µÚ10ÕÂÏ°Ìâ´ð°¸ ÏÂÔر¾ÎÄ

µÚ10Õ ͼ

Ï°Ìâ10

1.(1)ͼGµÄ¶ÈÊýÁÐΪ2¡¢2¡¢3¡¢3¡¢4£¬ÔòGµÄ±ßÊýÊǶàÉÙ£¿

(2)3¡¢3¡¢2¡¢3ºÍ5¡¢2¡¢3¡¢1¡¢4ÄܳÉΪͼµÄ¶ÈÊýÁÐÂð£¿ÎªÊ²Ã´£¿

(3)ͼGÓÐ12Ìõ±ß£¬¶ÈÊýΪ3µÄ½áµãÓÐ6¸ö£¬ÆäÓà½áµãµÄ¶ÈÊý¾ùСÓÚ3£¬ÎÊͼGÖÐÖÁ¶àÓм¸¸ö½áµã£¿ÎªÊ²Ã´£¿

½â (1)ÉèGÓÐmÌõ±ß£¬ÓÉÎÕÊÖ¶¨ÀíµÃ2m£½?d(v)£½2£«2£«3£«3£«4£½14£¬ËùÒÔGµÄ±ßÊý7Ìõ¡£

v?V(2)ÓÉÓÚÕâÁ½¸öÐòÁÐÖÐÓÐÆæÊý¸öÊÇÆæÊý£¬ÓÉÎÕÊÖ¶¨ÀíµÄÍÆÂÛÖª£¬ËüÃǶ¼²»ÄܳÉΪͼµÄ¶ÈÊýÁС£ (3) ÓÉÎÕÊÖ¶¨ÀíµÃ?d(v)£½2m£½24£¬¶ÈÊýΪ3µÄ½áµãÓÐ6¸öռȥ18¶È£¬»¹ÓÐ6¶ÈÓÉÆäËü½áµãÕ¼ÓУ¬

v?VÆäÓà½áµãµÄ¶ÈÊý¿ÉΪ0¡¢1¡¢2£¬µ±¾ùΪ2ʱËùÓýáµãÊý×îÉÙ£¬ËùÒÔÓ¦ÓÉ3¸ö½áµãÕ¼ÓÐÕâ6¶È£¬¼´Í¼GÖÐÖÁ¶àÓÐ9¸ö½áµã¡£

2.ÈôÓÐn¸öÈË£¬Ã¿¸öÈËÇ¡ÓÐ3¸öÅóÓÑ£¬Ôòn±ØΪżÊý¡£

Ö¤Ã÷ Éèv1¡¢v2¡¢?¡¢vn±íʾÈθøµÄn¸öÈË£¬ÒÔv1¡¢v2¡¢?¡¢vnΪ½áµã£¬µ±ÇÒ½öµ±Á½ÈËΪÅóÓÑʱÆä¶ÔÓ¦µÄ½áµãÖ®¼äÁ¬Ò»Ìõ±ß£¬ÕâÑùµÃµ½Ò»¸ö¼òµ¥Í¼G¡£ÓÉÎÕÊÖ¶¨ÀíÖª

?d(v)£½3n±ØΪżÊý£¬´Ó¶øn±ØΪżÊý¡£

kk?1n3.ÅжÏÏÂÁи÷·Ç¸ºÕûÊýÁÐÄÄЩÊÇ¿Éͼ»¯µÄ£¿ÄÄЩÊǿɼòµ¥Í¼»¯µÄ£¿ (1)(1£¬1£¬1£¬2£¬3)¡£ (2)(2£¬2£¬2£¬2£¬2)¡£ (3)(3£¬3£¬3£¬3)¡£ (4)(1£¬2£¬3£¬4£¬5)¡£ (5)(1£¬3£¬3£¬3)¡£

½â ÓÉÓڷǸºÕûÊýÁÐd£½(d1£¬d2£¬¡­£¬dn)ÊÇ¿Éͼ»¯µÄµ±ÇÒ½öµ±?di¡Ô0(mod 2)£¬ËùÒÔ(1)¡¢(2)¡¢

i?1n(3)¡¢(5)Äܹ¹³ÉÎÞÏòͼµÄ¶ÈÊýÁС£

(1)¡¢(2)¡¢(3)Êǿɼòµ¥Í¼»¯µÄ¡£Æä¶ÔÓ¦µÄÎÞÏò¼òµ¥Í¼ÈçͼËùʾ¡£

(5)ÊDz»¿É¼òµ¥Í¼»¯µÄ¡£Èô²»È»£¬´æÔÚÎÞÏòͼGÒÔΪ1£¬3£¬3£¬3¶ÈÊýÁУ¬²»·ÁÉèGÖнáµãΪv1¡¢v2¡¢

v3¡¢v4£¬ÇÒ

d(v1)£½1£¬d(v2)£½d(v3)£½d(v4)£½3¡£¶øv1Ö»ÄÜÓëv2¡¢v3¡¢v4Ö®Ò»ÏàÁÚ£¬Éèv1Óëv2ÏàÁÚ£¬ÓÚ

1

µÚ10Õ ͼ

ÊÇd(v3)£½d(v4)£½3²»³ÉÁ¢£¬Ã¬¶Ü¡£

4.ÊÔÖ¤Ã÷ͼ10-48ÖеÄÁ½¸öÎÞÏòͼÊDz»Í¬¹¹µÄ¡£

Ö¤Ã÷ ÒòΪÁ½Í¼Öж¼ÓÐ4¸ö3¶È½áµã£¬×óͼÖÐÿ¸ö3¶È½áµã¾ùÓë2¸ö2¶È½áµãÁÚ½Ó£¬¶øÓÒͼÖÐÿ¸ö3¶È½áµã¾ùÖ»Óë1¸ö2¶È½áµãÁÚ½Ó£¬ËùÒÔÕâÁ½¸öÎÞÏòͼÊDz»Í¬¹¹µÄ¡£

5.ÔÚͼͬ¹¹ÒâÒåÏ£¬ÊÔ»­³ö¾ßÓÐÈý¸ö½áµãµÄËùÓмòµ¥ÓÐÏòͼ¡£

½â ¾ßÓÐÈý¸ö½áµãµÄËùÓзÇͬ¹¹µÄ¼òµ¥ÓÐÏòͼ¹²16¸ö£¬ÈçͼËùʾ£¬ÆäÖÐ(8)?(16)ΪÆäÉú³É×Óͼ¡£

(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)6.¸ø¶¨ÎÞÏòÍêȫͼG£½£¬ÇÒ|V|£½4¡£ÔÚͼͬ¹¹ÒâÒåÏ£¬ÊÔÇó£º (1)GµÄËùÓÐ×Óͼ¡£ (2)GµÄËùÓÐÉú³É×Óͼ¡£ ½â (1)GµÄËùÓÐ×ÓͼÈçͼËùʾ¡£ (2)ͼ(8)?(18)ÊÇGµÄËùÓÐÉú³É×Óͼ¡£

2

(13)(14)(15)(16)(17)(18)(7)(8)(9)(10)(11)(12)(1)(2)(3)(4)(5)(6)µÚ10Õ ͼ

7.(1)ÊÔ¸ø³öÒ»¸öÎå¸ö½áµãµÄ×Ô²¹Í¼¡£ (2)ÊÇ·ñÓÐÈý¸ö½áµã»òÁù¸ö½áµãµÄ×Ô²¹Í¼¡£

(3)Ò»¸öͼÊÇ×Ô²¹Í¼£¬ÔòÆä¶ÔÓ¦µÄÍêȫͼµÄ±ßÊý±ØÊÇżÊý¡£ (4)Ò»¸ö×Ô²¹Í¼µÄ½áµãÊý±ØÊÇ4k»ò4k£«1¡£

½â (1)Îå¸ö½áµãµÄͼGÓëËüµÄ²¹Í¼GÈçͼËùʾ¡£¶ÔGÓëG½¨Á¢Ë«É䣺v1?v1£¬v2?v2£¬v3?v3£¬

v4?v4£¬v5?v5¡£ÏÔÈ»ÕâÁ½¸öͼ±£³ÖÏàÓ¦µã±ßÖ®¼äµÄ¶ÔÓ¦µÄ¹ØÁª¹Øϵ£¬¹Ê

G?G¡£Òò´Ë£¬GÊÇÎå¸ö½áµãµÄ

×Ô²¹Í¼¡£

£¨1£©G£¨2)G(3)ÉèͼGÊÇ×Ô²¹Í¼£¬ÓÐmÌõ±ß£¬G¶ÔÓ¦µÄÍêȫͼµÄ±ßÊýΪs£¬ÔòG¶ÔÓ¦µÄ²¹Í¼GµÄ±ßÊýΪs£­m¡£ÒòΪG?G£¬¹Ê±ßÊýÏàµÈ£¬¼´ÓÐm£½s£­m£¬s£½2m£¬Òò´ËG¶ÔÓ¦µÄÍêȫͼµÄ±ßÊýsΪżÊý¡£

(2)ÓÉ(3)Öª£¬×Ô²¹Í¼¶ÔÓ¦µÄÍêȫͼµÄ±ßÊýΪżÊý¡£n¸ö½áµãµÄÍêȫͼKnµÄ±ßÊýΪn(n£­1)£¬µ±n£½3»òn£½6ʱ£¬KnµÄ±ßÊýΪÆæÊý£¬Òò´Ë²»´æÔÚÈý¸ö½áµã»òÁù¸ö½áµãµÄ×Ô²¹Í¼¡£

(4)ÉèGΪn½××Ô²¹Í¼£¬ÔòÐèn(n£­1)Äܱ»2Õû³ý£¬Òò´Ën±ØΪ4k»ò4k£«1ÐÎʽ¡£

8.Ò»¸ön(n¡Ý2)½×ÎÞÏò¼òµ¥Í¼GÖУ¬nΪÆæÊý£¬ÒÑÖªGÖÐÓÐr¸öÆæÊý¶È½áµã£¬ÎÊGµÄ²¹Í¼GÖÐÓм¸¸öÆæÊý¶È½áµã£¿

½â ÓÉGµÄ²¹Í¼GµÄ¶¨Òå¿ÉÖª£¬G¡ÈGΪKn£¬ÓÉÓÚnΪÆæÊý£¬ËùÒÔKnÖи÷¶¥µãµÄ¶ÈÊýn£­1ΪżÊý¡£¶ÔÓÚͼGµÄÈÎÒâ½áµãv£¬Ó¦ÓÐvÒ²ÊÇGµÄ¶¥µã£¬ÇÒdG(v)£«dG(v)£½dKn(v)£½n£­1£¬ÓÉÓÚn£­1ΪżÊý£¬ËùÒÔdG(v)ºÍdG(v)ÆæżÐÔÏàͬ£¬Òò´ËÈôGÖÐÓÐr¸öÆæÊý¶È½áµã£¬ÔòGÖÐÒ²ÓÐr¸öÆæÊý¶È½áµã¡£

9.»­³ö4½×ÎÞÏòÍêȫͼK4µÄËùÓзÇͬ¹¹µÄÉú³É×Óͼ£¬²¢Ö¸³ö×Ô²¹Í¼À´¡£ ½â ÏÂͼÖеÄ11¸öͼÊÇK4µÄÈ«²¿µÄ·Çͬ¹¹µÄÉú³É×Óͼ£¬ÆäÖÐ(7)Ϊ×Ô²¹Í¼¡£

3

1212µÚ10Õ ͼ

10.ÉèͼGÖÐÓÐ9¸ö½áµã£¬Ã¿¸ö½áµãµÄ¶È²»ÊÇ5¾ÍÊÇ6¡£ÊÔÖ¤Ã÷GÖÐÖÁÉÙÓÐ5¸ö6¶È½áµã»òÖÁÉÙÓÐ6¸ö5¶È½áµã¡£

Ö¤Ã÷ ÓÉÎÕÊÖ¶¨ÀíµÄÍÆÂÛ¿ÉÖª£¬GÖÐ5¶È½áµãÊýÖ»ÄÜÊÇ0¡¢2¡¢4¡¢6¡¢8ÎåÖÖÇé¿ö£¨´Ëʱ6¶È½áµãÊý·Ö±ðΪ9¡¢7¡¢5¡¢3¡¢1£©¡£ÒÔÉÏÎåÖÖÇé¿ö¶¼Âú×ãÖÁÉÙ5¸ö6¶È½áµã»òÖÁÉÙ6¸ö5¶È½áµãµÄÇé¿ö¡£

11.Ö¤Ã÷3¶ÈÕýÔòͼ±ØÓÐżÊý¸ö½áµã¡£

Ö¤Ã÷ ÉèGΪÈÎÒ»3¶ÈÕýÔòͼ£¬ÓÐn¸ö½áµãv1¡¢v2¡¢?¡¢vn£¬ÔòËùÓнáµã¶ÈÊýÖ®ºÍnΪÆæÊý£¬Ôò3nҲΪÆæÊý£¬ÓëÎÕÊÖ¶¨Àíì¶Ü¡£¹ÊnΪżÊý¡£

12.ÉèGΪÖÁÉÙÓÐÁ½¸ö½áµãµÄ¼òµ¥Í¼£¬Ö¤Ã÷£ºGÖÐÖÁÉÙÓÐÁ½¸ö½áµã¶ÈÊýÏàͬ¡£

Ö¤Ã÷ ÈôGÖйÂÁ¢½áµãµÄ¸öÊý´óÓÚ2£¬½áÂÛÏÔÈ»³ÉÁ¢¡£ÈôGÖÐÓÐ1¸ö¹ÂÁ¢½áµã£¬ÔòGÖÐÖÁÉÙÓÐ3¸ö½áµã£¬Òò¶ø²»¿¼ÂǹÂÁ¢½áµã£¬¾ÍÊÇ˵GÖÐÿ¸ö½áµãµÄ¶ÈÊý¶¼´óÓÚµÈÓÚ1¡£ÓÖÒòΪGΪ¼òµ¥Í¼£¬ËùÒÔÿ¸ö½áµãµÄ¶ÈÊý¶¼Ð¡ÓÚµÈÓÚn-1¡£Òò¶øGÖнáµãµÄ¶ÈµÄÈ¡ÖµÖ»ÄÜÊÇ1£¬2£¬?£¬n-1Õân¸öÊý¡£ÓɳéÌëÔ­Àí¿ÉÖª£¬È¡n-1¸öÖµµÄn¸ö½áµãµÄ¶ÈÖÁÉÙÓÐÁ½¸öÊÇÏàͬµÄ¡£

13.¸ø¶¨ÎÞÏòͼG£½Èçͼ10-49Ëùʾ£¬ÊÔÇó£º (1)´Óaµ½dµÄËùÓлù±¾Â·¡£ (2)´Óaµ½dµÄËùÓмòµ¥Â·¡£

(3)³¤¶È·Ö±ðÊÇ×îСºÍ×î´óµÄ»ù±¾»Ø·¡£ (4)³¤¶È·Ö±ðÊÇ×îСºÍ×î´óµÄ¼òµ¥»Ø·¡£ (5)´Óaµ½dµÄ¾àÀë¡£

(6)?(G)¡¢?(G)¡¢?(G)¡¢?(G)·Ö±ðÊǶàÉÙ£¿

½â (1)´Óaµ½dµÄËùÓлù±¾Â·¹²ÓÐ10Ìõ£ºabd£¬abcd£¬abed£¬abced£¬abecd£¬afed£¬afecd£¬afebd£¬afebcd£¬afecbd¡£

(2)´Óaµ½dµÄËùÓмòµ¥Â·¹²ÓÐ14Ìõ£º³ý£¨1£©ÖеÄ10ÌõÍ⻹ÓÐabcebd£¬abecbd£¬afebced£¬afecbed¡£ (3)³¤¶È×îСµÄ»ù±¾»Ø·¹²4¸ö£ºbceb£¬bdeb£¬cdec£¬bcdb¡£³¤¶È×î´óµÄ»ù±¾»Ø·¹²1¸ö£ºabdcefa¡£ (4)³¤¶È×îСµÄ¼òµ¥»Ø·¹²4¸ö£ºbceb£¬bdeb£¬cdec£¬bcdb¡£³¤¶È×î´óµÄ¼òµ¥»Ø·2¸ö£ºabcebdefa£¬afebcedba¡£

(5)´Óaµ½dµÄ¾àÀëΪ2¡£

(6)?(G)£½2£¬?(G)£½2£¬?(G)£½2£¬?(G)£½4¡£ 14.¸ø¶¨ÓÐÏòͼG£½Èçͼ10-50Ëùʾ£¬ÊÔÇó£º (1)¸÷½áµãµÄ³ö¶È¡¢Èë¶ÈºÍ¶È¡£ (2)´Óaµ½dµÄËùÓлù±¾Â·ºÍ¼òµ¥Â·¡£ (3)ËùÓлù±¾»Ø·ºÍ¼òµ¥»Ø·¡£

½â (1)d(a)£½2£¬d(a)£½1£¬d(b)£½1£¬d(b)£½2£¬d(c)£½1£¬d(c)£½1£¬d(d)£½2£¬d(d)£½2£¬d(e)£½1£¬d(e)£½1¡£

4

-+

-+

-+

-+

-+

?d(v)£½3n¡£Èô

ii?1n