨɝɭɬ ɛɵɬɶ ɨɩɢɫɚɧɵ ɬɚɤ, ɤɚɤ ɷɬɨ ɫɞɟɥɚɧɨ ɜ ɩɪɢɦɟɪɟ
ɪɟɲɟɧɢɹ, ɢɥɢ ɞɪɭɝɢɦ ɫɩɨɫɨɛɨɦ.
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ȼɵɩɨɥɧɟɧɵ ɜɬɨɪɨɟ ɢ ɬɪɟɬɶɟ ɡɚɞɚɧɢɹ. ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ
ɩɨɥɧɨɫɬɶɸ ɢɥɢ ɱɚɫɬɢɱɧɨ. Ɂɞɟɫɶ ɢ ɞɚɥɟɟ ɞɨɩɭɫɤɚɸɬɫɹ ɚɪɢɮɦɟɬɢɱɟɫɤɢɟ
3
ɨɲɢɛɤɢ, ɤɨɬɨɪɵɟ ɧɟ ɢɫɤɚɠɚɸɬ ɫɭɬɢ ɪɟɲɟɧɢɹ ɢ ɧɟ ɩɪɢɜɨɞɹɬ
ɤ ɧɟɩɪɚɜɢɥɶɧɨɦɭ ɨɬɜɟɬɭ (ɫɦ. ɜɵɲɟ).
ɇɟ ɜɵɩɨɥɧɟɧɵ ɭɫɥɨɜɢɹ, ɩɨɡɜɨɥɹɸɳɢɟ ɩɨɫɬɚɜɢɬɶ 3 ɛɚɥɥɚ, ɢ ɜɵɩɨɥɧɟɧɨ
ɨɞɧɨ ɢɡ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɣ.
1. Ɂɚɞɚɧɢɟ 3 ɜɵɩɨɥɧɟɧɨ.
2
2. ɉɟɪɜɨɟ ɢ ɜɬɨɪɨɟ ɡɚɞɚɧɢɹ ɜɵɩɨɥɧɟɧɵ.
3. ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɩɨɥɧɨɫɬɶɸ ɢɥɢ ɱɚɫɬɢɱɧɨ; ɞɥɹ ɡɚɞɚɧɢɣ 2 ɢ 3
ɭɤɚɡɚɧɵ ɩɪɚɜɢɥɶɧɵɟ ɡɧɚɱɟɧɢɹ S.
ɇɟ ɜɵɩɨɥɧɟɧɵ ɭɫɥɨɜɢɹ, ɩɨɡɜɨɥɹɸɳɢɟ ɩɨɫɬɚɜɢɬɶ 3 ɢɥɢ 2 ɛɚɥɥɚ, ɢ
ɜɵɩɨɥɧɟɧɨ ɨɞɧɨ ɢɡ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɣ.
1. ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ.
2. ȼɨ ɜɬɨɪɨɦ ɡɚɞɚɧɢɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɨ ɨɞɧɨ ɢɡ ɞɜɭɯ ɜɨɡɦɨɠɧɵɯ
ɡɧɚɱɟɧɢɣ S, ɢ ɞɥɹ ɷɬɨɝɨ ɡɧɚɱɟɧɢɹ ɭɤɚɡɚɧɚ ɢ ɨɛɨɫɧɨɜɚɧɚ ɜɵɢɝɪɵɲɧɚɹ
1
ɫɬɪɚɬɟɝɢɹ ɉɚɲɢ.
3. ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɱɚɫɬɢɱɧɨ, ɢ ɞɥɹ ɨɞɧɨɝɨ ɢɡ ɨɫɬɚɥɶɧɵɯ ɡɚɞɚɧɢɣ
ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɨ ɡɧɚɱɟɧɢɟ S.
4. Ⱦɥɹ ɜɬɨɪɨɝɨ ɢ ɬɪɟɬɶɟɝɨ ɡɚɞɚɧɢɹ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɵ ɡɧɚɱɟɧɢɹ S.
ɇɟ ɜɵɩɨɥɧɟɧɨ ɧɢ ɨɞɧɨ ɢɡ ɭɫɥɨɜɢɣ, ɩɨɡɜɨɥɹɸɳɢɯ ɩɨɫɬɚɜɢɬɶ 3, 2 ɢɥɢ 1
0
ɛɚɥɥ.
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
3
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
C4
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɇɚ ɩɥɨɫɤɨɫɬɢ ɞɚɧ ɧɚɛɨɪ ɬɨɱɟɤ ɫ ɰɟɥɨɱɢɫɥɟɧɧɵɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ. ɇɟɨɛɯɨɞɢɦɨ
ɧɚɣɬɢ ɬɚɤɨɣ ɬɪɟɭɝɨɥɶɧɢɤ ɧɚɢɛɨɥɶɲɟɣ ɩɥɨɳɚɞɢ ɫ ɜɟɪɲɢɧɚɦɢ ɜ ɷɬɢɯ ɬɨɱɤɚɯ,
ɭ ɤɨɬɨɪɨɝɨ ɧɟɬ ɨɛɳɢɯ ɬɨɱɟɤ ɫ ɨɫɶɸ Oy, ɚ ɨɞɧɚ ɢɡ ɫɬɨɪɨɧ ɥɟɠɢɬ ɧɚ ɨɫɢ Ox.
ɇɚɩɢɲɢɬɟ ɷɮɮɟɤɬɢɜɧɭɸ, ɜ ɬɨɦ ɱɢɫɥɟ ɩɨ ɩɚɦɹɬɢ, ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɛɭɞɟɬ
ɪɟɲɚɬɶ ɷɬɭ ɡɚɞɚɱɭ. Ɋɚɡɦɟɪ ɩɚɦɹɬɢ, ɤɨɬɨɪɭɸ ɢɫɩɨɥɶɡɭɟɬ ȼɚɲɚ ɩɪɨɝɪɚɦɦɚ, ɧɟ
ɞɨɥɠɟɧ ɡɚɜɢɫɟɬɶ ɨɬ ɤɨɥɢɱɟɫɬɜɚ ɬɨɱɟɤ.
ɉɟɪɟɞ ɬɟɤɫɬɨɦ ɩɪɨɝɪɚɦɦɵ ɤɪɚɬɤɨ ɨɩɢɲɢɬɟ ɢɫɩɨɥɶɡɭɟɦɵɣ ɚɥɝɨɪɢɬɦ ɪɟɲɟɧɢɹ
ɡɚɞɚɱɢ ɢ ɭɤɚɠɢɬɟ ɢɫɩɨɥɶɡɭɟɦɵɣ ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɢ ɟɝɨ ɜɟɪɫɢɸ.
Ɉɩɢɫɚɧɢɟ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ
ȼ ɩɟɪɜɨɣ ɫɬɪɨɤɟ ɜɜɨɞɢɬɫɹ ɨɞɧɨ ɰɟɥɨɟ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɱɢɫɥɨ – ɤɨɥɢɱɟɫɬɜɨ
ɬɨɱɟɤ N.
Ʉɚɠɞɚɹ ɢɡ ɫɥɟɞɭɸɳɢɯ N ɫɬɪɨɤ ɫɨɞɟɪɠɢɬ ɞɜɚ ɰɟɥɵɯ ɱɢɫɥɚ – ɫɧɚɱɚɥɚ
ɤɨɨɪɞɢɧɚɬɚ x, ɡɚɬɟɦ ɤɨɨɪɞɢɧɚɬɚ y ɨɱɟɪɟɞɧɨɣ ɬɨɱɤɢ. ɑɢɫɥɚ ɪɚɡɞɟɥɟɧɵ
ɩɪɨɛɟɥɨɦ.
Ɉɩɢɫɚɧɢɟ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ
ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ – ɦɚɤɫɢɦɚɥɶɧɭɸ ɩɥɨɳɚɞɶ
ɬɪɟɭɝɨɥɶɧɢɤɚ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɝɨ ɭɫɥɨɜɢɹɦ ɡɚɞɚɱɢ. ȿɫɥɢ ɬɚɤɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ
ɧɟ ɫɭɳɟɫɬɜɭɟɬ, ɩɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɧɨɥɶ.
ɉɪɢɦɟɪ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ:
8
-10 0
2 0
0 4
3 3
7 0
5 5
4 0
9 -9
ɉɪɢɦɟɪ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ ɞɥɹ ɩɪɢɜɟɞɺɧɧɨɝɨ ɜɵɲɟ ɩɪɢɦɟɪɚ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ:
22.5
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
12
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
13
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
Ɍɪɟɭɝɨɥɶɧɢɤ ɧɟ ɢɦɟɟɬ ɨɛɳɢɯ ɬɨɱɟɤ ɫ ɨɫɶɸ Oy (ɨɫɶɸ ɨɪɞɢɧɚɬ), ɟɫɥɢ ɚɛɫɰɢɫɫɵ ɜɫɟɯ ɟɝɨ
ɜɟɪɲɢɧ ɢɦɟɸɬ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɡɧɚɤ, ɬ. ɟ. ɧɭɠɧɨ ɨɬɞɟɥɶɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɬɨɱɤɢ
ɫ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɦɢ ɚɛɫɰɢɫɫɚɦɢ. Ⱦɥɹ ɤɚɠɞɨɣ ɢɡ ɷɬɢɯ ɝɪɭɩɩ
ɬɪɟɭɝɨɥɶɧɢɤ ABC, ɢɦɟɸɳɢɣ ɦɚɤɫɢɦɚɥɶɧɭɸ ɩɥɨɳɚɞɶ, – ɷɬɨ ɬɪɟɭɝɨɥɶɧɢɤ, ɭ ɤɨɬɨɪɨɝɨ
ɜɟɪɲɢɧɵ A ɢ B ɥɟɠɚɬ ɧɚ ɨɫɢ ɚɛɫɰɢɫɫ ɩɨ ɨɞɧɭ ɫɬɨɪɨɧɭ ɨɬ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ, ɩɪɢɱɟɦ
ɭ ɨɞɧɨɣ ɢɡ ɷɬɢɯ ɬɨɱɟɤ ɚɛɫɰɢɫɫɚ ɢɦɟɟɬ ɧɚɢɛɨɥɶɲɭɸ ɚɛɫɨɥɸɬɧɭɸ ɜɟɥɢɱɢɧɭ, ɚ ɭ ɞɪɭɝɨɣ –
ɧɚɢɦɟɧɶɲɭɸ. Ɍɪɟɬɶɹ ɜɟɪɲɢɧɚ ɋ – ɷɬɨ ɜɟɪɲɢɧɚ, ɢɦɟɸɳɚɹ ɧɚɢɛɨɥɶɲɭɸ ɩɨ ɚɛɫɨɥɸɬɧɨɣ
ɜɟɥɢɱɢɧɟ ɨɪɞɢɧɚɬɭ ɫɪɟɞɢ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɩɨ ɬɭ ɠɟ ɫɬɨɪɨɧɭ ɨɬ ɨɫɢ ɨɪɞɢɧɚɬ, ɱɬɨ ɢ ɬɨɱɤɢ
A, B. ɂɡ ɞɜɭɯ ɬɚɤɢɯ «ɦɚɤɫɢɦɚɥɶɧɵɯ» ɬɪɟɭɝɨɥɶɧɢɤɨɜ (ɨɞɢɧ ɥɟɠɢɬ ɩɨ ɨɞɧɭ ɫɬɨɪɨɧɭ ɨɬ
ɨɫɢ ɨɪɞɢɧɚɬ, ɞɪɭɝɨɣ – ɩɨ ɞɪɭɝɭɸ) ɧɭɠɧɨ ɜɵɛɪɚɬɶ ɬɨɬ, ɤɨɬɨɪɵɣ ɢɦɟɟɬ ɛȩɥɶɲɭɸ
ɩɥɨɳɚɞɶ.
ɉɪɨɝɪɚɦɦɚ ɱɢɬɚɟɬ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ, ɧɟ ɡɚɩɨɦɢɧɚɹ ɜɫɟ ɬɨɱɤɢ ɜ ɦɚɫɫɢɜɟ.
ɉɨɫɥɟ ɨɛɪɚɛɨɬɤɢ ɨɱɟɪɟɞɧɨɣ ɬɨɱɤɢ ɩɪɨɝɪɚɦɦɚ ɯɪɚɧɢɬ ɡɧɚɱɟɧɢɹ ɫɥɟɞɭɸɳɢɯ ɜɟɥɢɱɢɧ:
– ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Pos_xmax ɚɛɫɰɢɫɫɵ ɞɥɹ ɜɫɟɯ ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ
ɧɚ ɨɫɢ Ox ɩɪɚɜɟɟ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ;
– ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Pos_xmin ɚɛɫɰɢɫɫɵ ɞɥɹ ɜɫɟɯ ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɧɚ
ɨɫɢ Ox ɩɪɚɜɟɟ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ;
– ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Pos_ymax ɚɛɫɨɥɸɬɧɨɣ ɜɟɥɢɱɢɧɵ ɨɪɞɢɧɚɬɵ ɞɥɹ ɜɫɟɯ
ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɩɪɚɜɟɟ ɨɫɢ ɨɪɞɢɧɚɬ;
– ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Neg_xmax ɚɛɫɰɢɫɫɵ ɞɥɹ ɜɫɟɯ ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ
ɧɚ ɨɫɢ Ox ɥɟɜɟɟ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ;
– ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Neg_xmin ɚɛɫɰɢɫɫɵ ɞɥɹ ɜɫɟɯ ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɧɚ
ɨɫɢ Ox ɥɟɜɟɟ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ;
– ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Neg_ymax ɚɛɫɨɥɸɬɧɨɣ ɜɟɥɢɱɢɧɵ ɨɪɞɢɧɚɬɵ ɞɥɹ ɜɫɟɯ
ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɥɟɜɟɟ ɨɫɢ ɨɪɞɢɧɚɬ.
ɉɨɫɥɟ ɬɨɝɨ ɤɚɤ ɜɫɟ ɬɨɱɤɢ ɩɪɨɱɢɬɚɧɵ, ɜɵɱɢɫɥɹɟɬɫɹ ɦɚɤɫɢɦɭɦ
S = max{(Pos_xmax – Pos_xmin)*Pos_ymax/2, (Neg_xmax-Neg_xmin)*Neg_ymax/2}
(ɟɫɥɢ ɨɛɚ ɡɧɚɱɟɧɢɹ ɧɟ ɨɩɪɟɞɟɥɟɧɵ, ɩɨɥɚɝɚɟɦ S=0).
ȼ ɤɚɱɟɫɬɜɟ ɨɬɜɟɬɚ ɜɵɜɨɞɢɬɫɹ ɱɢɫɥɨ S.
ɉɪɢɦɟɪ ɩɪɚɜɢɥɶɧɨɣ ɢ ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ ɹɡɵɤɟ ɉɚɫɤɚɥɶ
var
n: integer;
x, y: integer;
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
i: integer;
Pos_s, Neg_s: real;
begin
Pos_xsearch
Pos_xmin :=
Pos_ymax :=
Neg_xsearch
Neg_xmin :=
Neg_ymax :=
:=
0;
0;
:=
0;
0;
true;
Pos_xmax := 0;
true;
Neg_xmax := 0;
readln(n);
for i:=1 to n do begin
readln(x,y);
if x >0 then begin
if y=0 then begin
if Pos_xsearch or (x<Pos_xmin) then Pos_xmin:=x;
if Pos_xsearch or (x>Pos_xmax) then Pos_xmax:=x;
Pos_xsearch:=false;
end
else begin
if abs(y)>Pos_ymax then Pos_ymax:=abs(y);
end;
end;
if x < 0 then begin
if y=0 then begin
if Neg_xsearch or (x<Neg_xmin) then Neg_xmin:=x;
if Neg_xsearch or (x>Neg_xmax) then Neg_xmax:=x;
Neg_xsearch:=false;
end
else begin
if abs(y)>Neg_ymax then Neg_ymax:=abs(y);
end;
end;
end;
Pos_s := (Pos_xmax-Pos_xmin)*Pos_ymax/2;
Neg_s := (Neg_xmax-Neg_xmin)*Neg_ymax/2;
if Pos_s > Neg_s then writeln(Pos_s)
else writeln(Neg_s);
end.
Pos_xmin, Pos_xmax: integer;
Pos_xsearch: boolean;
Pos_ymax: integer;
Neg_xmin, Neg_xmax: integer;
Neg_xsearch: boolean;
Neg_ymax: integer;
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
14
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɉɪɢɦɟɪ ɩɪɚɜɢɥɶɧɨɣ ɢ ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ ɹɡɵɤɟ Ȼɟɣɫɢɤ
DIM
DIM
DIM
DIM
DIM
DIM
DIM
DIM
DIM
DIM
n AS INTEGER
x, y AS INTEGER
Pos_xmin, Pos_xmax AS INTEGER
Pos_xsearch AS INTEGER
Pos_ymax AS INTEGER
Neg_xmin, Neg_xmax AS INTEGER
Neg_xsearch AS INTEGER
Neg_ymax AS INTEGER
i AS INTEGER
Pos_s, Neg_s AS DOUBLE
Pos_xsearch = 1: Neg_xsearch = 1
Pos_ymax = 0: Neg_ymax = 0
Pos_xmin = 0: Pos_xmax = 0
Neg_xmin = 0: Neg_xmax = 0
INPUT n
FOR i = 1 TO n
INPUT x, y
IF x > 0 THEN
IF y = 0 THEN
IF Pos_xsearch = 1 OR x < Pos_xmin
IF Pos_xsearch = 1 OR x > Pos_xmax
Pos_xsearch = 0
ELSE
IF ABS(y) > Pos_ymax THEN Pos_ymax
END IF
END IF
IF x < 0 THEN
IF y = 0 THEN
IF Neg_xsearch = 1 OR x < Neg_xmin
IF Neg_xsearch = 1 OR x > Neg_xmax
Neg_xsearch = 0
ELSE
IF ABS(y) > Neg_ymax THEN Neg_ymax
END IF
END IF
NEXT i
Pos_s = (Pos_xmax – Pos_xmin) * Pos_ymax
Neg_s = (Neg_xmax – Neg_xmin) * Neg_ymax
IF Pos_s > Neg_s THEN
PRINT Pos_s
ELSE
PRINT Neg_s
END IF
THEN Pos_xmin = x
THEN Pos_xmax = x
= ABS(y)
THEN Neg_xmin = x
THEN Neg_xmax = x
= ABS(y)
/ 2
/ 2
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
15
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɉɪɢɦɟɪ ɩɪɚɜɢɥɶɧɨɣ ɢ ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ ɚɥɝɨɪɢɬɦɢɱɟɫɤɨɦ ɹɡɵɤɟ
ɚɥɝ
ɧɚɱ
ɰɟɥ n
ɰɟɥ x,y
ɰɟɥ Pos_xmin=0, Pos_xmax=0
ɥɨɝ Pos_xsearch=ɞɚ
ɰɟɥ Pos_ymax=0
ɰɟɥ Neg_xmin=0, Neg_xmax=0
ɥɨɝ Neg_xsearch=ɞɚ
ɰɟɥ Neg_ymax=0
ɜɟɳ Pos_s, Neg_s
ɜɜɨɞ n
ɧɰ n ɪɚɡ
ɜɜɨɞ x, y
ɟɫɥɢ x > 0 ɬɨ
ɟɫɥɢ y=0
ɬɨ
ɟɫɥɢ Pos_xsearch ɢɥɢ x<Pos_xmin ɬɨ Pos_xmin:=x ɜɫɟ
ɟɫɥɢ Pos_xsearch ɢɥɢ x>Pos_xmax ɬɨ Pos_xmax:=x ɜɫɟ
Pos_xsearch:=ɧɟɬ
ɢɧɚɱɟ
ɟɫɥɢ iabs(y)>Pos_ymax ɬɨ Pos_ymax:=iabs(y) ɜɫɟ
ɜɫɟ
ɜɫɟ
ɟɫɥɢ x < 0
ɟɫɥɢ y=0
ɬɨ
ɟɫɥɢ Neg_xsearch ɢɥɢ x<Neg_xmin ɬɨ Neg_xmin:=x ɜɫɟ
ɟɫɥɢ Neg_xsearch ɢɥɢ x>Neg_xmax ɬɨ Neg_xmax:=x ɜɫɟ
Neg_xsearch:=ɧɟɬ
ɢɧɚɱɟ
ɟɫɥɢ iabs(y)>Neg_ymax ɬɨ Neg_ymax:=iabs(y) ɜɫɟ
ɜɫɟ
ɜɫɟ
ɤɰ
Pos_s:=(Pos_xmax-Pos_xmin)*Pos_ymax/2
Neg_s:=(Neg_xmax-Neg_xmin)*Neg_ymax/2
ɟɫɥɢ Pos_s > Neg_s
ɬɨ ɜɵɜɨɞ Pos_s
ɢɧɚɱɟ ɜɵɜɨɞ Neg_s
ɜɫɟ
ɤɨɧ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
16
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɨɝɪɚɦɦɚ ɩɪɚɜɢɥɶɧɨ ɪɚɛɨɬɚɟɬ ɞɥɹ ɥɸɛɵɯ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ ɩɪɨɢɡɜɨɥɶɧɨɝɨ
ɪɚɡɦɟɪɚ ɢ ɧɚɯɨɞɢɬ ɨɬɜɟɬ, ɧɟ ɫɨɯɪɚɧɹɹ ɜɯɨɞɧɵɟ ɞɚɧɧɵɟ ɜ ɦɚɫɫɢɜɟ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɜ ɬɟɤɫɬɟ ɩɪɨɝɪɚɦɦɵ ɨɞɧɨɣ ɫɢɧɬɚɤɫɢɱɟɫɤɨɣ ɨɲɢɛɤɢ:
ɩɪɨɩɭɳɟɧ ɢɥɢ ɧɟɜɟɪɧɨ ɭɤɚɡɚɧ ɡɧɚɤ ɩɭɧɤɬɭɚɰɢɢ, ɧɟɜɟɪɧɨ ɧɚɩɢɫɚɧɨ ɢɥɢ
4
ɩɪɨɩɭɳɟɧɨ ɡɚɪɟɡɟɪɜɢɪɨɜɚɧɧɨɟ ɫɥɨɜɨ ɹɡɵɤɚ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɧɟ ɨɩɢɫɚɧɚ
ɢɥɢ ɧɟɜɟɪɧɨ ɨɩɢɫɚɧɚ ɩɟɪɟɦɟɧɧɚɹ, ɩɪɢɦɟɧɹɟɬɫɹ ɨɩɟɪɚɰɢɹ, ɧɟɞɨɩɭɫɬɢɦɚɹ ɞɥɹ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɬɢɩɚ ɞɚɧɧɵɯ (ɟɫɥɢ ɨɞɧɚ ɢ ɬɚ ɠɟ ɨɲɢɛɤɚ ɜɫɬɪɟɱɚɟɬɫɹ
ɧɟɫɤɨɥɶɤɨ ɪɚɡ, ɬɨ ɷɬɨ ɫɱɢɬɚɟɬɫɹ ɡɚ ɨɞɧɭ ɨɲɢɛɤɭ).
ɉɪɨɝɪɚɦɦɚ ɪɚɛɨɬɚɟɬ ɜɟɪɧɨ, ɧɨ ɪɚɡɦɟɪ ɢɫɩɨɥɶɡɭɟɦɨɣ ɩɚɦɹɬɢ ɡɚɜɢɫɢɬ ɨɬ
ɤɨɥɢɱɟɫɬɜɚ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ. ɇɚɩɪɢɦɟɪ, ɜɯɨɞɧɵɟ ɞɚɧɧɵɟ (ɤɨɨɪɞɢɧɚɬɵ
ɬɨɱɟɤ) ɡɚɩɨɦɢɧɚɸɬɫɹ ɜ ɦɚɫɫɢɜɟ ɢɥɢ ɞɪɭɝɨɣ ɫɬɪɭɤɬɭɪɟ ɞɚɧɧɵɯ, ɪɚɡɦɟɪ
ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɨɥɢɱɟɫɬɜɭ ɬɨɱɟɤ. ɉɪɢ ɷɬɨɦ ɨɛɪɚɛɨɬɤɚ ɞɚɧɧɵɯ
ɩɪɨɢɫɯɨɞɢɬ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɷɮɮɟɤɬɢɜɧɨɝɨ ɚɥɝɨɪɢɬɦɚ, ɚɧɚɥɨɝɢɱɧɨɝɨ
ɩɪɢɜɟɞɺɧɧɵɦ ɜɵɲɟ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɨɞɧɚ ɢɡ ɫɥɟɞɭɸɳɢɯ ɨɲɢɛɨɤ.
1) ɉɨɢɫɤ ɦɢɧɢɦɭɦɚ ɢɥɢ ɦɚɤɫɢɦɭɦɚ ɧɟ ɭɱɢɬɵɜɚɟɬ, ɱɬɨ ɩɟɪɜɵɣ ɩɨɞɯɨɞɹɳɢɣ
ɷɥɟɦɟɧɬ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɧɚ ɥɸɛɨɦ ɦɟɫɬɟ ɜ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢɥɢ ɜɨɨɛɳɟ
ɨɬɫɭɬɫɬɜɨɜɚɬɶ.
2)
ɉɟɪɟɩɭɬɚɧɵ ɤɨɨɪɞɢɧɚɬɵ x ɢ y ɩɪɢ ɩɨɢɫɤɟ ɨɫɧɨɜɚɧɢɹ, ɢɳɭɬɫɹ
ɦɚɤɫɢɦɚɥɶɧɵɟ ɢ ɦɢɧɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ y ɩɪɢ x = 0.
3) ɉɟɪɟɩɭɬɚɧɵ ɤɨɨɪɞɢɧɚɬɵ x ɢ y ɩɪɢ ɩɨɢɫɤɟ ɜɵɫɨɬɵ: ɢɳɟɬɫɹ ɦɚɤɫɢɦɚɥɶɧɨɟ
ɡɧɚɱɟɧɢɟ x.
4) ɉɪɢ ɩɨɢɫɤɟ ɜɵɫɨɬɵ ɢɳɟɬɫɹ ɦɚɤɫɢɦɭɦ ɡɧɚɱɟɧɢɹ ɤɨɨɪɞɢɧɚɬɵ y, ɚ ɧɟ ɟɺ
ɦɨɞɭɥɹ.
3
5) ɉɪɢ ɩɨɢɫɤɟ ɜɵɫɨɬɵ ɡɚɩɨɦɢɧɚɟɬɫɹ ɧɟ ɦɨɞɭɥɶ, ɚ ɡɧɚɱɟɧɢɟ y, ɩɪɢ ɷɬɨɦ ɩɪɢ
ɜɵɱɢɫɥɟɧɢɢ ɩɥɨɳɚɞɢ ɦɨɞɭɥɶ ɬɨɠɟ ɧɟ ɛɟɪɺɬɫɹ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɨɠɟɬ
ɩɨɥɭɱɢɬɶɫɹ ɨɬɪɢɰɚɬɟɥɶɧɚɹ ɩɥɨɳɚɞɶ.
6)
ȼɫɟ ɜɟɪɲɢɧɵ ɨɩɪɟɞɟɥɟɧɵ ɩɪɚɜɢɥɶɧɨ, ɧɨ ɩɥɨɳɚɞɶ ɬɪɟɭɝɨɥɶɧɢɤɚ
ɨɩɪɟɞɟɥɟɧɚ ɧɟɜɟɪɧɨ, ɧɚɩɪɢɦɟɪ, ɢɫɩɨɥɶɡɨɜɚɧɚ ɧɟɜɟɪɧɚɹ ɮɨɪɦɭɥɚ.
7) ɇɟ ɭɱɢɬɵɜɚɟɬɫɹ, ɱɬɨ ɜɵɱɢɫɥɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɩɥɨɳɚɞɢ ɦɨɠɟɬ ɛɵɬɶ
ɧɟɰɟɥɵɦ. ɇɚɩɪɢɦɟɪ, ɡɧɚɱɟɧɢɟ ɩɥɨɳɚɞɢ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɩɟɪɟɦɟɧɧɨɣ ɰɟɥɨɝɨ
ɬɢɩɚ, ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɩɥɨɳɚɞɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɩɟɪɚɰɢɹ ɰɟɥɨɱɢɫɥɟɧɧɨɝɨ
ɞɟɥɟɧɢɹ (div ɜ ɉɚɫɤɚɥɟ, ɞɟɥɟɧɢɟ ɰɟɥɵɯ ɜɟɥɢɱɢɧ ɛɟɡ ɩɪɢɜɟɞɟɧɢɹ ɬɢɩɨɜ ɜ ɋɢ),
ɩɪɢ ɮɨɪɦɚɬɧɨɦ ɜɵɜɨɞɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɮɨɪɦɚɬ ɰɟɥɨɝɨ ɱɢɫɥɚ, ɢɥɢ
ɢɦɟɸɬɫɹ ɞɪɭɝɢɟ ɩɨɞɨɛɧɵɟ ɨɲɢɛɤɢ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɧɟɜɟɪɧɨɦɭ ɪɟɡɭɥɶɬɚɬɭ ɩɪɢ
ɞɪɨɛɧɨɦ ɨɬɜɟɬɟ.
8) ȼɟɪɲɢɧɵ ɢ ɩɥɨɳɚɞɢ ɞɜɭɯ ɬɪɟɭɝɨɥɶɧɢɤɨɜ ɨɩɪɟɞɟɥɟɧɵ ɜɟɪɧɨ, ɧɨ ɢɡ ɧɢɯ
ɜɵɛɢɪɚɟɬɫɹ ɧɟ ɛɨɥɶɲɢɣ, ɚ ɦɟɧɶɲɢɣ.
9)
ɇɟɜɟɪɧɨ ɨɛɪɚɛɚɬɵɜɚɟɬɫɹ ɫɢɬɭɚɰɢɹ, ɤɨɝɞɚ ɢɫɤɨɦɵɣ ɬɪɟɭɝɨɥɶɧɢɤ
ɨɬɫɭɬɫɬɜɭɟɬ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬ ɨɞɧɨɣ ɞɨ ɬɪɺɯ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ ɨɲɢɛɨɤ, ɨɩɢɫɚɧɧɵɯ
ɜɵɲɟ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
17
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɉɪɨɝɪɚɦɦɚ ɪɚɛɨɬɚɟɬ ɜ ɰɟɥɨɦ ɜɟɪɧɨ, ɷɮɮɟɤɬɢɜɧɨ ɢɥɢ ɧɟɬ. ȼɨɡɦɨɠɧɵ
ɩɟɪɟɛɨɪɧɵɟ ɪɟɲɟɧɢɹ, ɩɪɢ ɤɨɬɨɪɵɯ ɜɫɟ ɬɨɱɤɢ ɯɪɚɧɹɬɫɹ ɜ ɦɚɫɫɢɜɟ, ɢɡ ɧɢɯ
ɜɵɛɢɪɚɸɬɫɹ ɩɨɞɯɨɞɹɳɢɟ ɬɪɟɭɝɨɥɶɧɢɤɢ, ɜɵɱɢɫɥɹɟɬɫɹ ɢ ɫɪɚɜɧɢɜɚɟɬɫɹ ɢɯ
ɩɥɨɳɚɞɶ.
ȼ ɪɟɚɥɢɡɚɰɢɢ ɚɥɝɨɪɢɬɦɚ ɞɨɩɭɳɟɧɨ ɛɨɥɟɟ 1 ɨɲɢɛɤɢ ɢɡ ɱɢɫɥɚ ɩɟɪɟɱɢɫɥɟɧɧɵɯ
ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɭɧɤɬɟ ɢɥɢ ɞɨɩɭɳɟɧɵ ɞɪɭɝɢɟ ɨɲɢɛɤɢ, ɩɪɢɜɨɞɹɳɢɟ
ɤ ɧɟɜɟɪɧɨɣ ɪɚɛɨɬɟ ɩɪɨɝɪɚɦɦɵ ɜ ɨɬɞɟɥɶɧɵɯ ɫɥɭɱɚɹɯ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬ ɨɞɧɨɣ ɞɨ ɩɹɬɢ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ ɨɲɢɛɨɤ, ɨɩɢɫɚɧɧɵɯ
ɜɵɲɟ.
ɉɪɨɝɪɚɦɦɚ ɪɚɛɨɬɚɟɬ ɜ ɨɬɞɟɥɶɧɵɯ ɱɚɫɬɧɵɯ ɫɥɭɱɚɹɯ.
Ɉɞɢɧ ɛɚɥɥ ɬɚɤɠɟ ɫɬɚɜɢɬɫɹ, ɟɫɥɢ ɩɪɨɝɪɚɦɦɚ ɧɚɩɢɫɚɧɚ ɧɟɜɟɪɧɨ, ɧɨ ɢɡ
ɨɩɢɫɚɧɢɹ ɚɥɝɨɪɢɬɦɚ ɢ ɨɛɳɟɣ ɫɬɪɭɤɬɭɪɵ ɩɪɨɝɪɚɦɦɵ ɜɢɞɧɨ, ɱɬɨ
ɷɤɡɚɦɟɧɭɟɦɵɣ ɜ ɰɟɥɨɦ ɩɪɚɜɢɥɶɧɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɩɭɬɶ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ.
ɇɟ ɜɵɩɨɥɧɟɧɨ ɧɢ ɨɞɧɨ ɢɡ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜɵɲɟ ɭɫɥɨɜɢɣ.
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
2
1
0
4
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
18
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
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1
C1
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ
ɚɥɝ
ɧɚɱ
Ɍɪɟɛɨɜɚɥɨɫɶ ɧɚɩɢɫɚɬɶ ɩɪɨɝɪɚɦɦɭ, ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɤɨɬɨɪɨɣ ɫ ɤɥɚɜɢɚɬɭɪɵ
ɫɱɢɬɵɜɚɟɬɫɹ ɤɨɨɪɞɢɧɚɬɚ ɬɨɱɤɢ ɧɚ ɩɪɹɦɨɣ (x – ɞɟɣɫɬɜɢɬɟɥɶɧɨɟ ɱɢɫɥɨ) ɢ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɷɬɨɣ ɬɨɱɤɢ ɨɞɧɨɦɭ ɢɡ ɜɵɞɟɥɟɧɧɵɯ ɨɬɪɟɡɤɨɜ
(ɜɤɥɸɱɚɹ ɝɪɚɧɢɰɵ). ɉɪɨɝɪɚɦɦɢɫɬ ɬɨɪɨɩɢɥɫɹ ɢ ɧɚɩɢɫɚɥ ɩɪɨɝɪɚɦɦɭ
ɧɟɩɪɚɜɢɥɶɧɨ.
Ⱥɥɝɨɪɢɬɦɢɱɟɫɤɢɣ
ɹɡɵɤ
Ȼɟɣɫɢɤ
INPUT x
IF x>=-5 OR x<=1 THEN
IF x>=-3 AND x<=3 THEN
IF x>=-1 AND x<=5 THEN
PRINT "ɩɪɢɧɚɞɥɟɠɢɬ"
ELSE
PRINT "ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ"
END IF
END IF
END IF
END
ɉɚɫɤɚɥɶ
var x: real;
begin
readln(x);
if (x>=-5) or (x<=1) then
if (x>=-3) and (x<=3) then
if (x>=-1) and (x<=5) then
write('ɩɪɢɧɚɞɥɟɠɢɬ')
else
write('ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ')
end.
ɋɢ
#include <stdio.h>
void main(){
float x;
scanf("%f",&x);
if (x>=-5 || x<=1)
if (x>=-3 && x<=3)
if (x>=-1 && x<=5)
printf("ɩɪɢɧɚɞɥɟɠɢɬ");
else
printf("ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ");
}
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɤɨɧ
ɜɟɳ x
ɜɜɨɞ x
ɟɫɥɢ x>=-5 ɢɥɢ x<=1 ɬɨ
ɟɫɥɢ x>=-3 ɢ x<=3 ɬɨ
ɟɫɥɢ x>=-1 ɢ x<=5 ɬɨ
ɜɵɜɨɞ 'ɩɪɢɧɚɞɥɟɠɢɬ'
ɢɧɚɱɟ
ɜɵɜɨɞ 'ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ'
ɜɫɟ
ɜɫɟ
ɜɫɟ
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɵɩɨɥɧɢɬɟ ɫɥɟɞɭɸɳɟɟ.
1. ɉɟɪɟɪɢɫɭɣɬɟ ɢ ɡɚɩɨɥɧɢɬɟ ɬɚɛɥɢɰɭ, ɤɨɬɨɪɚɹ ɩɨɤɚɡɵɜɚɟɬ, ɤɚɤ ɪɚɛɨɬɚɟɬ
ɩɪɨɝɪɚɦɦɚ ɩɪɢ ɚɪɝɭɦɟɧɬɟ, ɩɪɢɧɚɞɥɟɠɚɳɟɦ ɪɚɡɥɢɱɧɵɦ ɨɛɥɚɫɬɹɦ (A, B, C, D,
E, F, G). Ɍɨɱɤɢ, ɥɟɠɚɳɢɟ ɧɚ ɝɪɚɧɢɰɚɯ ɨɛɥɚɫɬɟɣ, ɨɬɞɟɥɶɧɨ ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɬɶ.
ɍɫɥɨɜɢɟ 1 ɍɫɥɨɜɢɟ 2 ɍɫɥɨɜɢɟ 3 ɉɪɨɝɪɚɦɦɚ
Ɉɛɥɚɫɬɶ
Ɉɛɥɚɫɬɶ (x>= –5 ɢɥɢ (x>= –3 ɢ (x>= –1 ɢ
ɨɛɪɚɛɚɬɵɜɚɟɬɫɹ
ɜɵɜɟɞɟɬ
x<=1)
x<=3)
x<=5)
ɜɟɪɧɨ
A
B
C
D
E
F
G
ȼ ɫɬɨɥɛɰɚɯ ɭɫɥɨɜɢɣ ɭɤɚɠɢɬɟ «ɞɚ», ɟɫɥɢ ɭɫɥɨɜɢɟ ɜɵɩɨɥɧɢɬɫɹ, «ɧɟɬ», ɟɫɥɢ
ɭɫɥɨɜɢɟ ɧɟ ɜɵɩɨɥɧɢɬɫɹ, «—» (ɩɪɨɱɟɪɤ), ɟɫɥɢ ɭɫɥɨɜɢɟ ɧɟ ɛɭɞɟɬ ɩɪɨɜɟɪɹɬɶɫɹ,
«ɧɟ ɢɡɜ.», ɟɫɥɢ ɩɪɨɝɪɚɦɦɚ ɜɟɞɺɬ ɫɟɛɹ ɩɨ-ɪɚɡɧɨɦɭ ɞɥɹ ɪɚɡɧɵɯ ɡɧɚɱɟɧɢɣ,
ɩɪɢɧɚɞɥɟɠɚɳɢɯ ɞɚɧɧɨɣ ɨɛɥɚɫɬɢ.
ȼ ɫɬɨɥɛɰɟ «ɉɪɨɝɪɚɦɦɚ ɜɵɜɟɞɟɬ» ɭɤɚɠɢɬɟ, ɱɬɨ ɩɪɨɝɪɚɦɦɚ ɜɵɜɟɞɟɬ ɧɚ ɷɤɪɚɧ.
ȿɫɥɢ ɩɪɨɝɪɚɦɦɚ ɧɢɱɟɝɨ ɧɟ ɜɵɜɨɞɢɬ, ɧɚɩɢɲɢɬɟ «—» (ɩɪɨɱɟɪɤ). ȿɫɥɢ ɞɥɹ
ɪɚɡɧɵɯ ɡɧɚɱɟɧɢɣ, ɩɪɢɧɚɞɥɟɠɚɳɢɯ ɨɛɥɚɫɬɢ, ɛɭɞɭɬ ɜɵɜɟɞɟɧɵ ɪɚɡɧɵɟ ɬɟɤɫɬɵ,
ɧɚɩɢɲɢɬɟ «ɧɟ ɢɡɜ.». ȼ ɩɨɫɥɟɞɧɟɦ ɫɬɨɥɛɰɟ ɭɤɚɠɢɬɟ «ɞɚ» ɢɥɢ «ɧɟɬ».
2. ɍɤɚɠɢɬɟ, ɤɚɤ ɧɭɠɧɨ ɞɨɪɚɛɨɬɚɬɶ ɩɪɨɝɪɚɦɦɭ, ɱɬɨɛɵ ɧɟ ɛɵɥɨ ɫɥɭɱɚɟɜ ɟɺ
ɧɟɩɪɚɜɢɥɶɧɨɣ ɪɚɛɨɬɵ. (ɗɬɨ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɧɟɫɤɨɥɶɤɢɦɢ ɫɩɨɫɨɛɚɦɢ,
ɞɨɫɬɚɬɨɱɧɨ ɭɤɚɡɚɬɶ ɥɸɛɨɣ ɫɩɨɫɨɛ ɞɨɪɚɛɨɬɤɢ ɢɫɯɨɞɧɨɣ ɩɪɨɝɪɚɦɦɵ.)
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
2
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ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ɗɥɟɦɟɧɬɵ ɨɬɜɟɬɚ:
ɉɪɚɜɢɥɶɧɨ ɡɚɩɨɥɧɟɧɧɚɹ ɬɚɛɥɢɰɚ:
Ɉɛɥɚɫɬɶ
ɍɫɥɨɜɢɟ 1
ɍɫɥɨɜɢɟ 2
(x>= –5 ɢɥɢ
(x>= –3 ɢ
x<=1)
x<=3)
A
Ⱦɚ
ɇɟɬ
B
Ⱦɚ
ɇɟɬ
C
Ⱦɚ
Ⱦɚ
D
E
F
G
Ⱦɚ
Ⱦɚ
Ⱦɚ
Ⱦɚ
Ⱦɚ
Ⱦɚ
ɇɟɬ
ɇɟɬ
ɍɫɥɨɜɢɟ 3
(x>= –1 ɢ
x<=5)
–
–
ɇɟɬ
Ⱦɚ
Ⱦɚ
–
–
ɉɪɨɝɪɚɦɦɚ
ɜɵɜɟɞɟɬ
–
–
ɧɟ
ɩɪɢɧɚɞɥɟɠɢɬ
ɩɪɢɧɚɞɥɟɠɢɬ
ɩɪɢɧɚɞɥɟɠɢɬ
–
–
3
Ɉɛɥɚɫɬɶ
ɨɛɪɚɛɚɬɵɜɚɟɬɫɹ
ɜɟɪɧɨ
ɇɟɬ
ɇɟɬ
Ⱦɚ
Ⱦɚ
ɇɟɬ
ɇɟɬ
ɇɟɬ
ȼɨɡɦɨɠɧɵ ɪɚɡɥɢɱɧɵɟ ɫɩɨɫɨɛɵ ɞɨɪɚɛɨɬɤɢ ɩɪɨɝɪɚɦɦɵ. ɇɢɠɟ ɩɪɢɜɟɞɟɧɵ ɪɚɡɥɢɱɧɵɟ
ɩɪɚɜɢɥɶɧɵɟ ɪɟɲɟɧɢɹ, ɡɚɩɢɫɚɧɧɵɟ ɧɚ ɪɚɡɧɵɯ ɹɡɵɤɚɯ. Ⱦɚɧɧɵɟ ɪɟɲɟɧɢɹ ɧɟ ɩɪɢɜɹɡɚɧɵ
ɤ ɹɡɵɤɚɦ: ɥɸɛɭɸ ɢɡ ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɧɢɯ ɢɞɟɣ ɦɨɠɧɨ ɩɪɢɦɟɧɢɬɶ, ɢɫɩɨɥɶɡɭɹ ɥɸɛɨɣ
ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ.
ɉɪɢɦɟɪ ɧɚ ɚɥɝɨɪɢɬɦɢɱɟɫɤɨɦ ɹɡɵɤɟ
ɟɫɥɢ -5<=x<=-3 ɢɥɢ -1<=x<=1 ɢɥɢ 3<=x<=5 ɬɨ
ɜɵɜɨɞ 'ɩɪɢɧɚɞɥɟɠɢɬ'
ɢɧɚɱɟ
ɜɵɜɨɞ 'ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ'
ɜɫɟ
ɉɪɢɦɟɪ ɧɚ ɉɚɫɤɚɥɟ
if (abs(x)<=1) or (3<=abs(x)) and (abs(x)<=5) then
write('ɩɪɢɧɚɞɥɟɠɢɬ')
else
write('ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ');
ɉɪɢɦɟɪ ɧɚ Ȼɟɣɫɢɤɟ
T = ABS(ABS(x)-2)
IF 1<=T AND T<=3 THEN
PRINT "ɩɪɢɧɚɞɥɟɠɢɬ"
ELSE
PRINT "ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ"
END IF
ȼɨɡɦɨɠɧɵ ɢ ɞɪɭɝɢɟ ɫɩɨɫɨɛɵ ɞɨɪɚɛɨɬɤɢ.
Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ! ȼ ɡɚɞɚɱɟ ɬɪɟɛɭɟɬɫɹ ɜɵɩɨɥɧɢɬɶ ɬɪɢ ɞɟɣɫɬɜɢɹ.
1. Ɂɚɩɨɥɧɢɬɶ ɬɚɛɥɢɰɭ.
2. ɂɫɩɪɚɜɢɬɶ ɨɲɢɛɤɭ ɜ ɭɫɥɨɜɧɨɦ ɨɩɟɪɚɬɨɪɟ.
3. ɂɫɩɪɚɜɢɬɶ ɨɲɢɛɤɭ, ɫɜɹɡɚɧɧɭɸ ɫ ɧɟɩɪɚɜɢɥɶɧɵɦ ɧɚɛɨɪɨɦ ɭɫɥɨɜɢɣ.
Ȼɚɥɥɵ ɡɚ ɞɚɧɧɨɟ ɡɚɞɚɧɢɟ ɧɚɱɢɫɥɹɸɬɫɹ ɤɚɤ ɫɭɦɦɚ ɛɚɥɥɨɜ ɡɚ ɜɟɪɧɨɟ ɜɵɩɨɥɧɟɧɢɟ ɤɚɠɞɨɝɨ
ɞɟɣɫɬɜɢɹ. Ɋɚɫɫɦɨɬɪɢɦ ɨɬɞɟɥɶɧɨ ɤɚɠɞɨɟ ɞɟɣɫɬɜɢɟ.
1. Ⱦɟɣɫɬɜɢɟ ɩɨ ɡɚɩɨɥɧɟɧɢɸ ɬɚɛɥɢɰɵ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɜ ɬɚɛɥɢɰɟ ɧɟɬ
ɨɲɢɛɨɤ ɢɥɢ ɨɲɢɛɤɢ ɩɪɢɫɭɬɫɬɜɭɸɬ ɬɨɥɶɤɨ ɜ ɨɞɧɨɣ ɫɬɪɨɤɟ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
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4
2. ɇɟɩɪɚɜɢɥɶɧɨɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɭɫɥɨɜɧɨɝɨ ɨɩɟɪɚɬɨɪɚ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɩɪɢ
ɧɟɜɵɩɨɥɧɟɧɢɢ ɩɟɪɜɨɝɨ ɢɥɢ ɜɬɨɪɨɝɨ ɭɫɥɨɜɢɹ ɩɪɨɝɪɚɦɦɚ ɧɟ ɜɵɞɚɜɚɥɚ ɧɢɱɟɝɨ
(ɨɬɫɭɬɫɬɜɭɸɬ ɫɥɭɱɚɢ ELSE). ɂɫɩɪɚɜɥɟɧɢɟɦ ɷɬɨɣ ɨɲɢɛɤɢ ɦɨɠɟɬ ɛɵɬɶ ɥɢɛɨ ɞɨɛɚɜɥɟɧɢɟ
ɫɥɭɱɚɹ ELSE ɤ ɤɚɠɞɨɦɭ ɭɫɥɨɜɢɸ IF, ɥɢɛɨ ɨɛɴɟɞɢɧɟɧɢɟ ɜɫɟɯ ɭɫɥɨɜɢɣ IF ɜ ɨɞɧɨ ɩɪɢ
ɩɨɦɨɳɢ ɤɨɧɴɸɧɤɰɢɢ.
ȼ ɫɥɨɠɧɵɯ ɫɥɭɱɚɹɯ ɷɬɨ ɞɟɣɫɬɜɢɟ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɩɪɨɝɪɚɦɦɚ ɜɵɞɚɺɬ
ɨɞɧɨ ɢɡ ɞɜɭɯ ɫɨɨɛɳɟɧɢɣ: «ɩɪɢɧɚɞɥɟɠɢɬ» ɢɥɢ «ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ» – ɞɥɹ ɥɸɛɵɯ ɱɢɫɟɥ x,
ɩɪɢ ɷɬɨɦ ɩɪɨɝɪɚɦɦɚ ɧɟ ɫɬɚɥɚ ɪɚɛɨɬɚɬɶ ɯɭɠɟ, ɱɟɦ ɪɚɧɶɲɟ, ɬ. ɟ. ɞɥɹ ɜɫɟɯ ɬɨɱɟɤ, ɞɥɹ
ɤɨɬɨɪɵɯ ɩɪɨɝɪɚɦɦɚ ɪɚɧɟɟ ɜɵɞɚɜɚɥɚ ɜɟɪɧɵɣ ɨɬɜɟɬ, ɞɨɪɚɛɨɬɚɧɧɚɹ ɩɪɨɝɪɚɦɦɚ ɬɚɤɠɟ
ɞɨɥɠɧɚ ɜɵɞɚɜɚɬɶ ɜɟɪɧɵɣ ɨɬɜɟɬ.
3. ɉɪɢɜɟɞɺɧɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ ɧɟ ɨɩɢɫɵɜɚɸɬ ɬɪɟɛɭɟɦɵɟ ɨɛɥɚɫɬɢ. ɉɟɪɜɨɟ ɭɫɥɨɜɢɟ ɜɟɪɧɨ
ɞɥɹ ɥɸɛɵɯ x, ɬɨ ɟɫɬɶ ɧɟ ɩɨɡɜɨɥɹɟɬ ɩɪɢɧɹɬɶ ɧɢɤɚɤɢɯ ɪɟɲɟɧɢɣ, ɜɬɨɪɨɟ ɢ ɬɪɟɬɶɟ ɧɟ
ɡɚɯɜɚɬɵɜɚɸɬ ɨɛɥɚɫɬɢ B ɢ F ɢ ɧɟ ɩɨɡɜɨɥɹɸɬ ɨɬɞɟɥɢɬɶ ɞɪɭɝ ɨɬ ɞɪɭɝɚ ɨɛɥɚɫɬɢ D ɢ E.
ɂɫɩɪɚɜɥɟɧɢɟɦ ɷɬɨɣ ɨɲɢɛɤɢ ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɛɢɟɧɢɟ ɨɛɥɚɫɬɢ ɧɚ ɱɚɫɬɢ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɟ
ɞɢɡɴɸɧɤɰɢɢ ɥɢɛɨ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɤɨɦɛɢɧɚɰɢɢ ɤɚɫɤɚɞɧɵɯ ɭɫɥɨɜɢɣ. ɇɟɫɤɨɥɶɤɨ
ɩɪɢɦɟɪɨɜ ɪɚɡɥɢɱɧɵɯ ɜɟɪɧɵɯ ɪɟɲɟɧɢɣ ɩɪɢɜɟɞɟɧɵ ɜɵɲɟ.
ȼ ɫɥɨɠɧɵɯ ɫɥɭɱɚɹɯ ɷɬɨ ɞɟɣɫɬɜɢɟ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɜɟɪɧɨ ɨɩɪɟɞɟɥɟɧɵ
ɡɚɲɬɪɢɯɨɜɚɧɧɵɟ ɨɛɥɚɫɬɢ, ɬ. ɟ. ɩɪɨɝɪɚɦɦɚ ɜɵɜɨɞɢɬ ɫɨɨɛɳɟɧɢɟ «ɩɪɢɧɚɞɥɟɠɢɬ» ɞɥɹ ɜɫɟɯ
ɬɨɱɟɤ ɡɚɤɪɚɲɟɧɧɵɯ ɨɛɥɚɫɬɟɣ ɢ ɬɨɥɶɤɨ ɞɥɹ ɧɢɯ, ɞɥɹ ɬɨɱɟɤ ɜɧɟ ɡɚɲɬɪɢɯɨɜɚɧɧɵɯ
ɨɛɥɚɫɬɟɣ ɩɪɨɝɪɚɦɦɚ ɜɵɜɨɞɢɬ «ɧɟ ɩɪɢɧɚɞɥɟɠɢɬ» ɢɥɢ ɧɟ ɜɵɜɨɞɢɬ ɧɢɱɟɝɨ.
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɟɧɵ ɨɛɚ ɩɭɧɤɬɚ ɡɚɞɚɧɢɹ. ȼɟɪɧɨ ɡɚɩɨɥɧɟɧɚ ɬɚɛɥɢɰɚ,
ɢɫɩɪɚɜɥɟɧɵ ɞɜɟ ɨɲɢɛɤɢ. ɉɪɨɝɪɚɦɦɚ ɞɥɹ ɜɫɟɯ ɱɢɫɟɥ x ɜɟɪɧɨ ɨɩɪɟɞɟɥɹɟɬ
ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɬɨɱɤɢ ɡɚɤɪɚɲɟɧɧɨɣ ɨɛɥɚɫɬɢ. ȼ ɪɚɛɨɬɟ (ɜɨ ɮɪɚɝɦɟɧɬɚɯ
3
ɩɪɨɝɪɚɦɦ) ɞɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬɞɟɥɶɧɵɯ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ ɨɲɢɛɨɤ, ɧɟ
ɢɫɤɚɠɚɸɳɢɯ ɡɚɦɵɫɥɚ ɚɜɬɨɪɚ ɪɟɲɟɧɢɹ.
1. ɉɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɟɧɵ ɞɜɚ ɞɟɣɫɬɜɢɹ ɢɡ ɬɪɺɯ (ɢɫɩɪɚɜɥɟɧɵ ɨɛɟ ɨɲɢɛɤɢ, ɧɨ
ɜ ɩɟɪɜɨɦ ɩɭɧɤɬɟ ɡɚɞɚɧɢɹ ɧɟ ɩɪɢɜɟɞɟɧɚ ɬɚɛɥɢɰɚ (ɥɢɛɨ ɬɚɛɥɢɰɚ ɫɨɞɟɪɠɢɬ
ɨɲɢɛɤɢ ɜ ɞɜɭɯ ɢ ɛɨɥɟɟ ɫɬɪɨɤɚɯ), ɥɢɛɨ ɩɪɢɜɟɞɟɧɚ ɬɚɛɥɢɰɚ (ɤɨɬɨɪɚɹ ɫɨɞɟɪɠɢɬ
ɨɲɢɛɤɢ ɧɟ ɛɨɥɟɟ ɱɟɦ ɜ ɨɞɧɨɣ ɫɬɪɨɤɟ), ɧɨ ɢɫɩɪɚɜɥɟɧɚ ɬɨɥɶɤɨ ɨɞɧɚ ɨɲɢɛɤɚ
ɩɪɨɝɪɚɦɦɵ).
ɉɪɢ ɧɚɩɢɫɚɧɢɢ ɨɩɟɪɚɰɢɣ ɫɪɚɜɧɟɧɢɹ ɞɨɩɭɫɤɚɟɬɫɹ ɨɞɧɨ ɧɟɩɪɚɜɢɥɶɧɨɟ
2
ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɫɬɪɨɝɢɯ/ɧɟɫɬɪɨɝɢɯ ɧɟɪɚɜɟɧɫɬɜ (ɫɱɢɬɚɟɬɫɹ ɧɟɫɭɳɟɫɬɜɟɧɧɨɣ
ɨɲɢɛɤɨɣ, ɩɨɝɪɟɲɧɨɫɬɶɸ ɡɚɩɢɫɢ). ɇɚɩɪɢɦɟɪ, ɜɦɟɫɬɨ «x>=5» ɢɫɩɨɥɶɡɭɟɬɫɹ
«x>5».
2. ɂɥɢ ɜɵɩɨɥɧɟɧɵ ɜɫɟ ɬɪɢ ɞɟɣɫɬɜɢɹ, ɧɨ ɩɪɢ ɷɬɨɦ ɜ ɥɨɝɢɱɟɫɤɨɦ ɜɵɪɚɠɟɧɢɢ
ɧɟɜɟɪɧɨ ɭɱɬɟɧɵ ɩɪɢɨɪɢɬɟɬɵ ɥɨɝɢɱɟɫɤɢɯ ɨɩɟɪɚɰɢɣ (ɧɟ ɪɚɫɫɬɚɜɥɟɧɵ ɢɥɢ
ɧɟɩɪɚɜɢɥɶɧɨ ɪɚɫɫɬɚɜɥɟɧɵ ɫɤɨɛɤɢ ɜ ɜɵɪɚɠɟɧɢɹɯ).
ɉɪɚɜɢɥɶɧɨ ɜɵɩɨɥɧɟɧɨ ɬɨɥɶɤɨ ɨɞɧɨ ɞɟɣɫɬɜɢɟ ɢɡ ɬɪɺɯ, ɬɨ ɟɫɬɶ ɥɢɛɨ ɬɨɥɶɤɨ
ɩɪɢɜɟɞɟɧɚ ɬɚɛɥɢɰɚ, ɤɨɬɨɪɚɹ ɫɨɞɟɪɠɢɬ ɨɲɢɛɤɢ ɜ ɧɟ ɛɨɥɟɟ ɱɟɦ ɨɞɧɨɣ ɫɬɪɨɤɟ,
ɥɢɛɨ ɬɚɛɥɢɰɚ ɧɟ ɩɪɢɜɟɞɟɧɚ (ɢɥɢ ɩɪɢɜɟɞɟɧɚ ɢ ɫɨɞɟɪɠɢɬ ɨɲɢɛɤɢ ɛɨɥɟɟ ɱɟɦ
ɜ ɨɞɧɨɣ ɫɬɪɨɤɟ), ɧɨ ɢɫɩɪɚɜɥɟɧɚ ɨɞɧɚ ɨɲɢɛɤɚ ɩɪɨɝɪɚɦɦɵ. ɉɪɢ ɨɰɟɧɢɜɚɧɢɢ
1
ɷɬɨɝɨ ɡɚɞɚɧɢɹ ɧɚ 1 ɛɚɥɥ ɞɨɩɭɫɤɚɟɬɫɹ ɧɟ ɭɱɢɬɵɜɚɬɶ ɤɨɪɪɟɤɬɧɨɫɬɶ ɪɚɛɨɬɵ
ɩɪɨɝɪɚɦɦ ɧɚ ɬɨɱɤɚɯ ɝɪɚɧɢɰ ɨɛɥɚɫɬɟɣ (ɜɦɟɫɬɨ ɧɟɫɬɪɨɝɢɯ ɧɟɪɚɜɟɧɫɬɜ
ɜ ɪɟɲɟɧɢɢ ɛɵɥɢ ɢɫɩɨɥɶɡɨɜɚɧɵ ɫɬɪɨɝɢɟ ɧɟɪɚɜɟɧɫɬɜɚ ɢɥɢ ɧɚɨɛɨɪɨɬ).
ȼɫɟ ɩɭɧɤɬɵ ɡɚɞɚɧɢɹ ɜɵɩɨɥɧɟɧɵ ɧɟɜɟɪɧɨ (ɬɚɛɥɢɰɚ ɚɧɚɥɢɡɚ ɩɪɚɜɢɥɶɧɨɫɬɢ
ɚɥɝɨɪɢɬɦɚ ɧɟ ɩɪɢɜɟɞɟɧɚ, ɥɢɛɨ ɫɨɞɟɪɠɢɬ ɨɲɢɛɤɢ ɜ ɞɜɭɯ ɢ ɛɨɥɟɟ ɫɬɪɨɤɚɯ,
0
ɩɪɨɝɪɚɦɦɚ ɧɟ ɩɪɢɜɟɞɟɧɚ, ɥɢɛɨ ɧɢ ɨɞɧɚ ɢɡ ɞɜɭɯ ɨɲɢɛɨɤ ɧɟ ɢɫɩɪɚɜɥɟɧɚ).
3
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
C2
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5
Ⱦɚɧ ɦɚɫɫɢɜ, ɫɨɞɟɪɠɚɳɢɣ 70 ɰɟɥɵɯ ɱɢɫɟɥ. Ɉɩɢɲɢɬɟ ɧɚ ɨɞɧɨɦ ɢɡ ɹɡɵɤɨɜ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɚɥɝɨɪɢɬɦ, ɩɨɡɜɨɥɹɸɳɢɣ ɧɚɣɬɢ ɢ ɜɵɜɟɫɬɢ ɧɚɢɦɟɧɶɲɟɟ
ɫɨɞɟɪɠɚɳɟɟɫɹ ɜ ɦɚɫɫɢɜɟ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɱɢɫɥɨ, ɞɟɫɹɬɢɱɧɚɹ ɡɚɩɢɫɶ ɤɨɬɨɪɨɝɨ
ɧɟ ɨɤɚɧɱɢɜɚɟɬɫɹ ɰɢɮɪɨɣ 7. Ƚɚɪɚɧɬɢɪɭɟɬɫɹ, ɱɬɨ ɜ ɦɚɫɫɢɜɟ ɟɫɬɶ ɯɨɬɹ ɛɵ ɨɞɢɧ
ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɷɥɟɦɟɧɬ, ɞɟɫɹɬɢɱɧɚɹ ɡɚɩɢɫɶ ɤɨɬɨɪɨɝɨ ɧɟ ɨɤɚɧɱɢɜɚɟɬɫɹ
ɰɢɮɪɨɣ 7.
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɨɛɴɹɜɥɟɧɵ ɬɚɤ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɢɠɟ. Ɂɚɩɪɟɳɚɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɟɪɟɦɟɧɧɵɟ, ɧɟ ɨɩɢɫɚɧɧɵɟ ɧɢɠɟ, ɧɨ ɪɚɡɪɟɲɚɟɬɫɹ ɧɟ ɢɫɩɨɥɶɡɨɜɚɬɶ
ɱɚɫɬɶ ɢɡ ɧɢɯ.
ɉɚɫɤɚɥɶ
const
N=70;
var
a: array [1..N] of integer;
i, j, m: integer;
begin
for i:=1 to N do
readln(a[i]);
…
end.
Ȼɟɣɫɢɤ
N=70
DIM A(N) AS INTEGER
DIM I, J, M AS INTEGER
FOR I = 1 TO N
INPUT A(I)
NEXT I
…
END
ɋɢ
#include <stdio.h>
#define N 70
void main(){
int a[N];
int I, j, m;
for (i=0; i<N; i++)
scanf("%d", &a[i]);
…
}
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ɚɥɝ
ɧɚɱ
Ⱥɥɝɨɪɢɬɦɢɱɟɫɤɢɣ
ɹɡɵɤ
ɤɨɧ
6
ɰɟɥ N=70
ɰɟɥɬɚɛ a[1:N]
ɰɟɥ i, j, m
ɧɰ ɞɥɹ i ɨɬ 1 ɞɨ N
ɜɜɨɞ a[i]
ɤɰ
…
ȼ ɤɚɱɟɫɬɜɟ ɨɬɜɟɬɚ ȼɚɦ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɜɟɫɬɢ ɮɪɚɝɦɟɧɬ ɩɪɨɝɪɚɦɦɵ, ɤɨɬɨɪɵɣ
ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɧɚ ɦɟɫɬɟ ɦɧɨɝɨɬɨɱɢɹ. ȼɵ ɦɨɠɟɬɟ ɡɚɩɢɫɚɬɶ ɪɟɲɟɧɢɟ ɬɚɤɠɟ
ɧɚ ɞɪɭɝɨɦ ɹɡɵɤɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ (ɭɤɚɠɢɬɟ ɧɚɡɜɚɧɢɟ ɢ ɢɫɩɨɥɶɡɭɟɦɭɸ
ɜɟɪɫɢɸ ɹɡɵɤɚ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɧɚɩɪɢɦɟɪ Free Pascal 2.4) ɢɥɢ ɜ ɜɢɞɟ ɛɥɨɤɫɯɟɦɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ȼɵ ɞɨɥɠɧɵ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɟ ɠɟ ɫɚɦɵɟ ɢɫɯɨɞɧɵɟ
ɞɚɧɧɵɟ ɢ ɩɟɪɟɦɟɧɧɵɟ, ɤɚɤɢɟ ɛɵɥɢ ɩɪɟɞɥɨɠɟɧɵ ɜ ɭɫɥɨɜɢɢ.
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
ȼ ɡɚɞɚɱɟ ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɦɢɧɢɦɚɥɶɧɵɣ ɫɪɟɞɢ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɯ
ɡɚɞɚɧɧɨɦɭ ɜ ɭɫɥɨɜɢɢ ɨɝɪɚɧɢɱɟɧɢɸ. ɉɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɬɚɧɞɚɪɬɧɨɣ ɡɚɞɚɱɟɣ ɩɨɢɫɤɚ
ɦɢɧɢɦɚɥɶɧɨɝɨ ɫɪɟɞɢ ɜɫɟɯ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ ɞɨɩɨɥɧɢɬɟɥɶɧɚɹ ɫɥɨɠɧɨɫɬɶ ɞɚɧɧɨɣ
ɡɚɞɚɱɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɧɟɥɶɡɹ ɛɪɚɬɶ ɜ ɤɚɱɟɫɬɜɟ ɩɟɪɜɨɝɨ ɡɧɚɱɟɧɢɹ ɦɢɧɢɦɭɦɚ
ɩɟɪɜɵɣ ɷɥɟɦɟɧɬ ɦɚɫɫɢɜɚ, ɬɚɤ ɤɚɤ ɷɬɨɬ ɷɥɟɦɟɧɬ ɦɨɠɟɬ ɧɟ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɡɚɞɚɧɧɵɦ
ɨɝɪɚɧɢɱɟɧɢɹɦ. ɇɟɥɶɡɹ ɬɚɤɠɟ ɩɪɢɧɹɬɶ ɜ ɤɚɱɟɫɬɜɟ ɩɟɪɜɨɝɨ ɡɧɚɱɟɧɢɹ ɛɨɥɶɲɨɟ ɱɢɫɥɨ,
ɡɚɜɟɞɨɦɨ ɩɪɟɜɨɫɯɨɞɹɳɟɟ ɜɫɟ ɜɨɡɦɨɠɧɵɟ ɡɧɚɱɟɧɢɹ ɞɚɧɧɵɯ, ɬɚɤ ɤɚɤ ɜ ɭɫɥɨɜɢɢ ɧɟ ɭɤɚɡɚɧ
ɞɢɚɩɚɡɨɧ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ.
ɇɢɠɟ
ɩɪɟɞɫɬɚɜɥɟɧɵ
ɧɟɫɤɨɥɶɤɨ
ɜɨɡɦɨɠɧɵɯ
ɫɩɨɫɨɛɨɜ
ɪɟɲɟɧɢɹ
ɡɚɞɚɱɢ,
ɩɪɨɢɥɥɸɫɬɪɢɪɨɜɚɧɧɵɟ ɮɪɚɝɦɟɧɬɚɦɢ ɩɪɨɝɪɚɦɦ ɧɚ ɪɚɡɧɵɯ ɹɡɵɤɚɯ. ɋɩɨɫɨɛɵ ɪɟɲɟɧɢɹ ɧɟ
ɩɪɢɜɹɡɚɧɵ ɤ ɹɡɵɤɚɦ: ɥɸɛɨɣ ɢɡ ɷɬɢɯ ɫɩɨɫɨɛɨɜ ɦɨɠɟɬ ɛɵɬɶ ɪɟɚɥɢɡɨɜɚɧ ɧɚ ɥɸɛɨɦ
ɞɨɩɭɫɬɢɦɨɦ ɹɡɵɤɟ.
ɋɩɨɫɨɛ 1.
ȼ ɤɚɱɟɫɬɜɟ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɦɢɧɢɦɭɦɚ ɩɪɢɧɢɦɚɟɬɫɹ ɡɧɚɱɟɧɢɟ, ɡɚɜɟɞɨɦɨ ɧɟ
ɩɨɞɯɨɞɹɳɟɟ ɩɨɞ ɡɚɞɚɧɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ, ɧɚɩɪɢɦɟɪ 0.
ɉɪɢɦɟɪ ɩɪɨɝɪɚɦɦɵ ɧɚ ɉɚɫɤɚɥɟ
m:=0;
for i:=1 to N do begin
if (a[i]>0) and (a[i] mod 10<>7) and ((m=0) or (a[i]<m))
then m := a[i];
end;
writeln(m);
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
7
ɋɩɨɫɨɛ 2.
ȼɦɟɫɬɨ ɩɪɨɜɟɪɤɢ ɫɩɟɰɢɚɥɶɧɨɝɨ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɬɞɟɥɶɧɚɹ
ɩɟɪɟɦɟɧɧɚɹ, ɩɨɤɚɡɵɜɚɸɳɚɹ, ɛɵɥ ɥɢ ɭɠɟ ɧɚɣɞɟɧ ɯɨɬɹ ɛɵ ɨɞɢɧ ɩɨɞɯɨɞɹɳɢɣ ɩɨɞ
ɨɝɪɚɧɢɱɟɧɢɹ ɷɥɟɦɟɧɬ. Ⱦɥɹ ɷɬɨɣ ɩɟɪɟɦɟɧɧɨɣ ɫɥɟɞɨɜɚɥɨ ɛɵ ɢɫɩɨɥɶɡɨɜɚɬɶ ɥɨɝɢɱɟɫɤɢɣ
ɬɢɩ, ɧɨ ɜ ɭɫɥɨɜɢɢ ɪɚɡɪɟɲɟɧɵ ɬɨɥɶɤɨ ɰɟɥɵɟ ɩɟɪɟɦɟɧɧɵɟ, ɩɨɷɬɨɦɭ ɥɨɝɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ
ɦɨɞɟɥɢɪɭɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɰɟɥɨɝɨ.
ɉɪɢɦɟɪ ɩɪɨɝɪɚɦɦɵ ɧɚ Ȼɟɣɫɢɤɟ
M = 0: J = 0
FOR I = 1 TO N
IF A(I)>0 AND A(i) MOD 10 <> 7 AND (J=0 OR A(I)<M) THEN
M = A(I)
J = 1
END IF
NEXT I
PRINT M
ɋɩɨɫɨɛ 3.
ɋɧɚɱɚɥɚ ɜ ɦɚɫɫɢɜɟ ɢɳɟɬɫɹ ɩɟɪɜɵɣ ɷɥɟɦɟɧɬ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɨɝɪɚɧɢɱɟɧɢɹɦ. Ɂɚɬɟɦ
ɜ ɨɫɬɚɜɲɟɣɫɹ ɱɚɫɬɢ ɦɚɫɫɢɜɚ ɢɳɟɬɫɹ ɩɨɞɯɨɞɹɳɢɣ ɧɚɢɦɟɧɶɲɢɣ ɷɥɟɦɟɧɬ. ɗɬɨɬ ɫɩɨɫɨɛ
ɩɪɢɜɨɞɢɬ ɤ ɛɨɥɟɟ ɞɥɢɧɧɨɣ (ɬɪɟɛɭɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɜɚ ɰɢɤɥɚ), ɧɨ ɧɟ ɦɟɧɟɟ
ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɟ.
ɉɪɢɦɟɪ ɩɪɨɝɪɚɦɦɵ ɧɚ ɚɥɝɨɪɢɬɦɢɱɟɫɤɨɦ ɹɡɵɤɟ
i:=1
ɧɰ ɩɨɤɚ ɧɟ (a[i]>0 ɢ mod(a[i],10)<>7)
i := i+1
ɤɰ
m := a[i]
ɧɰ ɞɥɹ i ɨɬ i+1 ɞɨ N
ɟɫɥɢ a[i]>0 ɢ mod(a[i],10)<>7 ɢ a[i]<m
ɬɨ m:=a[i]
ɜɫɟ
ɤɰ
ɜɵɜɨɞ m
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
8
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ɉɪɟɞɥɨɠɟɧ ɩɪɚɜɢɥɶɧɵɣ ɚɥɝɨɪɢɬɦ, ɜɵɞɚɸɳɢɣ ɜɟɪɧɨɟ ɡɧɚɱɟɧɢɟ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɡɚɩɢɫɶ ɚɥɝɨɪɢɬɦɚ ɧɚ ɞɪɭɝɨɦ ɹɡɵɤɟ, ɢɫɩɨɥɶɡɭɸɳɚɹ ɚɧɚɥɨɝɢɱɧɵɟ
ɩɟɪɟɦɟɧɧɵɟ. ȼ ɫɥɭɱɚɟ ɟɫɥɢ ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɢɫɩɨɥɶɡɭɟɬ
ɬɢɩɢɡɢɪɨɜɚɧɧɵɟ ɩɟɪɟɦɟɧɧɵɟ, ɨɩɢɫɚɧɢɹ ɩɟɪɟɦɟɧɧɵɯ ɞɨɥɠɧɵ ɛɵɬɶ
ɚɧɚɥɨɝɢɱɧɵ ɨɩɢɫɚɧɢɹɦ ɩɟɪɟɦɟɧɧɵɯ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɦ ɹɡɵɤɟ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ
2
ɧɟɬɢɩɢɡɢɪɨɜɚɧɧɵɯ ɢɥɢ ɧɟɨɛɴɹɜɥɟɧɧɵɯ ɩɟɪɟɦɟɧɧɵɯ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ
ɜ ɫɥɭɱɚɟ, ɟɫɥɢ ɷɬɨ ɞɨɩɭɫɤɚɟɬɫɹ ɹɡɵɤɨɦ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɩɪɢ ɷɬɨɦ
ɤɨɥɢɱɟɫɬɜɨ ɩɟɪɟɦɟɧɧɵɯ ɢ ɢɯ ɢɞɟɧɬɢɮɢɤɚɬɨɪɵ ɞɨɥɠɧɵ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ
ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ. ȼ ɚɥɝɨɪɢɬɦɟ, ɡɚɩɢɫɚɧɧɨɦ ɧɚ ɹɡɵɤɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ,
ɞɨɩɭɫɤɚɟɬɫɹ ɧɚɥɢɱɢɟ ɨɬɞɟɥɶɧɵɯ ɫɢɧɬɚɤɫɢɱɟɫɤɢɯ ɨɲɢɛɨɤ, ɧɟ ɢɫɤɚɠɚɸɳɢɯ
ɡɚɦɵɫɥɚ ɚɜɬɨɪɚ ɩɪɨɝɪɚɦɦɵ.
ȼ ɥɸɛɨɦ ɜɚɪɢɚɧɬɟ ɪɟɲɟɧɢɹ ɦɨɠɟɬ ɩɪɢɫɭɬɫɬɜɨɜɚɬɶ ɧɟ ɛɨɥɟɟ ɨɞɧɨɣ ɨɲɢɛɤɢ ɢɡ
ɱɢɫɥɚ ɫɥɟɞɭɸɳɢɯ:
1. ɇɟ ɢɧɢɰɢɚɥɢɡɢɪɭɟɬɫɹ ɢɥɢ ɧɟɜɟɪɧɨ ɢɧɢɰɢɚɥɢɡɢɪɭɟɬɫɹ ɩɟɪɟɦɟɧɧɚɹ m.
ȼ ɱɚɫɬɧɨɫɬɢ, ɧɟɥɶɡɹ ɢɧɢɰɢɚɥɢɡɢɪɨɜɚɬɶ ɷɬɭ ɩɟɪɟɦɟɧɧɭɸ ɩɟɪɜɵɦ ɷɥɟɦɟɧɬɨɦ
ɦɚɫɫɢɜɚ. ɇɟɥɶɡɹ ɬɚɤɠɟ ɢɧɢɰɢɚɥɢɡɢɪɨɜɚɬɶ ɟɺ ɤɚɤɢɦ-ɬɨ ɨɱɟɧɶ ɛɨɥɶɲɢɦ
ɡɧɚɱɟɧɢɟɦ (ɧɚɩɪɢɦɟɪ, maxInt ɜ ɉɚɫɤɚɥɟ)
2. ɇɟɜɟɪɧɨ ɩɪɨɜɟɪɹɟɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨɫɬɶ ɷɥɟɦɟɧɬɨɜ ɦɚɫɫɢɜɚ
3. ɇɟɜɟɪɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɫɥɟɞɧɹɹ ɰɢɮɪɚ ɞɟɫɹɬɢɱɧɨɣ ɡɚɩɢɫɢ ɱɢɫɥɚ
4. ȼ ɫɥɨɠɧɨɦ ɥɨɝɢɱɟɫɤɨɦ ɭɫɥɨɜɢɢ ɩɪɨɫɬɵɟ ɩɪɨɜɟɪɤɢ ɜɟɪɧɵ, ɧɨ ɭɫɥɨɜɢɟ
ɜ ɰɟɥɨɦ ɩɨɫɬɪɨɟɧɨ ɧɟɜɟɪɧɨ (ɧɚɩɪɢɦɟɪ, ɩɟɪɟɩɭɬɚɧɵ ɨɩɟɪɚɰɢɢ ɂ ɢ ɂɅɂ,
ɧɟɜɟɪɧɨ ɪɚɫɫɬɚɜɥɟɧɵ ɫɤɨɛɤɢ ɜ ɥɨɝɢɱɟɫɤɨɦ ɜɵɪɚɠɟɧɢɢ).
5. ȼɦɟɫɬɨ ɡɧɚɱɟɧɢɹ ɷɥɟɦɟɧɬɚ ɩɪɨɜɟɪɹɟɬɫɹ ɟɝɨ ɢɧɞɟɤɫ.
6. Ɉɬɫɭɬɫɬɜɭɟɬ ɜɵɜɨɞ ɨɬɜɟɬɚ.
7.
ɂɫɩɨɥɶɡɭɟɬɫɹ ɩɟɪɟɦɟɧɧɚɹ, ɧɟ ɨɛɴɹɜɥɟɧɧɚɹ ɜ ɪɚɡɞɟɥɟ ɨɩɢɫɚɧɢɹ
ɩɟɪɟɦɟɧɧɵɯ.
8. ɇɟ ɭɤɚɡɚɧɨ ɢɥɢ ɧɟɜɟɪɧɨ ɭɤɚɡɚɧɨ ɭɫɥɨɜɢɟ ɡɚɜɟɪɲɟɧɢɹ ɰɢɤɥɚ.
9. ɂɧɞɟɤɫɧɚɹ ɩɟɪɟɦɟɧɧɚɹ ɜ ɰɢɤɥɟ ɧɟ ɦɟɧɹɟɬɫɹ (ɧɚɩɪɢɦɟɪ, ɜ ɰɢɤɥɟ while)
ɢɥɢ ɦɟɧɹɟɬɫɹ ɧɟɜɟɪɧɨ.
Ɉɲɢɛɨɤ, ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜ ɩ. 1–9, ɞɜɟ ɢɥɢ ɛɨɥɶɲɟ, ɢɥɢ ɚɥɝɨɪɢɬɦ
ɫɮɨɪɦɭɥɢɪɨɜɚɧ ɧɟɜɟɪɧɨ.
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
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ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
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Ⱦɜɚ ɢɝɪɨɤɚ, ɉɚɲɚ ɢ ȼɨɜɚ, ɢɝɪɚɸɬ ɜ ɫɥɟɞɭɸɳɭɸ ɢɝɪɭ. ɉɟɪɟɞ ɢɝɪɨɤɚɦɢ ɥɟɠɢɬ
ɤɭɱɚ ɤɚɦɧɟɣ. ɂɝɪɨɤɢ ɯɨɞɹɬ ɩɨ ɨɱɟɪɟɞɢ, ɩɟɪɜɵɣ ɯɨɞ ɞɟɥɚɟɬ ɉɚɲɚ. Ɂɚ ɨɞɢɧ ɯɨɞ
ɢɝɪɨɤ ɦɨɠɟɬ ɞɨɛɚɜɢɬɶ ɜ ɤɭɱɭ 1 ɤɚɦɟɧɶ ɢɥɢ 10 ɤɚɦɧɟɣ. ɇɚɩɪɢɦɟɪ, ɢɦɟɹ ɤɭɱɭ
ɢɡ 7 ɤɚɦɧɟɣ, ɡɚ ɨɞɢɧ ɯɨɞ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɤɭɱɭ ɢɡ 8 ɢɥɢ 17 ɤɚɦɧɟɣ. ɍ ɤɚɠɞɨɝɨ
ɢɝɪɨɤɚ, ɱɬɨɛɵ ɞɟɥɚɬɶ ɯɨɞɵ, ɟɫɬɶ ɧɟɨɝɪɚɧɢɱɟɧɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ.
ɂɝɪɚ ɡɚɜɟɪɲɚɟɬɫɹ ɜ ɬɨɬ ɦɨɦɟɧɬ, ɤɨɝɞɚ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ ɜ ɤɭɱɟ ɫɬɚɧɨɜɢɬɫɹ
ɧɟ ɦɟɧɟɟ 41. ɉɨɛɟɞɢɬɟɥɟɦ ɫɱɢɬɚɟɬɫɹ ɢɝɪɨɤ, ɫɞɟɥɚɜɲɢɣ ɩɨɫɥɟɞɧɢɣ ɯɨɞ, ɬɨ ɟɫɬɶ
ɩɟɪɜɵɦ ɩɨɥɭɱɢɜɲɢɣ ɤɭɱɭ, ɜ ɤɨɬɨɪɨɣ ɛɭɞɟɬ 41 ɢɥɢ ɛɨɥɶɲɟ ɤɚɦɧɟɣ.
ȼ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜ ɤɭɱɟ ɛɵɥɨ S ɤɚɦɧɟɣ, 1S40.
Ȼɭɞɟɦ ɝɨɜɨɪɢɬɶ, ɱɬɨ ɢɝɪɨɤ ɢɦɟɟɬ ɜɵɢɝɪɵɲɧɭɸ ɫɬɪɚɬɟɝɢɸ, ɟɫɥɢ ɨɧ ɦɨɠɟɬ
ɜɵɢɝɪɚɬɶ ɩɪɢ ɥɸɛɵɯ ɯɨɞɚɯ ɩɪɨɬɢɜɧɢɤɚ. Ɉɩɢɫɚɬɶ ɫɬɪɚɬɟɝɢɸ ɢɝɪɨɤɚ – ɡɧɚɱɢɬ
ɨɩɢɫɚɬɶ, ɤɚɤɨɣ ɯɨɞ ɨɧ ɞɨɥɠɟɧ ɫɞɟɥɚɬɶ ɜ ɥɸɛɨɣ ɫɢɬɭɚɰɢɢ, ɤɨɬɨɪɚɹ ɟɦɭ ɦɨɠɟɬ
ɜɫɬɪɟɬɢɬɶɫɹ ɩɪɢ ɪɚɡɥɢɱɧɨɣ ɢɝɪɟ ɩɪɨɬɢɜɧɢɤɚ.
ȼɵɩɨɥɧɢɬɟ ɫɥɟɞɭɸɳɢɟ ɡɚɞɚɧɢɹ. ȼɨ ɜɫɟɯ ɫɥɭɱɚɹɯ ɨɛɨɫɧɨɜɵɜɚɣɬɟ ɫɜɨɣ ɨɬɜɟɬ.
1. ɚ) ɍɤɚɠɢɬɟ ɜɫɟ ɬɚɤɢɟ ɡɧɚɱɟɧɢɹ ɱɢɫɥɚ S, ɩɪɢ ɤɨɬɨɪɵɯ ɉɚɲɚ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ
ɜ ɨɞɢɧ ɯɨɞ. Ɉɛɨɫɧɭɣɬɟ, ɱɬɨ ɧɚɣɞɟɧɵ ɜɫɟ ɧɭɠɧɵɟ ɡɧɚɱɟɧɢɹ S, ɢ ɭɤɚɠɢɬɟ
ɜɵɢɝɪɵɜɚɸɳɢɟ ɯɨɞɵ.
ɛ) ɍɤɚɠɢɬɟ ɬɚɤɨɟ ɡɧɚɱɟɧɢɟ S, ɩɪɢ ɤɨɬɨɪɨɦ ɉɚɲɚ ɧɟ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɡɚ ɨɞɢɧ
ɯɨɞ, ɧɨ ɩɪɢ ɥɸɛɨɦ ɯɨɞɟ ɉɚɲɢ ȼɨɜɚ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɫɜɨɢɦ ɩɟɪɜɵɦ ɯɨɞɨɦ.
Ɉɩɢɲɢɬɟ ɜɵɢɝɪɵɲɧɭɸ ɫɬɪɚɬɟɝɢɸ ȼɨɜɵ.
2. ɍɤɚɠɢɬɟ ɞɜɚ ɡɧɚɱɟɧɢɹ S, ɩɪɢ ɤɨɬɨɪɵɯ ɭ ɉɚɲɢ ɟɫɬɶ ɜɵɢɝɪɵɲɧɚɹ ɫɬɪɚɬɟɝɢɹ,
ɩɪɢɱɺɦ ɉɚɲɚ ɧɟ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɡɚ ɨɞɢɧ ɯɨɞ, ɧɨ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɫɜɨɢɦ
ɜɬɨɪɵɦ ɯɨɞɨɦ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɬɨɝɨ, ɤɚɤ ɛɭɞɟɬ ɯɨɞɢɬɶ ȼɨɜɚ. Ⱦɥɹ ɭɤɚɡɚɧɧɵɯ
ɡɧɚɱɟɧɢɣ S ɨɩɢɲɢɬɟ ɜɵɢɝɪɵɲɧɭɸ ɫɬɪɚɬɟɝɢɸ ɉɚɲɢ.
3. ɍɤɚɠɢɬɟ ɡɧɚɱɟɧɢɟ S, ɩɪɢ ɤɨɬɨɪɨɦ ɭ ȼɨɜɵ ɟɫɬɶ ɜɵɢɝɪɵɲɧɚɹ ɫɬɪɚɬɟɝɢɹ,
ɩɨɡɜɨɥɹɸɳɚɹ ɟɦɭ ɜɵɢɝɪɚɬɶ ɩɟɪɜɵɦ ɢɥɢ ɜɬɨɪɵɦ ɯɨɞɨɦ ɩɪɢ ɥɸɛɨɣ ɢɝɪɟ ɉɚɲɢ,
ɨɞɧɚɤɨ ɭ ȼɨɜɵ ɧɟɬ ɫɬɪɚɬɟɝɢɢ, ɤɨɬɨɪɚɹ ɩɨɡɜɨɥɢɬ ɟɦɭ ɝɚɪɚɧɬɢɪɨɜɚɧɧɨ ɜɵɢɝɪɚɬɶ
ɩɟɪɜɵɦ ɯɨɞɨɦ. Ⱦɥɹ ɭɤɚɡɚɧɧɨɝɨ ɡɧɚɱɟɧɢɹ S ɨɩɢɲɢɬɟ ɜɵɢɝɪɵɲɧɭɸ ɫɬɪɚɬɟɝɢɸ
ȼɨɜɵ. ɉɨɫɬɪɨɣɬɟ ɞɟɪɟɜɨ ɜɫɟɯ ɩɚɪɬɢɣ, ɜɨɡɦɨɠɧɵɯ ɩɪɢ ɷɬɨɣ ɜɵɢɝɪɵɲɧɨɣ
ɫɬɪɚɬɟɝɢɢ ȼɨɜɵ (ɜ ɜɢɞɟ ɪɢɫɭɧɤɚ ɢɥɢ ɬɚɛɥɢɰɵ). ɇɚ ɪɟɛɪɚɯ ɞɟɪɟɜɚ ɭɤɚɡɵɜɚɣɬɟ,
ɤɬɨ ɞɟɥɚɟɬ ɯɨɞ, ɜ ɭɡɥɚɯ – ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ ɜ ɤɭɱɟ.
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
1. ɚ) ɉɚɲɚ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɩɟɪɜɵɦ ɯɨɞɨɦ, ɟɫɥɢ S =31, …, 40. ȼɨ ɜɫɟɯ ɫɥɭɱɚɹɯ ɦɨɠɧɨ
ɞɨɛɚɜɢɬɶ ɜ ɤɭɱɭ 10 ɤɚɦɧɟɣ. ɉɪɢ ɦɟɧɶɲɢɯ ɡɧɚɱɟɧɢɹɯ S ɡɚ ɨɞɢɧ ɯɨɞ ɧɟɥɶɡɹ ɩɨɥɭɱɢɬɶ
ɤɭɱɭ, ɜ ɤɨɬɨɪɨɣ ɛɨɥɶɲɟ 40 ɤɚɦɧɟɣ.
ɛ) ȼɨɜɚ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ ɩɟɪɜɵɦ ɯɨɞɨɦ (ɤɚɤ ɛɵ ɧɢ ɢɝɪɚɥ ɉɚɲɚ), ɟɫɥɢ ɢɫɯɨɞɧɨ ɜ ɤɭɱɟ
ɛɭɞɟɬ S=30 ɤɚɦɧɟɣ. Ɍɨɝɞɚ ɩɨɫɥɟ ɩɟɪɜɨɝɨ ɯɨɞɚ ɉɚɲɢ ɜ ɤɭɱɟ ɛɭɞɟɬ 31 ɤɚɦɟɧɶ ɢɥɢ 40
ɤɚɦɧɟɣ. ȼ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ȼɨɜɚ ɦɨɠɟɬ ɞɨɛɚɜɢɬɶ ɜ ɤɭɱɭ 10 ɤɚɦɧɟɣ ɢ ɜɵɢɝɪɚɬɶ ɩɟɪɜɵɦ
ɯɨɞɨɦ.
2. ȼɨɡɦɨɠɧɵɟ ɡɧɚɱɟɧɢɹ S: 20 ɢ 29. ȼ ɷɬɢɯ ɫɥɭɱɚɹɯ ɉɚɲɚ, ɨɱɟɜɢɞɧɨ, ɧɟ ɦɨɠɟɬ ɜɵɢɝɪɚɬɶ
ɩɟɪɜɵɦ ɯɨɞɨɦ. Ɉɞɧɚɤɨ ɨɧ ɦɨɠɟɬ ɩɨɥɭɱɢɬɶ ɤɭɱɭ ɢɡ 30 ɤɚɦɧɟɣ. ɗɬɚ ɩɨɡɢɰɢɹ ɪɚɡɨɛɪɚɧɚ
ɜ ɩ. 1ɛ. ȼ ɧɟɣ ɢɝɪɨɤ, ɤɨɬɨɪɵɣ ɛɭɞɟɬ ɯɨɞɢɬɶ (ɬɟɩɟɪɶ ɷɬɨ ȼɨɜɚ), ɜɵɢɝɪɚɬɶ ɧɟ ɦɨɠɟɬ, ɚ ɟɝɨ
ɩɪɨɬɢɜɧɢɤ (ɬɨ ɟɫɬɶ ɉɚɲɚ) ɫɥɟɞɭɸɳɢɦ ɯɨɞɨɦ ɜɵɢɝɪɚɟɬ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
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3. ȼɨɡɦɨɠɧɨɟ ɡɧɚɱɟɧɢɟ S: 28. ɉɨɫɥɟ ɩɟɪɜɨɝɨ ɯɨɞɚ ɉɚɲɢ ɜ ɤɭɱɟ ɛɭɞɟɬ 29 ɢɥɢ 38 ɤɚɦɧɟɣ.
ȿɫɥɢ ɜ ɤɭɱɟ ɫɬɚɧɟɬ 38 ɤɚɦɧɟɣ, ȼɨɜɚ ɞɨɛɚɜɢɬ ɜ ɤɭɱɭ 10 ɤɚɦɧɟɣ ɢ ɜɵɢɝɪɚɟɬ ɩɟɪɜɵɦ
ɯɨɞɨɦ. ɋɢɬɭɚɰɢɹ, ɤɨɝɞɚ ɜ ɤɭɱɟ 29 ɤɚɦɧɟɣ, ɪɚɡɨɛɪɚɧɚ ɜ ɩ. 2. ȼ ɷɬɨɣ ɫɢɬɭɚɰɢɢ ɢɝɪɨɤ,
ɤɨɬɨɪɵɣ ɛɭɞɟɬ ɯɨɞɢɬɶ (ɬɟɩɟɪɶ ɷɬɨ ȼɨɜɚ), ɜɵɢɝɪɵɜɚɟɬ ɫɜɨɢɦ ɜɬɨɪɵɦ ɯɨɞɨɦ.
ȼ ɬɚɛɥɢɰɟ ɢɡɨɛɪɚɠɟɧɨ ɞɟɪɟɜɨ ɜɨɡɦɨɠɧɵɯ ɩɚɪɬɢɣ ɩɪɢ ɨɩɢɫɚɧɧɨɣ ɫɬɪɚɬɟɝɢɢ ȼɨɜɵ.
Ɂɚɤɥɸɱɢɬɟɥɶɧɵɟ ɩɨɡɢɰɢɢ (ɜ ɧɢɯ ɜɵɢɝɪɵɜɚɟɬ ȼɨɜɚ) ɩɨɞɱɺɪɤɧɭɬɵ. ɇɚ ɪɢɫɭɧɤɟ ɷɬɨ ɠɟ
ɞɟɪɟɜɨ ɢɡɨɛɪɚɠɟɧɨ ɜ ɝɪɚɮɢɱɟɫɤɨɦ ɜɢɞɟ (ɨɛɚ ɫɩɨɫɨɛɚ ɢɡɨɛɪɚɠɟɧɢɹ ɞɟɪɟɜɚ ɞɨɩɭɫɬɢɦɵ).
ɂɫɯɨɞɧɚɹ
ɩɨɡɢɰɢɹ
28
ɉɨɥɨɠɟɧɢɹ ɩɨɫɥɟ ɨɱɟɪɟɞɧɵɯ ɯɨɞɨɜ
1-ɣ ɯɨɞ ɉɚɲɢ 1-ɣ ɯɨɞ ȼɨɜɵ 2-ɣ ɯɨɞ ɉɚɲɢ 2-ɣ ɯɨɞ ȼɨɜɵ
(ɪɚɡɨɛɪɚɧɵ ɜɫɟ (ɬɨɥɶɤɨ ɯɨɞ ɩɨ (ɪɚɡɨɛɪɚɧɵ ɜɫɟ (ɬɨɥɶɤɨ ɯɨɞ ɩɨ
ɯɨɞɵ)
ɫɬɪɚɬɟɝɢɢ)
ɯɨɞɵ)
ɫɬɪɚɬɟɝɢɢ)
30+1=31
31+10=41
28+1 =29
29+1=30
30+10=40
40+10=50
28+10=38
38+10=48
Ɋɢɫ. 1. Ⱦɟɪɟɜɨ ɜɫɟɯ ɩɚɪɬɢɣ, ɜɨɡɦɨɠɧɵɯ ɩɪɢ ȼɨɜɢɧɨɣ ɫɬɪɚɬɟɝɢɢ.
Ɂɧɚɤɨɦ >> ɨɛɨɡɧɚɱɟɧɵ ɩɨɡɢɰɢɢ, ɜ ɤɨɬɨɪɵɯ ɩɚɪɬɢɹ ɡɚɤɚɧɱɢɜɚɟɬɫɹ
ȼ ɡɚɞɚɱɟ ɨɬ ɭɱɟɧɢɤɚ ɬɪɟɛɭɟɬɫɹ ɜɵɩɨɥɧɢɬɶ 3 ɡɚɞɚɧɢɹ. ɂɯ ɬɪɭɞɧɨɫɬɶ ɜɨɡɪɚɫɬɚɟɬ.
Ʉɨɥɢɱɟɫɬɜɨ ɛɚɥɥɨɜ ɜ ɰɟɥɨɦ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɨɥɢɱɟɫɬɜɭ ɜɵɩɨɥɧɟɧɧɵɯ ɡɚɞɚɧɢɣ
(ɩɨɞɪɨɛɧɟɟ ɫɦ. ɧɢɠɟ).
Ɉɲɢɛɤɚ ɜ ɪɟɲɟɧɢɢ, ɧɟ ɢɫɤɚɠɚɸɳɚɹ ɨɫɧɨɜɧɨɝɨ ɡɚɦɵɫɥɚ, ɧɚɩɪɢɦɟɪ ɚɪɢɮɦɟɬɢɱɟɫɤɚɹ
ɨɲɢɛɤɚ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɤɨɥɢɱɟɫɬɜɚ ɤɚɦɧɟɣ ɜ ɡɚɤɥɸɱɢɬɟɥɶɧɨɣ ɩɨɡɢɰɢɢ, ɩɪɢ ɨɰɟɧɤɟ
ɪɟɲɟɧɢɹ ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ.
ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɜɵɩɨɥɧɟɧɵ ɨɛɚ ɩɭɧɤɬɚ ɚ) ɢ ɛ). ɉɭɧɤɬ ɚ)
ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɵ ɜɫɟ ɩɨɡɢɰɢɢ, ɜ ɤɨɬɨɪɵɯ ɉɚɲɚ
ɜɵɢɝɪɵɜɚɟɬ ɩɟɪɜɵɦ ɯɨɞɨɦ, ɢ ɭɤɚɡɚɧɨ, ɤɚɤɢɦ ɞɨɥɠɟɧ ɛɵɬɶ ɩɟɪɜɵɣ ɯɨɞ. ɉɭɧɤɬ ɛ)
ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɚ ɩɨɡɢɰɢɹ, ɜ ɤɨɬɨɪɨɣ ȼɨɜɚ ɜɵɢɝɪɵɜɚɟɬ
ɩɟɪɜɵɦ ɯɨɞɨɦ, ɢ ɨɩɢɫɚɧɚ ɫɬɪɚɬɟɝɢɹ ȼɨɜɵ, ɬ. ɟ. ɩɨɤɚɡɚɧɨ, ɤɚɤ ȼɨɜɚ ɦɨɠɟɬ ɩɨɥɭɱɢɬɶ
ɤɭɱɭ, ɜ ɤɨɬɨɪɨɣ ɫɨɞɟɪɠɢɬɫɹ ɧɭɠɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ, ɩɪɢ ɥɸɛɨɦ ɯɨɞɟ ɉɚɲɢ.
ɉɭɧɤɬ ɚ) ɩɟɪɜɨɝɨ ɡɚɞɚɧɢɹ ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ ɱɚɫɬɢɱɧɨ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɵ
ɜɫɟ ɩɨɡɢɰɢɢ, ɜ ɤɨɬɨɪɵɯ ɉɚɲɚ ɜɵɢɝɪɵɜɚɟɬ ɩɟɪɜɵɦ ɯɨɞɨɦ. ɉɭɧɤɬ ɛ) ɩɟɪɜɨɝɨ ɡɚɞɚɧɢɹ
ɫɱɢɬɚɟɬɫɹ ɜɵɩɨɥɧɟɧɧɵɦ ɱɚɫɬɢɱɧɨ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɚ ɩɨɡɢɰɢɹ, ɜ ɤɨɬɨɪɨɣ ȼɨɜɚ
ɜɵɢɝɪɵɜɚɟɬ ɩɟɪɜɵɦ ɯɨɞɨɦ, ɢ ɹɜɧɨ ɫɤɚɡɚɧɨ, ɱɬɨ ɩɪɢ ɥɸɛɨɦ ɯɨɞɟ ɉɚɲɢ ȼɨɜɚ ɦɨɠɟɬ
ɩɨɥɭɱɢɬɶ ɤɭɱɭ, ɤɨɬɨɪɚɹ ɫɨɞɟɪɠɢɬ ɧɭɠɧɨɟ ɞɥɹ ɜɵɢɝɪɵɲɚ ɤɨɥɢɱɟɫɬɜɨ ɤɚɦɧɟɣ.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
11
ȼɬɨɪɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɵ ɨɛɟ ɩɨɡɢɰɢɢ, ɜɵɢɝɪɵɲɧɵɟ ɞɥɹ
ɉɚɲɢ, ɢ ɨɩɢɫɚɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɫɬɪɚɬɟɝɢɹ ɉɚɲɢ – ɬɚɤ, ɤɚɤ ɷɬɨ ɧɚɩɢɫɚɧɨ ɜ ɩɪɢɦɟɪɟ
ɪɟɲɟɧɢɹ, ɢɥɢ ɞɪɭɝɢɦ ɫɩɨɫɨɛɨɦ, ɧɚɩɪɢɦɟɪ ɫ ɩɨɦɨɳɶɸ ɞɟɪɟɜɚ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɩɚɪɬɢɣ.
Ɍɪɟɬɶɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ, ɟɫɥɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɚ ɩɨɡɢɰɢɹ, ɜɵɢɝɪɵɲɧɚɹ ɞɥɹ ȼɨɜɵ, ɢ
ɩɨɫɬɪɨɟɧɨ ɞɟɪɟɜɨ ɜɫɟɯ ɩɚɪɬɢɣ, ɜɨɡɦɨɠɧɵɯ ɩɪɢ ȼɨɜɢɧɨɣ ɫɬɪɚɬɟɝɢɢ. Ⱦɨɥɠɧɨ ɛɵɬɶ ɹɜɧɨ
ɫɤɚɡɚɧɨ, ɱɬɨ ɜ ɷɬɨɦ ɞɟɪɟɜɟ ɜ ɤɚɠɞɨɣ ɩɨɡɢɰɢɢ, ɝɞɟ ɞɨɥɠɟɧ ɯɨɞɢɬɶ ɉɚɲɚ, ɪɚɡɨɛɪɚɧɵ ɜɫɟ
ɜɨɡɦɨɠɧɵɟ ɯɨɞɵ, ɚ ɞɥɹ ɩɨɡɢɰɢɣ, ɝɞɟ ɞɨɥɠɟɧ ɯɨɞɢɬɶ ȼɨɜɚ, – ɬɨɥɶɤɨ ɯɨɞ,
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɫɬɪɚɬɟɝɢɢ, ɤɨɬɨɪɭɸ ɜɵɛɪɚɥ ȼɨɜɚ.
ȼɨ ɜɫɟɯ ɫɥɭɱɚɹɯ ɫɬɪɚɬɟɝɢɢ ɦɨɝɭɬ ɛɵɬɶ ɨɩɢɫɚɧɵ ɬɚɤ, ɤɚɤ ɷɬɨ ɫɞɟɥɚɧɨ ɜ ɩɪɢɦɟɪɟ
ɪɟɲɟɧɢɹ, ɢɥɢ ɞɪɭɝɢɦ ɫɩɨɫɨɛɨɦ.
ɍɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
Ȼɚɥɥɵ
ȼɵɩɨɥɧɟɧɵ ɜɬɨɪɨɟ ɢ ɬɪɟɬɶɟ ɡɚɞɚɧɢɹ. ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ
ɩɨɥɧɨɫɬɶɸ ɢɥɢ ɱɚɫɬɢɱɧɨ. Ɂɞɟɫɶ ɢ ɞɚɥɟɟ ɞɨɩɭɫɤɚɸɬɫɹ ɚɪɢɮɦɟɬɢɱɟɫɤɢɟ
3
ɨɲɢɛɤɢ, ɤɨɬɨɪɵɟ ɧɟ ɢɫɤɚɠɚɸɬ ɫɭɬɢ ɪɟɲɟɧɢɹ ɢ ɧɟ ɩɪɢɜɨɞɹɬ
ɤ ɧɟɩɪɚɜɢɥɶɧɨɦɭ ɨɬɜɟɬɭ (ɫɦ. ɜɵɲɟ).
ɇɟ ɜɵɩɨɥɧɟɧɵ ɭɫɥɨɜɢɹ, ɩɨɡɜɨɥɹɸɳɢɟ ɩɨɫɬɚɜɢɬɶ 3 ɛɚɥɥɚ, ɢ ɜɵɩɨɥɧɟɧɨ
ɨɞɧɨ ɢɡ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɣ.
1. Ɂɚɞɚɧɢɟ 3 ɜɵɩɨɥɧɟɧɨ.
2
2. ɉɟɪɜɨɟ ɢ ɜɬɨɪɨɟ ɡɚɞɚɧɢɹ ɜɵɩɨɥɧɟɧɵ.
3. ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɩɨɥɧɨɫɬɶɸ ɢɥɢ ɱɚɫɬɢɱɧɨ; ɞɥɹ ɡɚɞɚɧɢɣ 2 ɢ 3
ɭɤɚɡɚɧɵ ɩɪɚɜɢɥɶɧɵɟ ɡɧɚɱɟɧɢɹ S.
ɇɟ ɜɵɩɨɥɧɟɧɵ ɭɫɥɨɜɢɹ, ɩɨɡɜɨɥɹɸɳɢɟ ɩɨɫɬɚɜɢɬɶ 3 ɢɥɢ 2 ɛɚɥɥɚ, ɢ
ɜɵɩɨɥɧɟɧɨ ɨɞɧɨ ɢɡ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɣ.
1. ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ.
2. ȼɨ ɜɬɨɪɨɦ ɡɚɞɚɧɢɢ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɨ ɨɞɧɨ ɢɡ ɞɜɭɯ ɜɨɡɦɨɠɧɵɯ
ɡɧɚɱɟɧɢɣ S, ɢ ɞɥɹ ɷɬɨɝɨ ɡɧɚɱɟɧɢɹ ɭɤɚɡɚɧɚ ɢ ɨɛɨɫɧɨɜɚɧɚ ɜɵɢɝɪɵɲɧɚɹ
1
ɫɬɪɚɬɟɝɢɹ ɉɚɲɢ.
3. ɉɟɪɜɨɟ ɡɚɞɚɧɢɟ ɜɵɩɨɥɧɟɧɨ ɱɚɫɬɢɱɧɨ, ɢ ɞɥɹ ɨɞɧɨɝɨ ɢɡ ɨɫɬɚɥɶɧɵɯ ɡɚɞɚɧɢɣ
ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɨ ɡɧɚɱɟɧɢɟ S.
4. Ⱦɥɹ ɜɬɨɪɨɝɨ ɢ ɬɪɟɬɶɟɝɨ ɡɚɞɚɧɢɹ ɩɪɚɜɢɥɶɧɨ ɭɤɚɡɚɧɵ ɡɧɚɱɟɧɢɹ S.
ɇɟ ɜɵɩɨɥɧɟɧɨ ɧɢ ɨɞɧɨ ɢɡ ɭɫɥɨɜɢɣ, ɩɨɡɜɨɥɹɸɳɢɯ ɩɨɫɬɚɜɢɬɶ 3, 2 ɢɥɢ 1
0
ɛɚɥɥ.
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɚɥɥ
3
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
C4
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
12
ɇɚ ɩɥɨɫɤɨɫɬɢ ɞɚɧ ɧɚɛɨɪ ɬɨɱɟɤ ɫ ɰɟɥɨɱɢɫɥɟɧɧɵɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ. ɇɟɨɛɯɨɞɢɦɨ
ɧɚɣɬɢ ɬɚɤɨɣ ɬɪɟɭɝɨɥɶɧɢɤ ɧɚɢɛɨɥɶɲɟɣ ɩɥɨɳɚɞɢ ɫ ɜɟɪɲɢɧɚɦɢ ɜ ɷɬɢɯ ɬɨɱɤɚɯ,
ɭ ɤɨɬɨɪɨɝɨ ɧɟɬ ɨɛɳɢɯ ɬɨɱɟɤ ɫ ɨɫɶɸ Ox, ɚ ɨɞɧɚ ɢɡ ɫɬɨɪɨɧ ɥɟɠɢɬ ɧɚ ɨɫɢ Oy.
ɇɚɩɢɲɢɬɟ ɷɮɮɟɤɬɢɜɧɭɸ, ɜ ɬɨɦ ɱɢɫɥɟ ɩɨ ɩɚɦɹɬɢ, ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɛɭɞɟɬ
ɪɟɲɚɬɶ ɷɬɭ ɡɚɞɚɱɭ. Ɋɚɡɦɟɪ ɩɚɦɹɬɢ, ɤɨɬɨɪɭɸ ɢɫɩɨɥɶɡɭɟɬ ȼɚɲɚ ɩɪɨɝɪɚɦɦɚ, ɧɟ
ɞɨɥɠɟɧ ɡɚɜɢɫɟɬɶ ɨɬ ɤɨɥɢɱɟɫɬɜɚ ɬɨɱɟɤ.
ɉɟɪɟɞ ɬɟɤɫɬɨɦ ɩɪɨɝɪɚɦɦɵ ɤɪɚɬɤɨ ɨɩɢɲɢɬɟ ɢɫɩɨɥɶɡɭɟɦɵɣ ɚɥɝɨɪɢɬɦ ɪɟɲɟɧɢɹ
ɡɚɞɚɱɢ ɢ ɭɤɚɠɢɬɟ ɢɫɩɨɥɶɡɭɟɦɵɣ ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɢ ɟɝɨ ɜɟɪɫɢɸ.
Ɉɩɢɫɚɧɢɟ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ
ȼ ɩɟɪɜɨɣ ɫɬɪɨɤɟ ɜɜɨɞɢɬɫɹ ɨɞɧɨ ɰɟɥɨɟ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɱɢɫɥɨ – ɤɨɥɢɱɟɫɬɜɨ
ɬɨɱɟɤ N.
Ʉɚɠɞɚɹ ɢɡ ɫɥɟɞɭɸɳɢɯ N ɫɬɪɨɤ ɫɨɞɟɪɠɢɬ ɞɜɚ ɰɟɥɵɯ ɱɢɫɥɚ – ɫɧɚɱɚɥɚ
ɤɨɨɪɞɢɧɚɬɚ x, ɡɚɬɟɦ ɤɨɨɪɞɢɧɚɬɚ y ɨɱɟɪɟɞɧɨɣ ɬɨɱɤɢ. ɑɢɫɥɚ ɪɚɡɞɟɥɟɧɵ
ɩɪɨɛɟɥɨɦ.
Ɉɩɢɫɚɧɢɟ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ
ɉɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɨɞɧɨ ɱɢɫɥɨ – ɦɚɤɫɢɦɚɥɶɧɭɸ ɩɥɨɳɚɞɶ
ɬɪɟɭɝɨɥɶɧɢɤɚ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɝɨ ɭɫɥɨɜɢɹɦ ɡɚɞɚɱɢ. ȿɫɥɢ ɬɚɤɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ
ɧɟ ɫɭɳɟɫɬɜɭɟɬ, ɩɪɨɝɪɚɦɦɚ ɞɨɥɠɧɚ ɜɵɜɟɫɬɢ ɧɨɥɶ.
ɉɪɢɦɟɪ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ:
8
0 -10
0 2
4 0
3 3
0 7
0 4
5 5
-9 9
ɉɪɢɦɟɪ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ ɞɥɹ ɩɪɢɜɟɞɺɧɧɨɝɨ ɜɵɲɟ ɩɪɢɦɟɪɚ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ:
22.5
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
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13
ɋɨɞɟɪɠɚɧɢɟ ɜɟɪɧɨɝɨ ɨɬɜɟɬɚ ɢ ɭɤɚɡɚɧɢɹ ɩɨ ɨɰɟɧɢɜɚɧɢɸ
(ɞɨɩɭɫɤɚɸɬɫɹ ɢɧɵɟ ɮɨɪɦɭɥɢɪɨɜɤɢ ɨɬɜɟɬɚ, ɧɟ ɢɫɤɚɠɚɸɳɢɟ ɟɝɨ ɫɦɵɫɥɚ)
Ɍɪɟɭɝɨɥɶɧɢɤ ɧɟ ɢɦɟɟɬ ɨɛɳɢɯ ɬɨɱɟɤ ɫ ɨɫɶɸ Ox (ɨɫɶɸ ɚɛɫɰɢɫɫ), ɟɫɥɢ ɨɪɞɢɧɚɬɵ ɜɫɟɯ ɟɝɨ
ɜɟɪɲɢɧ ɢɦɟɸɬ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɡɧɚɤ, ɬ. ɟ. ɧɭɠɧɨ ɨɬɞɟɥɶɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɬɨɱɤɢ
ɫ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɦɢ ɨɪɞɢɧɚɬɚɦɢ. Ⱦɥɹ ɤɚɠɞɨɣ ɢɡ ɷɬɢɯ ɝɪɭɩɩ
ɬɪɟɭɝɨɥɶɧɢɤ ABC, ɢɦɟɸɳɢɣ ɦɚɤɫɢɦɚɥɶɧɭɸ ɩɥɨɳɚɞɶ, – ɷɬɨ ɬɪɟɭɝɨɥɶɧɢɤ, ɭ ɤɨɬɨɪɨɝɨ
ɜɟɪɲɢɧɵ A ɢ B ɥɟɠɚɬ ɧɚ ɨɫɢ ɨɪɞɢɧɚɬ ɩɨ ɨɞɧɭ ɫɬɨɪɨɧɭ ɨɬ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ, ɩɪɢɱɟɦ
ɭ ɨɞɧɨɣ ɢɡ ɷɬɢɯ ɬɨɱɟɤ ɨɪɞɢɧɚɬɚ ɢɦɟɟɬ ɧɚɢɛɨɥɶɲɭɸ ɚɛɫɨɥɸɬɧɭɸ ɜɟɥɢɱɢɧɭ, ɚ ɭ ɞɪɭɝɨɣ –
ɧɚɢɦɟɧɶɲɭɸ. Ɍɪɟɬɶɹ ɜɟɪɲɢɧɚ ɋ – ɷɬɨ ɜɟɪɲɢɧɚ, ɢɦɟɸɳɚɹ ɧɚɢɛɨɥɶɲɭɸ ɩɨ ɚɛɫɨɥɸɬɧɨɣ
ɜɟɥɢɱɢɧɟ ɚɛɫɰɢɫɫɭ ɫɪɟɞɢ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɩɨ ɬɭ ɠɟ ɫɬɨɪɨɧɭ ɨɬ ɨɫɢ ɚɛɫɰɢɫɫ, ɱɬɨ ɢ ɬɨɱɤɢ
A, B. ɂɡ ɞɜɭɯ ɬɚɤɢɯ «ɦɚɤɫɢɦɚɥɶɧɵɯ» ɬɪɟɭɝɨɥɶɧɢɤɨɜ (ɨɞɢɧ ɥɟɠɢɬ ɩɨ ɨɞɧɭ ɫɬɨɪɨɧɭ ɨɬ
ɨɫɢ ɚɛɫɰɢɫɫ, ɞɪɭɝɨɣ – ɩɨ ɞɪɭɝɭɸ) ɧɭɠɧɨ ɜɵɛɪɚɬɶ ɬɨɬ, ɤɨɬɨɪɵɣ ɢɦɟɟɬ ɛȩɥɶɲɭɸ
ɩɥɨɳɚɞɶ.
ɉɪɨɝɪɚɦɦɚ ɱɢɬɚɟɬ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ, ɧɟ ɡɚɩɨɦɢɧɚɹ ɜɫɟ ɬɨɱɤɢ ɜ ɦɚɫɫɢɜɟ.
ɉɨɫɥɟ ɨɛɪɚɛɨɬɤɢ ɨɱɟɪɟɞɧɨɣ ɬɨɱɤɢ ɩɪɨɝɪɚɦɦɚ ɯɪɚɧɢɬ ɡɧɚɱɟɧɢɹ ɫɥɟɞɭɸɳɢɯ ɜɟɥɢɱɢɧ:
– ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Pos_ymax ɨɪɞɢɧɚɬɵ ɞɥɹ ɜɫɟɯ ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ
ɧɚ ɨɫɢ Oy ɜɵɲɟ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ;
– ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Pos_ymin ɨɪɞɢɧɚɬɵ ɞɥɹ ɜɫɟɯ ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɧɚ
ɨɫɢ Oy ɜɵɲɟ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ;
– ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Pos_xmax ɚɛɫɨɥɸɬɧɨɣ ɜɟɥɢɱɢɧɵ ɚɛɫɰɢɫɫɵ ɞɥɹ ɜɫɟɯ
ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɜɵɲɟ ɨɫɢ ɚɛɫɰɢɫɫ;
– ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Neg_ymax ɨɪɞɢɧɚɬɵ ɞɥɹ ɜɫɟɯ ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ
ɧɚ ɨɫɢ Oy ɧɢɠɟ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ;
- ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Neg_ymin ɨɪɞɢɧɚɬɵ ɞɥɹ ɜɫɟɯ ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɧɚ
ɨɫɢ Oy ɧɢɠɟ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ;
– ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Neg_xmax ɚɛɫɨɥɸɬɧɨɣ ɜɟɥɢɱɢɧɵ ɚɛɫɰɢɫɫɵ ɞɥɹ ɜɫɟɯ
ɩɪɨɱɢɬɚɧɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɧɢɠɧ ɨɫɢ ɚɛɫɰɢɫɫ.
ɉɨɫɥɟ ɬɨɝɨ, ɤɚɤ ɜɫɟ ɬɨɱɤɢ ɩɪɨɱɢɬɧɵ, ɜɵɱɢɫɥɹɟɬɫɹ ɦɚɤɫɢɦɭɦ
S = max{(Pos_ymax – Pos_ymin)*Pos_xmax/2, (Neg_ymax-Neg_ymin)*Neg_xmax/2}
(ɟɫɥɢ ɨɛɚ ɡɧɚɱɟɧɢɹ ɧɟ ɨɩɪɟɞɟɥɟɧɵ, ɩɨɥɚɝɚɟɦ S=0).
ȼ ɤɚɱɟɫɬɜɟ ɨɬɜɟɬɚ ɜɵɜɨɞɢɬɫɹ ɱɢɫɥɨ S.
ɉɪɢɦɟɪ ɩɪɚɜɢɥɶɧɨɣ ɢ ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ ɹɡɵɤɟ ɉɚɫɤɚɥɶ
var
n: integer;
x, y: integer;
Pos_ymin, Pos_ymax: integer;
Pos_ysearch: boolean;
Pos_xmax: integer;
Neg_ymin, Neg_ymax: integer;
Neg_ysearch: boolean;
Neg_xmax: integer;
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
i: integer;
Pos_s, Neg_s: real;
begin
Pos_ysearch := true; Neg_ysearch := true;
Pos_ymin := 0; Pos_ymax := 0;
Neg_ymin := 0; Neg_ymax := 0;
Pos_xmax := 0; Neg_xmax := 0;
readln(n);
for i:=1 to n do begin
readln(x, y);
if y >0 then begin
if x=0 then begin
if Pos_ysearch or (y<Pos_ymin) then Pos_ymin:=y;
if Pos_ysearch or (y>Pos_ymax) then Pos_ymax:=y;
Pos_ysearch:=false;
end
else begin
if abs(x)>Pos_xmax then Pos_xmax:=abs(x);
end;
end;
if y < 0 then begin
if x=0 then begin
if Neg_ysearch or (y<Neg_ymin) then Neg_ymin:=y;
if Neg_ysearch or (y>Neg_ymax) then Neg_ymax:=y;
Neg_ysearch:=false;
end
else begin
if abs(x)>Neg_xmax then Neg_xmax:=abs(x);
end;
end;
end;
Pos_s := (Pos_ymax-Pos_ymin)*Pos_xmax/2;
Neg_s := (Neg_ymax-Neg_ymin)*Neg_xmax/2;
if Pos_s > Neg_s then writeln(Pos_s)
else writeln(Neg_s);
end.
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
14
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
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15
ɂɧɮɨɪɦɚɬɢɤɚ. 11 ɤɥɚɫɫ. ȼɚɪɢɚɧɬ 2
ȼɢɞɟɨɪɚɡɛɨɪ ɧɚ ɫɚɣɬɟ www.statgrad.cde.ru
ɉɪɢɦɟɪ ɩɪɚɜɢɥɶɧɨɣ ɢ ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ ɹɡɵɤɟ Ȼɟɣɫɢɤ
ɉɪɢɦɟɪ ɩɪɚɜɢɥɶɧɨɣ ɢ ɷɮɮɟɤɬɢɜɧɨɣ ɩɪɨɝɪɚɦɦɵ ɧɚ ɚɥɝɨɪɢɬɦɢɱɟɫɤɨɦ ɹɡɵɤɟ
DIM
DIM
DIM
DIM
DIM
DIM
DIM
DIM
DIM
DIM
ɚɥɝ
ɧɚɱ
ɰɟɥ n
ɰɟɥ x, y
ɰɟɥ Pos_ymin=0, Pos_ymax=0
ɥɨɝ Pos_ysearch=ɞɚ
ɰɟɥ Pos_xmax=0
ɰɟɥ Neg_ymin=0, Neg_ymax=0
ɥɨɝ Neg_ysearch=ɞɚ
ɰɟɥ Neg_xmax=0
ɜɟɳ Pos_s, Neg_s
ɜɜɨɞ n
ɧɰ n ɪɚɡ
ɜɜɨɞ x, y
ɟɫɥɢ y > 0 ɬɨ
ɟɫɥɢ x=0
ɬɨ
ɟɫɥɢ Pos_ysearch ɢɥɢ y<Pos_ymin ɬɨ Pos_ymin:=y
ɟɫɥɢ Pos_ysearch ɢɥɢ y>Pos_ymax ɬɨ Pos_ymax:=y
Pos_ysearch:=ɧɟɬ
ɢɧɚɱɟ
ɟɫɥɢ iabs(x)>Pos_xmax ɬɨ Pos_xmax:=iabs(x) ɜɫɟ
ɜɫɟ
ɜɫɟ
ɟɫɥɢ y < 0 ɬɨ
ɟɫɥɢ x=0
ɬɨ
ɟɫɥɢ Neg_ysearch ɢɥɢ y<Neg_ymin ɬɨ Neg_ymin:=y
ɟɫɥɢ Neg_ysearch ɢɥɢ y>Neg_ymax ɬɨ Neg_ymax:=y
Neg_ysearch:=ɧɟɬ
ɢɧɚɱɟ
ɟɫɥɢ iabs(x)>Neg_xmax ɬɨ Neg_xmax:=iabs(x) ɜɫɟ
ɜɫɟ
ɜɫɟ
ɤɰ
Pos_s:=(Pos_ymax-Pos_ymin)*Pos_xmax/2
Neg_s:=(Neg_ymax-Neg_ymin)*Neg_xmax/2
ɟɫɥɢ Pos_s > Neg_s
ɬɨ ɜɵɜɨɞ Pos_s
ɢɧɚɱɟ ɜɵɜɨɞ Neg_s
ɜɫɟ
ɤɨɧ
n AS INTEGER
x, y AS INTEGER
Pos_ymin, Pos_ymax AS INTEGER
Pos_ysearch AS INTEGER
Pos_xmax AS INTEGER
Neg_ymin, Neg_ymax AS INTEGER
Neg_ysearch AS INTEGER
Neg_xmax AS INTEGER
i AS INTEGER
Pos_s, Neg_s AS DOUBLE
Pos_ysearch = 1: Neg_ysearch = 1
Pos_ymin = 0: Pos_ymax = 0
Neg_ymin = 0: Neg_ymax = 0
Pos_xmax = 0: Neg_xmax = 0
INPUT n
FOR i = 1 TO n
INPUT x, y
IF y > 0 THEN
IF x = 0 THEN
IF Pos_ysearch = 1 OR y < Pos_ymin
IF Pos_ysearch = 1 OR y > Pos_ymax
Pos_ysearch = 0
ELSE
IF ABS(x) > Pos_xmax THEN Pos_xmax
END IF
END IF
IF y < 0 THEN
IF x = 0 THEN
IF Neg_ysearch = 1 OR y < Neg_ymin
IF Neg_ysearch = 1 OR y > Neg_ymax
Neg_ysearch = 0
ELSE
IF ABS(x) > Neg_xmax THEN Neg_xmax
END IF
END IF
NEXT i
Pos_s = (Pos_ymax – Pos_ymin) * Pos_xmax
Neg_s = (Neg_ymax – Neg_ymin) * Neg_xmax
IF Pos_s > Neg_s THEN
PRINT Pos_s
ELSE
PRINT Neg_s
END IF
THEN Pos_ymin = y
THEN Pos_ymax = y
= ABS(x)
THEN Neg_ymin = y
THEN Neg_ymax = y
= ABS(x)
/ 2
/ 2
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
ɜɫɟ
ɜɫɟ
ɜɫɟ
ɜɫɟ
© ɆɂɈɈ 2012 ɝ. ɉɭɛɥɢɤɚɰɢɹ ɜ ɂɧɬɟɪɧɟɬɟ ɢɥɢ ɩɟɱɚɬɧɵɯ ɢɡɞɚɧɢɹɯ ɛɟɡ ɩɢɫɶɦɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɆɂɈɈ ɡɚɩɪɟɳɟɧɚ
16
Информатика. 11 класс. Вариант 2
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Указания по оцениванию
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размера и находит ответ, не сохраняя входные данные в массиве.
Допускается наличие в тексте программы одной синтаксической ошибки:
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пропущено зарезервированное слово языка программирования, не описана
или неверно описана переменная, применяется операция, недопустимая для
соответствующего типа данных (если одна и та же ошибка встречается
несколько раз, то это считается за одну ошибку).
Программа работает верно, но размер используемой памяти зависит от
количества исходных данных. Например, входные данные (координаты
точек) запоминаются в массиве или другой структуре данных, размер
которой соответствует количеству точек. При этом обработка данных
происходит с использованием эффективного алгоритма, аналогичного
приведённым выше.
Допускается одна из следующих ошибок.
1) Поиск минимума или максимума не учитывает, что первый подходящий
элемент может оказаться на любом месте в исходных данных или вообще
отсутствовать
2) Перепутаны координаты y и x при поиске основания: ищутся
максимальные и минимальные значения x при y = 0.
3) Перепутаны координаты y и x при поиске высоты: ищется максимальное
значение y
4) При поиске высоты ищется максимум значения координаты x, а не её
модуля.
5) При поиске высоты запоминается не модуль, а значение x, при этом при
вычислении площади модуль тоже не берётся, в результате может
получиться отрицательная площадь.
6) Все вершины определены правильно, но площадь треугольника
определена неверно, например, использована неверная формула
7) Не учитывается, что вычисленное значение площади может быть
нецелым. Например, значение площади присваивается переменной целого
типа, при вычислении площади используется операция целочисленного
деления (div в Паскале, деление целых величин без приведения типов в Си),
при форматном выводе используется формат целого числа или допущены
другие подобные ошибки, приводящие к неверному результату при дробном
ответе.
8) Вершины и площади двух треугольников определены верно, но из них
выбирается не больший, а меньший.
9) Неверно обрабатывается ситуация, когда искомый треугольник
отсутствует
Информатика. 11 класс. Вариант 2
Видеоразбор на сайте www.statgrad.cde.ru 18
Баллы
4
Программа работает в целом верно, эффективно или нет. Возможны
переборные решения, при которых все точки хранятся в массиве, из них
выбираются подходящие треугольники, вычисляется и сравнивается их
площадь.
В реализации алгоритма допущено более 1 ошибки из числа перечисленных
в предыдущем пункте или допущены другие ошибки, приводящие к
неверной работе программы в отдельных случаях.
Допускается наличие от одной до пяти синтаксических ошибок, описанных
выше.
Программа работает в отдельных частных случаях.
Один балл также ставится, если программа написана неверно, но из
описания алгоритма и общей структуры программы видно, что
экзаменуемый в целом правильно представляет путь решения задачи.
Не выполнено ни одно из перечисленных выше условий.
Максимальный балл
2
1
0
4
3
Допускается наличие от одной до трёх синтаксических ошибок,
описанных выше
© МИОО 2012 г. Публикация в Интернете или печатных изданиях без письменного согласия МИОО запрещена
© МИОО 2012 г. Публикация в Интернете или печатных изданиях без письменного согласия МИОО запрещена
```
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