ÔÚÈý¹úɱ¶Ô¾ÖÖУ¬“Âí” ÊǺËÐÄ×°±¸ÅÆÓë¼¼Äܹؼü´Ê£¬ÎÞÂÛÊÇ×°±¸ÇøµÄ + 1 Âí¡¢-1 Âí£¬»¹ÊÇÎ佫×Ô´øµÄ “ÂíÊõ” ¼¼ÄÜ£¬¶¼Ö±½ÓÓ°Ïì¾àÀëÅж¨Óë¹¥»÷²ßÂÔ¡£Íæ¼Ò³£Òò¾àÀë¼ÆËã¡¢ÉúЧʱ»úµÈÎÊÌâ²úÉúÕùÒ飬ÒÔϽáºÏ¹Ù·½¹æÔòÓëʵս°¸ÀýÖðÒ»½â´ð¡£
Ò»¡¢»ù´¡ÈÏÖª£º×°±¸ÂíµÄºËÐŦÄÜÓë·ÖÀà
Èý¹úɱÖеÄ×°±¸Âí·ÖΪ “+1 Âí” ºÍ “-1 Âí” Á½À࣬Ãû³Æ²»Í¬µ«Í¬ÀàÐÍЧ¹ûÒ»Ö£¬ºËÐÄ×÷ÓÃÊǵ÷½Ú½ÇÉ«¼äµÄ “¹¥»÷¾àÀ딣¨¼´½ÇɫʹÓá¾É±¡¿¡¢¡¾Ë³ÊÖÇ£Ñò¡¿µÈ¿¨ÅÆÊ±µÄÓÐЧ·¶Î§£©¡£
1. +1 Âí£º·ÀÓùÐÍ×°±¸£¬À¿ª±»¹¥»÷¾àÀë
ºËÐÄЧ¹û£ºÆäËû½ÇÉ«¼ÆËãÓëÄãµÄ¾àÀëʱ£¬½á¹û + 1£¨½öÓ°ÏìËûÈ˶ÔÄãµÄ¹¥»÷£¬²»Ó°ÏìÄã¶ÔËûÈ˵Ĺ¥»÷£©¡£
³£¼û¿¨ÅÆ£º×¦»Æ·Éµç¡¢æèæòµÈ£¬¾ùÊôÓÚ + 1 Âí£¬Ð§¹ûÎÞ²îÒì¡£
ʵս³¡¾°£ºÈôÄãÓëÏàÁÚ½ÇÉ«µÄ»ù´¡¾àÀëΪ 1£¬×°±¸ + 1 Âíºó£¬¸Ã½ÇÉ«Ðè×°±¸ - 1 Âí»òÎäÆ÷£¨ÈçÇàâG½££¬¹¥»÷¾àÀë 2£©²ÅÄܶÔÄãʹÓá¾É±¡¿¡£
2. -1 Âí£º½ø¹¥ÐÍ×°±¸£¬Ëõ¶Ì¹¥»÷¾àÀë
ºËÐÄЧ¹û£ºÄã¼ÆËãÓëÆäËû½ÇÉ«µÄ¾àÀëʱ£¬½á¹û - 1£¨½öÓ°ÏìÄã¶ÔËûÈ˵Ĺ¥»÷£¬²»Ó°ÏìËûÈ˶ÔÄãµÄ¹¥»÷£©¡£
³£¼û¿¨ÅÆ£ºµÄ¬¡¢¾øÓ°µÈ£¬¾ùÊôÓÚ - 1 Âí£¬Ð§¹ûÎÞ²îÒì¡£
ʵս³¡¾°£ºÈôÄãÓë¸ôλ½ÇÉ«µÄ»ù´¡¾àÀëΪ 2£¬×°±¸ - 1 Âíºó£¬¿ÉÖ±½Ó¶ÔÆäʹÓá¾É±¡¿»ò¡¾Ë³ÊÖÇ£Ñò¡¿£¬ÎÞÐè¶îÍâÎäÆ÷Ö§³Å¡£
¶þ¡¢¸ßƵ½áËãÕùÒ飺¾àÀ롢ʱ»úÓ뻥¶¯¹æÔò
1. ¾àÀëµþ¼Ó¼ÆË㣺+1 ÂíÓë - 1 ÂíµÄ³åÍ»´¦Àí
µ±¹¥»÷·½×°±¸ - 1 Âí¡¢·ÀÊØ·½×°±¸ + 1 Âíʱ£¬¾àÀëÐè “µþ¼Ó¼ÆË㔣¬ºËÐĹæÔòΪ “¸÷×ÔÐÞÕýºóÈ¡×îÖÕ½á¹û”¡£
¼ÆË㹫ʽ£º×îÖÕ¹¥»÷¾àÀë = »ù´¡¾àÀë + ·ÀÊØ·½ + 1 ÂíÐÞÕý - ¹¥»÷·½ - 1 ÂíÐÞÕý
ʵս°¸Àý£º
A Óë B »ù´¡¾àÀëΪ 2£¬A ×°±¸ - 1 Âí£¬B ×°±¸ + 1 Âí£º
×îÖÕ¾àÀë = 2 + 1 - 1 = 2£¬´Ëʱ A Ðè×°±¸¹¥»÷¾àÀë≥2 µÄÎäÆ÷£¨ÈçÕɰËÉß죩²ÅÄÜ¶Ô B ʹÓá¾É±¡¿¡£
Èô A δװ±¸ÎäÆ÷£¬½ö¿¿ - 1 ÂíÎÞ·¨Í»ÆÆ B µÄ + 1 Âí·ÀÓù¡£
2. ÉúЧÓëʧЧʱ»ú£º×°±¸¡¢¸ü»»ÓëʧȥµÄ¹æÔò
×°±¸¼´ÉúЧ£º³öÅÆ½×¶Î×°±¸Âíºó£¬±¾»ØºÏÁ¢¼´ÉúЧ£¬¿ÉÖ±½ÓʹÓá¾É±¡¿¹¥»÷Ô±¾¾àÀë²»¹»µÄ½ÇÉ«¡£
¸ü»»ÂíµÄ´¦Àí£ºÈôÏë¸ü»»ÆäËûÂí£¬ÐèÏÈÆúÖõ±Ç°×°±¸µÄÂí£¨ÖÃÈëÆúÅÆ¶Ñ£©£¬ÔÙ×°±¸ÐÂÂí£¬ÆúÖúóÔÂíЧ¹ûÁ¢¼´Ïûʧ¡£
ʧȥÂíµÄÓ°Ï죺ÈôÂí±»¡¾¹ýºÓ²ðÇÅ¡¿ÒƳý»ò½ÇÉ«±ôËÀÆúÖÃ×°±¸£¬¾àÀëÁ¢¼´»Ö¸´»ù´¡Öµ£¬Î´Íê³ÉµÄ¹¥»÷£¨È硾ɱ¡¿ÒÑÖ¸¶¨Ä¿±êµ«Âí±»ÒÆ³ý£©ÈÔÓÐЧ£¨Òò¾àÀëÅж¨ÔÚÖ¸¶¨Ä¿±êʱÍê³É£©¡£
3. ÓëÎäÆ÷¡¢½õÄҵĻ¥¶¯£º¾àÀëÅж¨ÓÅÏȼ¶
ÓëÎäÆ÷µÄµþ¼Ó£ºÎäÆ÷µÄ¹¥»÷¾àÀëÓë - 1 Âí¿Éµþ¼Ó¡£ÀýÈ磬װ±¸ÇàÁúÙÈÔµ¶£¨¹¥»÷¾àÀë 3£©+ -1 Âíºó£¬Êµ¼Ê¹¥»÷¾àÀëΪ 4£¬Äܸ²¸Ç¸üÔ¶Ä¿±ê¡£
½õÄҵľàÀëÏÞÖÆ£º¡¾Ë³ÊÖÇ£Ñò¡¿¡¾±øÁ¸´ç¶Ï¡¿µÄ¾àÀëÅж¨Ó롾ɱ¡¿Ò»Ö£¬ÊÜÂíµÄÓ°Ï죻¡¾ÄÏÂùÈëÇÖ¡¿¡¾Íò¼ýÆë·¢¡¿ÊÇȺÌåЧ¹û£¬²»ÊÜÂíµÄ¾àÀëÏÞÖÆ¡£
ÌØÊâÎäÆ÷³åÍ»£º×°±¸Öî¸ðÁ¬å󣨹¥»÷¾àÀë 1£©Ê±£¬-1 Âí¿É½«Æä¹¥»÷¾àÀëÀ©Õ¹Îª 2£¬ÊµÏÖ “¶ÌÎäÆ÷Ô¶³Ì¹¥»÷”¡£
Èý¡¢Î佫¼¼ÄÜÓë “Âí” µÄÁª¶¯½âÎö
²¿·ÖÎ佫¼¼ÄÜ×Ô´ø “ÂíÊõ” Ч¹û£¬Æä¹æÔòÓë×°±¸Âí¼ÈÓй²ÐÔÒ²ÓвîÒ죬ÊÇʵսÖеÄÒ×´íµã¡£
1. ×Ô´ø “ÂíÊõ” ¼¼ÄÜ£ºÓë×°±¸ÂíµÄµþ¼Ó¹æÔò
ÒÔÂí³¬µÄ “ÂíÊõ” ΪÀý£¬¼¼ÄÜÃèÊöΪ “Ëø¶¨¼¼£¬Äã¼ÆËãÓëÆäËû½ÇÉ«µÄ¾àÀë - 1”£¬Óë×°±¸ - 1 Âí¿Éµþ¼ÓÉúЧ¡£
ʵս°¸Àý£º
Âí³¬Î´×°±¸ÎäÆ÷£¬»ù´¡¹¥»÷¾àÀëΪ 1£¬×Ô´ø “ÂíÊõ”£¨-1£©+ ×°±¸ - 1 Âíºó£¬Êµ¼Ê¹¥»÷¾àÀëΪ 3£¬¿ÉÖ±½Ó¹¥»÷¸ôÁ½Î»µÄ½ÇÉ«¡£
×¢Ò⣺ËùÓÐ “ÂíÊõ” À༼ÄܾùΪ “¹¥»÷¾àÀë - 1”£¬ÎÞ “+1 Âí” ÀàÐ͵ķÀÓùÐÔ×Ô´ø¼¼ÄÜ¡£
2. ¼¼ÄÜ´¥·¢ÓëÂíµÄ¾àÀë¹ØÁª
Âí³¬ “ÌúÆï” ÓëÂíµÄ¹ØÏµ£º“ÌúÆï” µÄ·¢¶¯½öÐ衾ɱ¡¿Ö¸¶¨Ä¿±ê£¬ÓëÊÇ·ñ×°±¸ÂíÎ޹أ¬µ«ÂíÌṩµÄ¾àÀë¿ÉÈÃÂí³¬¸üÒ×´¥¼°Ä¿±ê¡£ÀýÈ磬Âí³¬×°±¸ - 1 Âíºó£¬¿É¶ÔÔ¶´¦µÄÕŽÇʹÓá¾É±¡¿²¢·¢¶¯ “ÌúÆï” Åж¨¡£
´óÇÇ “Á÷Àë” ÓëÂíµÄ½áË㣺´óÇǶԹ¥»÷Õß·¢¶¯ “Á÷Àë” Ê±£¬Ðè¼ÆËã¹¥»÷ÕßÓë±»Á÷ÀëÄ¿±êµÄ¾àÀ루ÊÜÂíÓ°Ï죩¡£Èô¹¥»÷Õß×°±¸ - 1 Âí£¬¿ÉÄÜÂú×ãÁ÷ÀëÄ¿±êµÄ¾àÀëÒªÇó¡£
¹«Ëïè¶ “Òå´Ó” ÓëÂíµÄµþ¼Ó£º¹«Ëïè¶ “Òå´Ó” ·¢¶¯Ê± “¹¥»÷¾àÀë + 1”£¬Óë×°±¸ - 1 Âíµþ¼Óºó£¬Êµ¼Ê¹¥»÷¾àÀëΪ “»ù´¡¾àÀë + 1-1 = »ù´¡¾àÀ딣¬Ï൱ÓÚµÖÏûЧ¹û¡£
3. ÌØÊâ¼¼ÄܶÔÂíµÄºöÂÔЧ¹û
ÉÙÊý¼¼ÄÜ¿ÉÎÞÊÓÂíµÄ¾àÀëÐÞÕý£º
»ÆÔÂÓ¢ “¼¯ÖÇ”¡¢Öî¸ðÁÁ “¿Õ³Ç” µÈ¼¼Äܲ»Éæ¼°¾àÀë¼ÆË㣬ÓëÂíÎÞÖ±½Ó»¥¶¯£»
µäΤ “ǿϮ” ͨ¹ýÆúÖÃÌåÁ¦·¢¶¯£¬ÎÞÐ迼Âǹ¥»÷¾àÀ룬ÂíµÄЧ¹û¶ÔÆäÎÞЧ¡£
ËÄ¡¢µäÐÍÎóÇø³ÎÇå
“+1 Âí¿ÉÃâÒßËùÓнü¾àÀë¹¥»÷”£º´íÎó¡£+1 Âí½öÔö¼ÓËûÈ˶ÔÄãµÄ¾àÀ룬Èô¹¥»÷Õß×°±¸ - 1 Âí»ò³¤¾àÀëÎäÆ÷£¨Èç·½Ìì»êª£©£¬ÈԿɶÔÄã·¢¶¯¹¥»÷¡£
“¸ü»»ÂíʱÔЧ¹û³ÖÐøµ½»ØºÏ½áÊø”£º´íÎ󡣯úÖÃÂíºóЧ¹ûÁ¢¼´Ïûʧ£¬ÐÂ×°±¸µÄÂí¼´Ê±ÉúЧ£¬²»´æÔÚ “Ч¹ûµþ¼ÓÆÚ”¡£
“ÂíÊõ¼¼ÄܵÈͬÓÚ×°±¸ - 1 Âí£¬²»Äܵþ¼Ó”£º´íÎó¡£¹Ù·½¹æÔòÃ÷È· “ÂíÊõ” Óë×°±¸ - 1 Âí¿Éµþ¼Ó£¬¶þÕßÊôÓÚ²»Í¬À´Ô´µÄ¾àÀëÐÞÕý¡£
“ÂíÄÜÓ°Ïì½ÇÉ«µÄλÖþàÀ딣º´íÎó¡£Âí½öÐÞÕý “¹¥»÷¾àÀë¼ÆËã½á¹û”£¬²»¸Ä±ä½ÇÉ«ÔÚ³¡ÉϵÄʵ¼Ê×ùλλÖá£
Îå¡¢ÌØÊâģʽ²¹³ä£º¹úÕ½ÖеÄÂí¹æÔò
¹úսģʽÖУ¬ÂíµÄ»ù´¡¹æÔòÓëÉí·Ý¾ÖÒ»Ö£¬µ«Ðè×¢Òâ “Ã÷ÖÃÎ佫ů” µÄ¹ØÁª£º
Âí³¬µÈ´ø “ÂíÊõ” µÄÎ佫£¬ÐèÃ÷ÖÃÎ佫ůºó£¬“¹¥»÷¾àÀë - 1” Ч¹û²ÅÉúЧ£»
¹úÕ½ÎÞרÊôÂí¿¨ÅÆ£¬ËùÓÐÂí¾ùÑØÓÃÉí·Ý¾ÖµÄ + 1 Âí¡¢-1 ÂíÉ趨£¬ÎÞ¶îÍâÌØÊâЧ¹û¡£
×ÛÉÏ£¬Èý¹úɱÖÐ “Âí” µÄºËÐÄÕùÒ鼯ÖÐÔÚ¾àÀë¼ÆËãÓë¼¼ÄÜÁª¶¯£¬ÀÎ¼Ç “+1 Âí·À¡¢-1 Âí¹¥¡¢¼¼ÄÜÓë×°±¸¿Éµþ¼Ó” µÄºËÐÄÂß¼£¬½áºÏ¾ßÌ峡¾°Åж¨£¬¼´¿É±ÜÃâ¶àÊý¶Ô¾Öì¶Ü¡£ÊµÕ½ÖÐÈôÓö¸´ÔÓÇé¿ö£¬¿ÉÓÅÏÈÒÀ¾Ý “Ö¸¶¨Ä¿±êʱ¼ÆËã¾àÀë” µÄÔÔò¿ìËÙ½áËã¡£
Ò»¡¢»ù´¡ÈÏÖª£º×°±¸ÂíµÄºËÐŦÄÜÓë·ÖÀà
Èý¹úɱÖеÄ×°±¸Âí·ÖΪ “+1 Âí” ºÍ “-1 Âí” Á½À࣬Ãû³Æ²»Í¬µ«Í¬ÀàÐÍЧ¹ûÒ»Ö£¬ºËÐÄ×÷ÓÃÊǵ÷½Ú½ÇÉ«¼äµÄ “¹¥»÷¾àÀ딣¨¼´½ÇɫʹÓá¾É±¡¿¡¢¡¾Ë³ÊÖÇ£Ñò¡¿µÈ¿¨ÅÆÊ±µÄÓÐЧ·¶Î§£©¡£
1. +1 Âí£º·ÀÓùÐÍ×°±¸£¬À¿ª±»¹¥»÷¾àÀë
ºËÐÄЧ¹û£ºÆäËû½ÇÉ«¼ÆËãÓëÄãµÄ¾àÀëʱ£¬½á¹û + 1£¨½öÓ°ÏìËûÈ˶ÔÄãµÄ¹¥»÷£¬²»Ó°ÏìÄã¶ÔËûÈ˵Ĺ¥»÷£©¡£
³£¼û¿¨ÅÆ£º×¦»Æ·Éµç¡¢æèæòµÈ£¬¾ùÊôÓÚ + 1 Âí£¬Ð§¹ûÎÞ²îÒì¡£
ʵս³¡¾°£ºÈôÄãÓëÏàÁÚ½ÇÉ«µÄ»ù´¡¾àÀëΪ 1£¬×°±¸ + 1 Âíºó£¬¸Ã½ÇÉ«Ðè×°±¸ - 1 Âí»òÎäÆ÷£¨ÈçÇàâG½££¬¹¥»÷¾àÀë 2£©²ÅÄܶÔÄãʹÓá¾É±¡¿¡£
2. -1 Âí£º½ø¹¥ÐÍ×°±¸£¬Ëõ¶Ì¹¥»÷¾àÀë
ºËÐÄЧ¹û£ºÄã¼ÆËãÓëÆäËû½ÇÉ«µÄ¾àÀëʱ£¬½á¹û - 1£¨½öÓ°ÏìÄã¶ÔËûÈ˵Ĺ¥»÷£¬²»Ó°ÏìËûÈ˶ÔÄãµÄ¹¥»÷£©¡£
³£¼û¿¨ÅÆ£ºµÄ¬¡¢¾øÓ°µÈ£¬¾ùÊôÓÚ - 1 Âí£¬Ð§¹ûÎÞ²îÒì¡£
ʵս³¡¾°£ºÈôÄãÓë¸ôλ½ÇÉ«µÄ»ù´¡¾àÀëΪ 2£¬×°±¸ - 1 Âíºó£¬¿ÉÖ±½Ó¶ÔÆäʹÓá¾É±¡¿»ò¡¾Ë³ÊÖÇ£Ñò¡¿£¬ÎÞÐè¶îÍâÎäÆ÷Ö§³Å¡£
¶þ¡¢¸ßƵ½áËãÕùÒ飺¾àÀ롢ʱ»úÓ뻥¶¯¹æÔò
1. ¾àÀëµþ¼Ó¼ÆË㣺+1 ÂíÓë - 1 ÂíµÄ³åÍ»´¦Àí
µ±¹¥»÷·½×°±¸ - 1 Âí¡¢·ÀÊØ·½×°±¸ + 1 Âíʱ£¬¾àÀëÐè “µþ¼Ó¼ÆË㔣¬ºËÐĹæÔòΪ “¸÷×ÔÐÞÕýºóÈ¡×îÖÕ½á¹û”¡£
¼ÆË㹫ʽ£º×îÖÕ¹¥»÷¾àÀë = »ù´¡¾àÀë + ·ÀÊØ·½ + 1 ÂíÐÞÕý - ¹¥»÷·½ - 1 ÂíÐÞÕý
ʵս°¸Àý£º
A Óë B »ù´¡¾àÀëΪ 2£¬A ×°±¸ - 1 Âí£¬B ×°±¸ + 1 Âí£º
×îÖÕ¾àÀë = 2 + 1 - 1 = 2£¬´Ëʱ A Ðè×°±¸¹¥»÷¾àÀë≥2 µÄÎäÆ÷£¨ÈçÕɰËÉß죩²ÅÄÜ¶Ô B ʹÓá¾É±¡¿¡£
Èô A δװ±¸ÎäÆ÷£¬½ö¿¿ - 1 ÂíÎÞ·¨Í»ÆÆ B µÄ + 1 Âí·ÀÓù¡£
2. ÉúЧÓëʧЧʱ»ú£º×°±¸¡¢¸ü»»ÓëʧȥµÄ¹æÔò
×°±¸¼´ÉúЧ£º³öÅÆ½×¶Î×°±¸Âíºó£¬±¾»ØºÏÁ¢¼´ÉúЧ£¬¿ÉÖ±½ÓʹÓá¾É±¡¿¹¥»÷Ô±¾¾àÀë²»¹»µÄ½ÇÉ«¡£
¸ü»»ÂíµÄ´¦Àí£ºÈôÏë¸ü»»ÆäËûÂí£¬ÐèÏÈÆúÖõ±Ç°×°±¸µÄÂí£¨ÖÃÈëÆúÅÆ¶Ñ£©£¬ÔÙ×°±¸ÐÂÂí£¬ÆúÖúóÔÂíЧ¹ûÁ¢¼´Ïûʧ¡£
ʧȥÂíµÄÓ°Ï죺ÈôÂí±»¡¾¹ýºÓ²ðÇÅ¡¿ÒƳý»ò½ÇÉ«±ôËÀÆúÖÃ×°±¸£¬¾àÀëÁ¢¼´»Ö¸´»ù´¡Öµ£¬Î´Íê³ÉµÄ¹¥»÷£¨È硾ɱ¡¿ÒÑÖ¸¶¨Ä¿±êµ«Âí±»ÒÆ³ý£©ÈÔÓÐЧ£¨Òò¾àÀëÅж¨ÔÚÖ¸¶¨Ä¿±êʱÍê³É£©¡£
3. ÓëÎäÆ÷¡¢½õÄҵĻ¥¶¯£º¾àÀëÅж¨ÓÅÏȼ¶
ÓëÎäÆ÷µÄµþ¼Ó£ºÎäÆ÷µÄ¹¥»÷¾àÀëÓë - 1 Âí¿Éµþ¼Ó¡£ÀýÈ磬װ±¸ÇàÁúÙÈÔµ¶£¨¹¥»÷¾àÀë 3£©+ -1 Âíºó£¬Êµ¼Ê¹¥»÷¾àÀëΪ 4£¬Äܸ²¸Ç¸üÔ¶Ä¿±ê¡£
½õÄҵľàÀëÏÞÖÆ£º¡¾Ë³ÊÖÇ£Ñò¡¿¡¾±øÁ¸´ç¶Ï¡¿µÄ¾àÀëÅж¨Ó롾ɱ¡¿Ò»Ö£¬ÊÜÂíµÄÓ°Ï죻¡¾ÄÏÂùÈëÇÖ¡¿¡¾Íò¼ýÆë·¢¡¿ÊÇȺÌåЧ¹û£¬²»ÊÜÂíµÄ¾àÀëÏÞÖÆ¡£
ÌØÊâÎäÆ÷³åÍ»£º×°±¸Öî¸ðÁ¬å󣨹¥»÷¾àÀë 1£©Ê±£¬-1 Âí¿É½«Æä¹¥»÷¾àÀëÀ©Õ¹Îª 2£¬ÊµÏÖ “¶ÌÎäÆ÷Ô¶³Ì¹¥»÷”¡£
Èý¡¢Î佫¼¼ÄÜÓë “Âí” µÄÁª¶¯½âÎö
²¿·ÖÎ佫¼¼ÄÜ×Ô´ø “ÂíÊõ” Ч¹û£¬Æä¹æÔòÓë×°±¸Âí¼ÈÓй²ÐÔÒ²ÓвîÒ죬ÊÇʵսÖеÄÒ×´íµã¡£
1. ×Ô´ø “ÂíÊõ” ¼¼ÄÜ£ºÓë×°±¸ÂíµÄµþ¼Ó¹æÔò
ÒÔÂí³¬µÄ “ÂíÊõ” ΪÀý£¬¼¼ÄÜÃèÊöΪ “Ëø¶¨¼¼£¬Äã¼ÆËãÓëÆäËû½ÇÉ«µÄ¾àÀë - 1”£¬Óë×°±¸ - 1 Âí¿Éµþ¼ÓÉúЧ¡£
ʵս°¸Àý£º
Âí³¬Î´×°±¸ÎäÆ÷£¬»ù´¡¹¥»÷¾àÀëΪ 1£¬×Ô´ø “ÂíÊõ”£¨-1£©+ ×°±¸ - 1 Âíºó£¬Êµ¼Ê¹¥»÷¾àÀëΪ 3£¬¿ÉÖ±½Ó¹¥»÷¸ôÁ½Î»µÄ½ÇÉ«¡£
×¢Ò⣺ËùÓÐ “ÂíÊõ” À༼ÄܾùΪ “¹¥»÷¾àÀë - 1”£¬ÎÞ “+1 Âí” ÀàÐ͵ķÀÓùÐÔ×Ô´ø¼¼ÄÜ¡£
2. ¼¼ÄÜ´¥·¢ÓëÂíµÄ¾àÀë¹ØÁª
Âí³¬ “ÌúÆï” ÓëÂíµÄ¹ØÏµ£º“ÌúÆï” µÄ·¢¶¯½öÐ衾ɱ¡¿Ö¸¶¨Ä¿±ê£¬ÓëÊÇ·ñ×°±¸ÂíÎ޹أ¬µ«ÂíÌṩµÄ¾àÀë¿ÉÈÃÂí³¬¸üÒ×´¥¼°Ä¿±ê¡£ÀýÈ磬Âí³¬×°±¸ - 1 Âíºó£¬¿É¶ÔÔ¶´¦µÄÕŽÇʹÓá¾É±¡¿²¢·¢¶¯ “ÌúÆï” Åж¨¡£
´óÇÇ “Á÷Àë” ÓëÂíµÄ½áË㣺´óÇǶԹ¥»÷Õß·¢¶¯ “Á÷Àë” Ê±£¬Ðè¼ÆËã¹¥»÷ÕßÓë±»Á÷ÀëÄ¿±êµÄ¾àÀ루ÊÜÂíÓ°Ï죩¡£Èô¹¥»÷Õß×°±¸ - 1 Âí£¬¿ÉÄÜÂú×ãÁ÷ÀëÄ¿±êµÄ¾àÀëÒªÇó¡£
¹«Ëïè¶ “Òå´Ó” ÓëÂíµÄµþ¼Ó£º¹«Ëïè¶ “Òå´Ó” ·¢¶¯Ê± “¹¥»÷¾àÀë + 1”£¬Óë×°±¸ - 1 Âíµþ¼Óºó£¬Êµ¼Ê¹¥»÷¾àÀëΪ “»ù´¡¾àÀë + 1-1 = »ù´¡¾àÀ딣¬Ï൱ÓÚµÖÏûЧ¹û¡£
3. ÌØÊâ¼¼ÄܶÔÂíµÄºöÂÔЧ¹û
ÉÙÊý¼¼ÄÜ¿ÉÎÞÊÓÂíµÄ¾àÀëÐÞÕý£º
»ÆÔÂÓ¢ “¼¯ÖÇ”¡¢Öî¸ðÁÁ “¿Õ³Ç” µÈ¼¼Äܲ»Éæ¼°¾àÀë¼ÆË㣬ÓëÂíÎÞÖ±½Ó»¥¶¯£»
µäΤ “ǿϮ” ͨ¹ýÆúÖÃÌåÁ¦·¢¶¯£¬ÎÞÐ迼Âǹ¥»÷¾àÀ룬ÂíµÄЧ¹û¶ÔÆäÎÞЧ¡£
ËÄ¡¢µäÐÍÎóÇø³ÎÇå
“+1 Âí¿ÉÃâÒßËùÓнü¾àÀë¹¥»÷”£º´íÎó¡£+1 Âí½öÔö¼ÓËûÈ˶ÔÄãµÄ¾àÀ룬Èô¹¥»÷Õß×°±¸ - 1 Âí»ò³¤¾àÀëÎäÆ÷£¨Èç·½Ìì»êª£©£¬ÈԿɶÔÄã·¢¶¯¹¥»÷¡£
“¸ü»»ÂíʱÔЧ¹û³ÖÐøµ½»ØºÏ½áÊø”£º´íÎ󡣯úÖÃÂíºóЧ¹ûÁ¢¼´Ïûʧ£¬ÐÂ×°±¸µÄÂí¼´Ê±ÉúЧ£¬²»´æÔÚ “Ч¹ûµþ¼ÓÆÚ”¡£
“ÂíÊõ¼¼ÄܵÈͬÓÚ×°±¸ - 1 Âí£¬²»Äܵþ¼Ó”£º´íÎó¡£¹Ù·½¹æÔòÃ÷È· “ÂíÊõ” Óë×°±¸ - 1 Âí¿Éµþ¼Ó£¬¶þÕßÊôÓÚ²»Í¬À´Ô´µÄ¾àÀëÐÞÕý¡£
“ÂíÄÜÓ°Ïì½ÇÉ«µÄλÖþàÀ딣º´íÎó¡£Âí½öÐÞÕý “¹¥»÷¾àÀë¼ÆËã½á¹û”£¬²»¸Ä±ä½ÇÉ«ÔÚ³¡ÉϵÄʵ¼Ê×ùλλÖá£
Îå¡¢ÌØÊâģʽ²¹³ä£º¹úÕ½ÖеÄÂí¹æÔò
¹úսģʽÖУ¬ÂíµÄ»ù´¡¹æÔòÓëÉí·Ý¾ÖÒ»Ö£¬µ«Ðè×¢Òâ “Ã÷ÖÃÎ佫ů” µÄ¹ØÁª£º
Âí³¬µÈ´ø “ÂíÊõ” µÄÎ佫£¬ÐèÃ÷ÖÃÎ佫ůºó£¬“¹¥»÷¾àÀë - 1” Ч¹û²ÅÉúЧ£»
¹úÕ½ÎÞרÊôÂí¿¨ÅÆ£¬ËùÓÐÂí¾ùÑØÓÃÉí·Ý¾ÖµÄ + 1 Âí¡¢-1 ÂíÉ趨£¬ÎÞ¶îÍâÌØÊâЧ¹û¡£
×ÛÉÏ£¬Èý¹úɱÖÐ “Âí” µÄºËÐÄÕùÒ鼯ÖÐÔÚ¾àÀë¼ÆËãÓë¼¼ÄÜÁª¶¯£¬ÀÎ¼Ç “+1 Âí·À¡¢-1 Âí¹¥¡¢¼¼ÄÜÓë×°±¸¿Éµþ¼Ó” µÄºËÐÄÂß¼£¬½áºÏ¾ßÌ峡¾°Åж¨£¬¼´¿É±ÜÃâ¶àÊý¶Ô¾Öì¶Ü¡£ÊµÕ½ÖÐÈôÓö¸´ÔÓÇé¿ö£¬¿ÉÓÅÏÈÒÀ¾Ý “Ö¸¶¨Ä¿±êʱ¼ÆËã¾àÀë” µÄÔÔò¿ìËÙ½áËã¡£

