锘??xml version="1.0" encoding="utf-8" standalone="yes"?> ===== 鐪熸寮虹殑涓滆タ鏉ヤ簡錛?nbsp; ===== 浠婂ぉ鎴戜滑鏉ョ湅涓や釜紼嶅井澶嶆潅涓鐐圭殑渚嬪瓙銆?br>
緇欏嚭n涓暟錛屾庢牱灝嗗畠浠粠灝忓埌澶ф帓搴忥紵涓嬮潰涓鍙f皵璁蹭笁縐嶅父鐢ㄧ殑綆楁硶錛屽畠浠槸鏈綆鍗曠殑銆?
鏈鏄劇劧鐨勩佹渶瀹規(guī)槗鎯沖埌鐨勩傞夋嫨鎺掑簭(Selection
Sort)鏄錛屾瘡嬈′粠鏁板垪涓壘鍑轟竴涓渶灝忕殑鏁版斁鍒版渶鍓嶉潰鏉ワ紝鍐嶄粠鍓╀笅鐨刵-1涓暟涓夋嫨涓涓渶灝忕殑錛屼笉鏂仛涓嬪幓銆傛彃鍏ユ帓搴?Insertion
Sort)鏄紝姣忔浠庢暟鍒椾腑鍙栦竴涓繕娌℃湁鍙栧嚭榪囩殑鏁幫紝騫舵寜鐓уぇ灝忓叧緋繪彃鍏ュ埌宸茬粡鍙栧嚭鐨勬暟涓嬌寰楀凡緇忓彇鍑虹殑鏁頒粛鐒舵湁搴忋傚啋娉℃帓搴?Bubble
Sort)鍒嗕負鑻ュ共瓚熻繘琛岋紝姣忎竴瓚熸帓搴忎粠鍓嶅線鍚庢瘮杈冩瘡涓や釜鐩擱偦鐨勫厓绱犵殑澶у皬錛堝洜姝や竴瓚熸帓搴忚姣旇緝n-1瀵逛綅緗浉閭?cè)潥勬晭图夠q跺湪姣忔鍙戠幇鍓嶉潰鐨勯偅涓暟姣旂揣鎺ュ畠
鍚庣殑鏁板ぇ鏃朵氦鎹綅緗紱榪涜瓚沖澶氳稛鐩村埌鏌愪竴瓚熻窇瀹屽悗鍙戠幇榪欎竴瓚熸病鏈夎繘琛屼換浣曚氦鎹㈡搷浣滐紙鏈鍧忔儏鍐典笅瑕佽窇n-1瓚燂紝榪欑鎯呭喌鍦ㄦ渶灝忕殑鏁頒綅浜庣粰瀹氭暟鍒楃殑鏈鍚庨潰鏃?
鍙戠敓錛夈備簨瀹炰笂錛屽湪絎竴瓚熷啋娉$粨鏉熷悗錛屾渶鍚庨潰閭d釜鏁拌偗瀹氭槸鏈澶х殑浜嗭紝浜庢槸絎簩嬈″彧闇瑕佸鍓嶉潰n-1涓暟鎺掑簭錛岃繖鍙堝皢鎶婅繖n-1涓暟涓渶灝忕殑鏁版斁鍒版暣涓暟鍒?
鐨勫掓暟絎簩涓綅緗傝繖鏍蜂笅鍘伙紝鍐掓場鎺掑簭絎琲瓚熺粨鏉熷悗鍚庨潰i涓暟閮藉凡緇忓埌浣嶄簡錛岀i+1瓚熷疄闄呬笂鍙冭檻鍓峮-i涓暟錛堥渶瑕佺殑姣旇緝嬈℃暟姣斿墠闈㈡墍璇寸殑n-1瑕?
灝忥級銆傝繖鐩稿綋浜庣敤鏁板褰掔撼娉曡瘉鏄庝簡鍐掓場鎺掑簭鐨勬紜э細瀹炶川涓庨夋嫨鎺掑簭鐩稿悓銆備笂闈㈢殑涓変釜綆楁硶鎻忚堪鍙兘鏈夌偣妯$硦浜嗭紝娌℃槑鐧界殑璇濈綉涓婃壘璧勬枡錛屼唬鐮佸拰鍔ㄧ敾婕旂ず閬嶅湴
閮芥槸銆?br>
榪?
涓夌綆楁硶闈炲父瀹規(guī)槗鐞嗚В錛屽洜涓烘垜浠敓媧誨綋涓粡甯稿湪鐢ㄣ傛瘮濡傦紝鐝笂鐨凪M鎼為夌編媧誨姩錛屾湁浜哄彨鎴戠粰鎵鏈塎M鎺掍釜鍚嶃傛垜浠氬父浼氱敤閫夋嫨鎺掑簭錛屽嵆鍏堟壘鍑鴻嚜宸辮涓烘渶婕?
浜殑錛岀劧鍚庢壘絎簩婕備寒鐨勶紝鐒跺悗鎵劇涓夋紓浜殑錛屼笉鏂壘鍓╀笅鐨勪漢涓渶婊℃剰鐨勩傛墦鎵戝厠鐗屾椂鎴戜滑甯屾湜鎶撳畬鐗屽悗鎵嬩笂鐨勭墝鏄湁搴忕殑錛屼笁涓?鎸ㄥ湪涓璧鳳紝鍚庨潰绱ф帴鐫涓や釜
9銆傝繖鏃訛紝鎴戜滑浼氫嬌鐢ㄦ彃鍏ユ帓搴忥紝姣忔鎷垮埌涓寮犵墝鍚庢妸瀹冩彃鍏ュ埌鎵嬩笂鐨勭墝涓傚綋鐨勪綅緗備粈涔堟椂鍊欐垜浠細鐢ㄥ啋娉℃帓搴忓憿錛熸瘮濡傦紝浣撹偛璇句笂浠庣煯鍒伴珮鎺掗槦鏃訛紝绔欓槦瀹屾瘯
鍚庢諱細鏈変漢鍑烘潵錛屾瘮杈冩尐鐫鐨勪袱涓漢鐨勮韓楂橈紝鎸囨尌鍒幫細浣犱滑淇╄皟鎹竴涓嬶紝浣犱滑淇╂崲涓涓嬨?br> 榪欐槸寰堟湁鍚彂鎬х殑銆傝繖鍛婅瘔鎴戜滑錛屼粈涔堟椂鍊欑敤浠涔堟帓搴忔渶
濂姐傚綋浜轟滑娓存湜鍏堢煡閬撴帓鍦ㄥ墠闈㈢殑鏄皝鏃訛紝鎴戜滑鐢ㄩ夋嫨鎺掑簭錛?strong style="color: #0000ff;">褰撴垜浠笉鏂嬁
鍒版柊鐨勬暟騫舵兂淇濇寔宸叉湁鐨勬暟濮嬬粓鏈夊簭鏃訛紝鎴戜滑鐢ㄦ彃鍏ユ帓搴忥紱褰撶粰鍑虹殑鏁板垪宸茬粡姣旇緝鏈夊簭錛屽彧闇瑕佸皬騫呭害鐨勮皟鏁翠竴涓嬫椂錛屾垜浠敤鍐掓場鎺掑簭銆?
鎴?
浠潵綆椾竴涓嬫渶鍧忔儏鍐典笅涓夌綆楁硶鍚勯渶瑕佸灝戞姣旇緝鍜岃祴鍊兼搷浣溿?br> 閫夋嫨鎺掑簭鍦ㄧi嬈¢夋嫨鏃惰祴鍊煎拰姣旇緝閮介渶瑕乶-i嬈★紙鍦╪-i+1涓暟涓変竴涓?
鍑烘潵浣滀負褰撳墠鏈灝忓鹼紝鍏朵綑n-i涓暟涓庡綋鍓嶆渶灝忓兼瘮杈冨茍涓嶆柇鏇存柊褰撳墠鏈灝忓鹼級錛岀劧鍚庨渶瑕佷竴嬈¤祴鍊兼搷浣溿傛誨叡闇瑕乶(n-1)/2嬈℃瘮杈冧笌n(n-1)
/2+n嬈¤祴鍊箋?br> 鎻掑叆鎺掑簭鍦ㄧi嬈″鎵炬彃鍏ヤ綅緗椂闇瑕佹渶澶歩-1嬈℃瘮杈冿紙浠庡悗寰鍓嶆壘鍒扮涓涓瘮寰呮彃鍏ョ殑鏁板皬鐨勬暟錛屾渶鍧忔儏鍐靛彂鐢熷湪榪欎釜鏁版槸
鎵鏈夊凡緇忓彇鍑虹殑鏁頒腑鏈灝忕殑涓涓殑鏃跺欙級錛屽湪宸叉湁鏁板垪涓粰鏂扮殑鏁拌吘鍑轟綅緗渶瑕乮-1嬈¤祴鍊兼搷浣滄潵瀹炵幇錛岃繕闇瑕佷袱嬈¤祴鍊煎熷姪涓存椂鍙橀噺鎶婃柊鍙栧嚭鐨勬暟鎼繘鎼嚭銆備篃
灝辨槸璇達紝鏈鍧忔儏鍐典笅姣旇緝闇瑕乶(n-1)/2嬈★紝璧嬪奸渶瑕乶(n-1)/2+2n嬈°傛垜榪欎箞鍐欐湁鐐硅瀵間漢錛屽ぇ瀹朵笉瑕佷互涓虹▼搴忕殑瀹炵幇鐢ㄤ簡涓や釜鏁扮粍鍝︼紝鍏跺疄涓
涓暟緇勫氨澶熶簡錛岀湅鐪嬩笂闈㈢殑婕旂ず灝辯煡閬撲簡銆傛垜鍙綆楁硶錛屼竴鑸笉鍐欏浣曞疄鐜般傚綆楁硶鐨勯兘鏄己浜猴紝鐭ラ亾綆楁硶浜嗛兘鑳藉啓鍑轟竴涓紓浜殑浠g爜鏉ャ?br> 鍐掓場鎺?
搴忕i瓚熸帓搴忛渶瑕佹瘮杈僴-i嬈★紝n-1瓚熸帓搴忔誨叡n(n-1)/2嬈°傜粰鍑虹殑搴忓垪閫嗗簭鎺掑垪鏄渶鍧忕殑鎯呭喌錛岃繖鏃舵瘡涓嬈℃瘮杈冮兘瑕佽繘琛屼氦鎹㈡搷浣溿備竴嬈′氦鎹㈡搷浣滈渶
瑕?嬈¤祴鍊煎疄鐜幫紝鍥犳鍐掓場鎺掑簭鏈鍧忔儏鍐典笅闇瑕佽祴鍊?n(n-1)/2嬈°?br> 鎸夌収娓愯繘澶嶆潅搴︾悊璁猴紝蹇界暐鎵鏈夌殑甯告暟錛屼笁縐嶆帓搴忕殑鏈鍧忔儏鍐典笅澶嶆潅
搴﹂兘鏄竴鏍風(fēng)殑錛歄(n^2)銆備絾瀹為檯搴旂敤涓笁縐嶆帓搴忕殑鏁堢巼騫朵笉鐩稿悓銆傚疄璺佃瘉鏄庯紙鏀挎不鑰冭瘯鏃舵瘡閬撳ぇ棰橀兘瑕佺敤榪欏洓涓瓧錛夛紝鎻掑叆鎺掑簭鏄渶蹇殑錛堣櫧鐒舵渶鍧忔儏鍐典笅涓?
閫夋嫨鎺掑簭鐩稿綋鐢氳嚦鏇寸碂錛夛紝鍥犱負姣忎竴嬈℃彃鍏ユ椂瀵繪壘鎻掑叆鐨勪綅緗鏁版儏鍐靛彧闇瑕佷笌宸叉湁鏁扮殑涓閮ㄥ垎榪涜姣旇緝錛堜綘鍙兘鐭ラ亾榪欒繕鑳戒簩鍒嗭級銆備綘鎴栬浼氳鍐掓場鎺掑簭涔熷彲浠ュ湪
鍗婅礬涓婂畬鎴愶紝榪樻病鏈夎窇鍒扮n-1瓚熷氨宸茬粡鏈夊簭銆備絾鍐掓場鎺掑簭鐨勪氦鎹㈡搷浣滄洿璐規(guī)椂錛岃屾彃鍏ユ帓搴忎腑鎵懼埌浜嗘彃鍏ョ殑浣嶇疆鍚庣Щ鍔ㄦ搷浣滃彧闇瑕佺敤璧嬪煎氨鑳藉畬鎴愶紙浣犲彲鑳界煡閬撹繖
榪樿兘鐢╩ove錛夈傛湰鏂囧悗闈㈠皢浠嬬粛鐨勪竴縐嶇畻娉曞氨鍒╃敤鎻掑叆鎺掑簭鐨勮繖浜涗紭鍔褲?br>
鎴戜滑璇佹槑浜嗭紝涓夌鎺掑簭鏂規(guī)硶鍦ㄦ渶鍧忔儏鍐典笅鏃墮棿澶嶆潅搴﹂兘鏄?
O(n^2)銆備絾澶у鎯寵繃鍚楋紝榪欏彧鏄渶鍧忔儏鍐典笅鐨勩傚湪寰堝鏃跺欙紝澶嶆潅搴︽病鏈夎繖涔堝ぇ錛屽洜涓烘彃鍏ュ拰鍐掓場鍦ㄦ暟鍒楀凡緇忔瘮杈冩湁搴忕殑鎯呭喌涓嬮渶瑕佺殑鎿嶄綔榪滆繙浣庝簬n^2嬈?
錛堟渶濂芥儏鍐典笅鐢氳嚦鏄嚎鎬х殑錛夈傛姏寮閫夋嫨鎺掑簭涓嶈錛堝洜涓哄畠鐨勫鏉傚害鏄?#8220;姝?#8221;鐨勶紝瀵逛簬閫夋嫨鎺掑簭娌℃湁浠涔?#8220;濂?#8221;鐨勬儏鍐碉級錛屾垜浠笅闈㈡帰璁ㄦ彃鍏ユ帓搴忓拰鍐掓場鎺掑簭鍦ㄧ壒瀹?
鏁版嵁鍜屽鉤鍧囨儏鍐典笅鐨勫鏉傚害銆?br> 浣犱細鍙戠幇錛屽鏋滄妸鎻掑叆鎺掑簭涓殑縐誨姩璧嬪兼搷浣滅湅浣滄槸鎶婂綋鍓嶅彇鍑虹殑鍏冪礌涓庡墠闈㈠彇鍑虹殑涓旀瘮瀹冨ぇ鐨勬暟閫愪竴浜ゆ崲錛岄偅鎻掑叆
鎺掑簭鍜屽啋娉℃帓搴忓鏁版嵁鐨勫彉鍔ㄥ叾瀹為兘鏄浉閭誨厓绱犵殑浜ゆ崲鎿嶄綔銆備笅闈㈡垜浠鏄庯紝鑻ュ彧鑳藉鏁板垪涓浉閭?cè)潥勬暟杩涜浜ゆ崲鎿嶄綔锛屽浣曡绠椾娇寰梟涓暟鍙樺緱鏈夊簭鏈灝戦渶瑕佺殑浜ゆ崲
嬈℃暟銆?br> 鎴戜滑瀹氫箟閫嗗簭瀵圭殑姒傚康銆傚亣璁炬垜浠鎶婃暟鍒椾粠灝忓埌澶ф帓搴忥紝涓涓嗗簭瀵規(guī)槸鎸囩殑鍦ㄥ師鏁板垪涓紝宸﹁竟鐨勬煇涓暟姣斿彸杈圭殑澶с備篃灝辨槸璇達紝濡傛灉鎵懼埌
浜嗘煇涓猧鍜宩浣垮緱i<j涓擜i>Aj錛屾垜浠氨璇存垜浠壘鍒頒簡涓涓嗗簭瀵廣傛瘮濡傝錛屾暟鍒?,1,4,2涓湁涓変釜閫嗗簭瀵癸紝鑰屼竴涓凡緇忔湁搴忕殑鏁板垪閫嗗簭
瀵逛釜鏁頒負0銆傛垜浠彂鐜幫紝浜ゆ崲涓や釜鐩擱偦鐨勬暟鏈澶氭秷闄や竴涓嗗簭瀵癸紝涓斿啋娉℃帓搴忥紙鎴栨彃鍏ユ帓搴忥級涓殑涓嬈′氦鎹㈡伆濂借兘娑堥櫎涓涓嗗簭瀵廣傞偅涔堟樉鐒訛紝鍘熸暟鍒椾腑鏈夊灝戜釜閫?
搴忓鍐掓場鎺掑簭錛堟垨鎻掑叆鎺掑簭錛夊氨闇瑕佸灝戞浜ゆ崲鎿嶄綔錛岃繖涓搷浣滄鏁頒笉鍙兘鍐嶅皯銆?br> 鑻ョ粰鍑虹殑n涓暟涓湁m涓嗗簭瀵癸紝鎻掑叆鎺掑簭鐨勬椂闂村鏉傚害鍙互璇?
鏄疧(m+n)鐨勶紝鑰屽啋娉℃帓搴忎笉鑳借繖涔堣錛屽洜涓哄啋娉℃帓搴忔湁寰堝“鏃犵敤”鐨勬瘮杈冿紙姣旇緝鍚庢病鏈変氦鎹級錛岃繖浜涙棤鐢ㄧ殑姣旇緝瓚呰繃浜哋(m+n)涓備粠榪欎釜鎰忎箟涓婅錛?
鎻掑叆鎺掑簭浠嶇劧鏇翠負浼樼錛屽洜涓哄啋娉℃帓搴忕殑澶嶆潅搴﹁鍙楀埌瀹冭窇鐨勮稛鏁扮殑鍒剁害銆備竴涓吀鍨嬬殑渚嬪瓙鏄繖鏍風(fēng)殑鏁板垪錛?, 2, 3, 4, 5, 6, 7,
1銆傚湪榪欐牱鐨勮緭鍏ユ暟鎹笅鎻掑叆鎺掑簭鐨勪紭鍔塊潪甯告槑鏄撅紝鍐掓場鎺掑簭鍙兘鍝潃鍠婁笂澶╀笉鍏?br> 鐒惰岋紝鎴戜滑騫朵笉鎯寵綆楁帓搴忕畻娉曞浜庢煇涓壒瀹氭暟鎹殑鏁堢巼銆傛垜
浠湡姝e叧蹇冪殑鏄紝瀵逛簬鎵鏈夊彲鑳藉嚭鐜扮殑鏁版嵁錛岀畻娉曠殑騫沖潎澶嶆潅搴︽槸澶氬皯銆備笉鐢ㄦ縺鍔ㄤ簡錛屽鉤鍧囧鏉傚害騫朵笉浼氫綆浜庡鉤鏂廣備笅闈㈣瘉鏄庯紝涓ょ綆楁硶鐨勫鉤鍧囧鏉傚害浠嶇劧鏄?
O(n^2)鐨勩?br> 鎴戜滑浠呬粎璇佹槑綆楁硶闇瑕佺殑浜ゆ崲嬈℃暟騫沖潎涓篛(n^2)灝辮凍澶熶簡銆傚墠闈㈠凡緇忚榪囷紝瀹冧滑闇瑕佺殑浜ゆ崲嬈℃暟涓庨嗗簭瀵圭殑涓暟鐩稿悓銆傛垜
浠皢璇佹槑錛宯涓暟鐨勬暟鍒椾腑閫嗗簭瀵逛釜鏁板鉤鍧嘜(n^2)涓?br> 璁$畻鐨勬柟娉曟槸鍗佸垎宸у鐨勩傚鏋滄妸緇欏嚭鐨勬暟鍒楀弽榪囨潵錛堜粠鍚庡線鍓嶅掕繃鏉ュ啓錛夛紝浣犱細鍙?
鐜板師鏉ョ殑閫嗗簭瀵圭幇鍦ㄥ彉鎴愰『搴忕殑浜嗭紝鑰屽師鏉ユ墍鏈夌殑闈為嗗簭瀵圭幇鍦ㄩ兘鎴愰嗗簭浜嗐傛鍙嶄袱涓暟鍒楃殑閫嗗簭瀵逛釜鏁板姞璧鋒潵姝eソ灝辨槸鏁板垪鎵鏈夋暟瀵圭殑涓暟錛屽畠絳変簬n(n-
1)/2銆備簬鏄紝騫沖潎姣忎釜鏁板垪鏈塶(n-1)/4涓嗗簭瀵廣傚拷鐣ュ父鏁幫紝閫嗗簭瀵瑰鉤鍧囦釜鏁癘(n^2)銆?br> 涓婇潰鐨勮璁哄惎紺烘垜浠紝瑕佹兂鎼炲嚭涓涓
鏉傚害浣庝簬騫蟲柟綰у埆鐨勬帓搴忕畻娉曪紝鎴戜滑闇瑕佹兂鍔炴硶鑳芥妸紱誨緱鑰佽繙鐨勪袱涓暟榪涜鎿嶄綔銆?br>
浜轟滑鎯沖晩鎯沖晩鎯沖晩錛屾庝箞閮芥兂涓嶅嚭鎬庢牱鎵嶈兘鎼炲嚭澶嶆潅搴?
浣庝簬騫蟲柟鐨勭畻娉曘傚悗鏉ワ紝鑻遍泟鍑虹幇浜嗭紝Donald Shell鍙戞槑浜嗕竴縐嶆柊鐨勭畻娉曪紝鎴戜滑灝嗚瘉鏄庡畠鐨勫鏉傚害鏈鍧忔儏鍐典笅涔熸病鏈塐(n^2)
錛堜技涔庢湁浜轟笉鍠滄鐮旂┒姝g‘鎬у拰澶嶆潅搴︾殑璇佹槑錛屾垜浼氱敤瀹炰緥鍛婅瘔澶у錛岃繖浜涜瘉鏄庢槸闈炲父鏈夋剰鎬濈殑錛夈備粬鎶婅繖縐嶇畻娉曞彨鍋歋hell澧為噺鎺掑簭綆楁硶錛堝ぇ瀹跺父璇寸殑甯屽皵鎺?
搴忥級銆?br> Shell鎺掑簭綆楁硶渚濊禆涓縐嶇О涔嬩負“鎺掑簭澧為噺”鐨勬暟鍒楋紝涓嶅悓鐨勫閲忓皢瀵艱嚧涓嶅悓鐨勬晥鐜囥傚亣濡傛垜浠20涓暟榪涜鎺掑簭錛屼嬌鐢ㄧ殑澧為噺涓?
1,3,7銆傞偅涔堬紝鎴戜滑棣栧厛瀵硅繖20涓暟榪涜“7-鎺掑簭”(7-sortedness)銆傛墍璋?-鎺掑簭錛屽氨鏄寜鐓т綅緗櫎浠?鐨勪綑鏁板垎緇勮繘琛屾帓搴忋傚叿浣撳湴
璇達紝鎴戜滑灝嗘妸鍦?銆?銆?5涓変釜浣嶇疆涓婄殑鏁拌繘琛屾帓搴忥紝灝嗙2銆?銆?6涓暟榪涜鎺掑簭錛屼緷姝ょ被鎺ㄣ傝繖鏍鳳紝瀵逛簬浠繪剰涓涓暟瀛梜錛屽崟鐪婣(k),
A(k+7), A(k+14),
…榪欎簺鏁版槸鏈夊簭鐨勩?-鎺掑簭鍚庯紝鎴戜滑鎺ョ潃鍙堣繘琛屼竴瓚?-鎺掑簭錛堝埆蹇樹簡鎴戜滑浣跨敤鐨勬帓搴忓閲忎負1,3,7錛夈傛渶鍚庤繘琛?-鎺掑簭錛堝嵆鏅氱殑鎺掑簭錛夊悗鏁翠釜
Shell綆楁硶瀹屾垚銆傜湅鐪嬫垜浠殑渚嬪瓙錛?br>
3 7 9 0 5 1 6
8 4 2 0 6 1 5 7 3 4 9 8 2 <-- 鍘熸暟鍒?br> 3 3 2 0 5 1 5 7 4 4 0 6 1 6 8
7 9 9 8 2 <-- 7-鎺掑簭鍚?br> 0 0 1 1 2 2 3 3 4 4 5 6 5 6 8 7 7 9 8
9 <-- 3-鎺掑簭鍚?br> 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 <--
1-鎺掑簭鍚庯紙瀹屾垚錛?br>
鍦ㄦ瘡涓瓚熴佹瘡涓緇勭殑鎺掑簭涓垜浠繪槸浣跨敤鎻掑叆鎺掑簭銆備粩緇嗚瀵熶笂闈㈢殑渚嬪瓙浣犱細鍙戠幇鏄粈涔堝鑷翠簡
Shell鎺掑簭鐨勯珮鏁堛傚錛屾瘡涓瓚熸帓搴忓皢浣垮緱鏁板垪閮ㄥ垎鏈夊簭錛屼粠鑰屼嬌寰椾互鍚庣殑鎻掑叆鎺掑簭寰堝揩鎵懼埌鎻掑叆浣嶇疆銆傛垜浠笅闈㈠皢绱х揣鍥寸粫榪欎竴鐐規(guī)潵璇佹槑Shell鎺掑簭綆楁硶
鐨勬椂闂村鏉傚害涓婄晫銆?br> 鍙鎺掑簭澧為噺鐨勭涓涓暟鏄?錛孲hell鎺掑簭綆楁硶灝辨槸姝g‘鐨勩備絾鏄笉鍚岀殑澧為噺灝嗗鑷翠笉鍚岀殑鏃墮棿澶嶆潅搴︺傛垜浠笂闈緥瀛愪腑
鐨勫閲?1, 3, 7, 15, 31, …,
2^k-1)鏄嬌鐢ㄦ渶騫挎硾鐨勫閲忓簭鍒椾箣涓錛屽彲浠ヨ瘉鏄庝嬌鐢ㄨ繖涓閲忕殑鏃墮棿澶嶆潅搴︿負O(n√n)銆傝繖涓瘉鏄庡緢綆鍗曪紝澶у鍙互鍙傜湅涓浜涘叾瀹冪殑璧勬枡錛屾垜浠粖澶╀笉璇?
鏄庡畠銆備粖澶╂垜浠瘉鏄庯紝浣跨敤澧為噺1, 2, 3, 4, 6, 8, 9, 12, 16, …, 2^p*3^q錛屾椂闂村鏉傚害涓篛(n*(log
n)^2)銆?br> 寰堟樉鐒訛紝浠諱綍涓涓ぇ浜?鐨勬鏁存暟閮藉彲浠ヨ〃紺轟負2x+3y錛屽叾涓瓁鍜寉鏄潪璐熸暣鏁般備簬鏄紝濡傛灉涓涓暟鍒楀凡緇忔槸2-鎺掑簭鐨勪笖鏄?
3-鎺掑簭鐨勶紝閭d箞瀵逛簬姝ゆ椂鏁板垪涓殑姣忎竴涓暟A(i)錛屽畠鐨勫乏杈規(guī)瘮瀹冨ぇ鐨勫彧鏈夊彲鑳芥槸A(i-1)銆侫2緇濆涓嶅彲鑳芥瘮A12澶э紝鍥犱負10鍙互琛ㄧず涓轟袱涓?鍜屼袱
涓?鐨勫拰錛屽垯A2<A4<A6<A9<A12銆傞偅涔堬紝鍦ㄨ繖涓閲忎腑鐨?-鎺掑簭鏃舵瘡涓暟鎵炬彃鍏ヤ綅緗彧闇瑕佹瘮杈冧竴嬈°備竴鍏辨湁n涓暟錛?
鎵浠?-鎺掑簭鏄疧(n)鐨勩備簨瀹炰笂錛岃繖涓閲忎腑鐨?-鎺掑簭涔熸槸O(n)錛屽洜涓哄湪2-鎺掑簭涔嬪墠錛岃繖涓暟鍒楀凡緇忔槸4-鎺掑簭涓?-鎺掑簭榪囩殑錛屽彧鐪嬫暟鍒楃殑濂囨暟欏規(guī)垨
鑰呭伓鏁伴」錛堝嵆鍗曠湅姣忎竴緇勶級鐨勮瘽灝卞張鎴愪簡鍒氭墠鐨勬牱瀛愩傝繖涓閲忓簭鍒楀閥濡欏氨宸у鍦紝濡傛灉鎴戜滑瑕佽繘琛宧-鎺掑簭錛岄偅涔堝畠涓瀹氭槸2h-鎺掑簭榪囦笖3h-鎺掑簭榪囷紝浜庢槸澶?
鐞嗘瘡涓暟A(i)鐨勬彃鍏ユ椂灝卞彧闇瑕佸拰A(i-h)榪涜姣旇緝銆傝繖涓粨璁哄浜庢渶寮濮嬪嚑嬈★紙h鍊艱緝澶ф椂錛夌殑h-鎺掑簭鍚屾牱鎴愮珛錛屽綋2h銆?h澶т簬n鏃訛紝鎸夌収瀹氫箟錛?
鎴戜滑涔熷彲浠ヨ涓烘暟鍒楁槸2h-鎺掑簭鍜?h-鎺掑簭鐨勶紝榪欏茍涓嶅獎鍝嶄笂榪扮粨璁虹殑姝g‘鎬э紙浣犱篃鍙互璁や負h澶ぇ浠ヨ嚧浜庢帓搴忔椂姣忎竴緇勯噷鐨勬暟瀛椾笉瓚呰繃3涓紝灞炰簬甯告暟綰э級銆?
鐜板湪錛岃繖涓閲忎腑鐨勬瘡涓瓚熸帓搴忛兘鏄疧(n)鐨勶紝鎴戜滑鍙渶瑕佹暟涓涓嬩竴鍏辮窇浜嗗灝戣稛銆備篃灝辨槸璇達紝鎴戜滑鐜板湪鍙渶瑕佺煡閬撳皬浜巒鐨勬暟涓湁澶氬皯涓暟鍏鋒湁2^p*3^q
鐨勫艦寮忋傝鎯?^p*3^q涓嶈秴榪噉錛宲鐨勫彇鍊兼渶澶歄(log n)涓紝q鐨勫彇鍊兼渶澶氫篃鏄疧(log
n)涓紝涓や袱緇勫悎鐨勮瘽鍏辨湁O(logn*logn)縐嶆儏鍐點備簬鏄紝榪欐牱鐨勫閲忔帓搴忛渶瑕佽窇O((log
n)^2)瓚燂紝姣忎竴瓚熺殑澶嶆潅搴(n)錛屾葷殑澶嶆潅搴︿負O(n*(log n)^2)銆傛棭灝辮榪囦簡錛岃瘉鏄庢椂闂村鏉傚害鍏跺疄寰堟湁鎰忔濄?br> 鎴戜滑鑷劧
浼氭兂錛屾湁娌℃湁鑳戒嬌澶嶆潅搴﹂檷鍒癘(nlogn)鐢氳嚦鏇翠綆鐨勫閲忓簭鍒椼傚緢閬楁喚錛岀幇鍦ㄦ病鏈変換浣曡抗璞¤〃鏄庡瓨鍦∣(nlogn)鐨勫閲忔帓搴忋備絾浜嬪疄涓婏紝寰堝鏃跺?
Shell鎺掑簭鐨勫疄闄呮晥鐜囪秴榪囦簡O(nlogn)鐨勬帓搴忕畻娉曘?br>
鍚庨潰鎴戜滑灝嗕粙緇嶄笁縐峅(nlogn)鐨勬帓搴忕畻娉曞拰涓夌綰挎ф椂闂寸殑鎺?
搴忕畻娉曘傛渶鍚庢垜浠皢浠ュ閮ㄦ帓搴忓拰鎺掑簭緗戠粶緇撴潫榪欎竴绔犺妭銆?br>
寰堝浜洪棶鍒版垜鍏充簬杞創(chuàng)鐨勯棶棰樸傛垜嬈㈣繋闄ゅ晢涓氱洰鐨勫浠諱綍褰㈠紡鐨勮漿璐達紙璁哄潧銆?
Blog銆乄iki銆佷釜浜虹綉绔欍丳odCast錛岀敋鑷沖仛鎴恜pt銆乸df錛夛紝浣嗕竴瀹氳娉ㄦ槑鍑哄錛屾渶濂戒繚鐣欏師濮嬮摼鎺ャ傛垜鐨勭綉绔欓渶瑕佺偣鍙嶅悜閾炬帴鎵嶈兘鍦ㄧ綉緇滀腑鐢?
瀛樹笅鍘伙紝澶у涔熼兘鍙互鍏蟲敞騫朵笖鎺ㄥ箍榪欎釜Blog銆傛垜涓鐩存敮鎸乧c鐗堟潈鍗忚錛屽洜姝ゅ彂鐜頒簡鏂囩珷涓殑闂鎴栬呮兂瑕佽ˉ鍏呬粈涔堜笢瑗垮敖綆℃彁鍑烘潵錛屽ソ璁╂洿澶氱殑浜哄涔?fàn)鍒板?
涓滆タ銆傛垜鏄ㄥぉ鐪婤log涓婂師鏉ュ啓鐨勪竴浜涗笢瑗匡紝灞呯劧榪炵潃鍙戠幇浜嗗嚑涓敊璇紡瀛愬拰閿欏埆瀛楋紝濂藉澶у灞呯劧娌℃湁鎻愬嚭鏉ャ傚彂鐜頒簡闂鐪熺殑瑕佸憡璇夋垜錛屽嵆浣挎牸寮忔湁鐐歸棶棰樹篃
瑕佽涓涓嬶紝鍐充笉鑳借瀹冮偅涔堥敊鐫銆傚彟澶栨湁浠涔堝緩璁垨鎯蟲硶涔熻璇翠竴涓嬶紝鎴戝笇鏈涘惉鍒頒笉鍚岀殑澹伴煶涓嶅悓鐨勮瑙o紝濂借鎴戝喅瀹氳繖綾繪枃绔犱互鍚庣殑鍙戝睍鏂瑰悜銆?br>
Matrix67
鍘熷垱
杞創(chuàng)璇鋒敞鏄庡嚭澶?br>
浠庨浂寮濮嬪綆楁硶錛氬崄縐嶆帓搴忕畻娉曚粙緇嶏紙涓級
鏈枃琚崕涓界殑鍒嗗壊綰垮垎涓轟簡鍥涙銆傚
浜嶰(nlogn)鐨勬帓搴忕畻娉曪紝鎴戜滑璇︾粏浠嬬粛褰掑茍鎺掑簭騫惰瘉鏄庡綊騫舵帓搴忕殑鏃墮棿澶嶆潅搴︼紝鐒跺悗綆鍗曚粙緇嶅爢鎺掑簭錛屼箣鍚庣粰鍑哄揩閫熸帓搴忕殑鍩烘湰鎬濇兂鍜屽鏉傚害璇佹槑銆傛渶鍚庢垜
浠皢璇佹槑錛孫(nlogn)鍦ㄧ悊璁轟笂宸茬粡杈懼埌浜嗘渶浼樸傚榪嘜I鐨勪漢涓鑸兘瀛﹁繃榪欎簺寰堝熀紜鐨勪笢瑗匡紝澶у鏁癘Ier浠笉蹇呯湅浜嗐備負浜嗕繚鎸佺郴鍒楁枃绔犵殑瀹屾暣鎬э紝鎴?
榪樻槸鑺辨椂闂村啓浜嗕竴涓嬨?br>
棣栧厛鑰冭檻涓涓畝鍗曠殑闂錛氬浣曞湪綰挎х殑鏃墮棿鍐呭皢涓や釜鏈夊簭闃熷垪鍚堝茍涓轟竴涓湁搴忛槦鍒楋紙騫惰緭鍑猴級錛?br>
A
闃熷垪錛? 3 5 7 9
B闃熷垪錛? 2 7 8 9
鐪嬩笂闈㈢殑渚嬪瓙錛孉B涓や釜搴忓垪閮芥槸宸茬粡鏈夊簭鐨勪簡銆傚湪緇欏嚭鏁版嵁宸茬粡鏈夊簭鐨勬儏鍐典笅錛屾垜
浠細鍙戠幇寰堝紲炲鐨勪簨錛屾瘮濡傦紝鎴戜滑灝嗚杈撳嚭鐨勭涓涓暟涓瀹氭潵鑷簬榪欎袱涓簭鍒楀悇鑷渶鍓嶉潰鐨勯偅涓暟銆備袱涓暟閮芥槸1錛岄偅涔堟垜浠殢渚垮彇鍑轟竴涓紙姣斿A闃熷垪鐨勯偅涓?
1錛夊茍杈撳嚭錛?br>
A闃熷垪錛?s>1 3 5 7 9
B闃熷垪錛?
2 7 8 9
杈撳嚭錛?
娉ㄦ剰錛屾垜浠彇鍑轟簡涓涓暟錛屽湪鍘熸暟鍒椾腑鍒犻櫎榪欎釜鏁般傚垹闄ゆ搷浣滄槸閫氳繃縐誨姩闃熼鎸囬拡瀹?
鐜扮殑錛屽惁鍒欏鏉傚害灝遍珮浜嗐?br> 鐜板湪錛孉闃熷垪鎵撳ご鐨勬暟鍙樻垚3浜嗭紝B闃熷垪鐨勯槦棣栦粛鐒舵槸1銆傛鏃訛紝鎴戜滑鍐嶆瘮杈?鍜?鍝釜澶у茍杈撳嚭灝忕殑閭d釜鏁幫細
A闃熷垪錛?s>1 3
5 7 9
B闃熷垪錛?s>1 2 7 8 9
杈撳嚭錛? 1
鎺?
涓嬫潵鐨勫嚑姝ュ涓嬶細
A闃熷垪錛?s>1 3 5 7
9 A闃熷垪錛?s>1 3 5 7 9 A闃熷垪錛?s>1 3 5 7
9 A闃熷垪錛?s>1 3 5 7 9
B闃熷垪錛?s>1 2 7 8 9 ==> B闃熷垪錛?s>1
2 7 8 9 ==> B闃熷垪錛?s>1 2 7 8 9 ==> B闃熷垪錛?s>1 2 7
8 9 ……
杈撳嚭錛? 1 2 杈撳嚭錛? 1 2 3 杈撳嚭錛? 1 2 3
5 杈撳嚭錛? 1 2 3 5 7
鎴戝笇鏈涗綘鏄庣櫧浜嗚繖鏄庝箞鍋氱殑銆傝繖涓仛娉曟樉鐒舵槸姝g‘鐨勶紝澶嶆潅
搴︽樉鐒舵槸綰挎с?br>
褰掑茍鎺掑簭(Merge
Sort)灝嗕細鐢ㄥ埌涓婇潰鎵璇寸殑鍚堝茍鎿嶄綔銆傜粰鍑轟竴涓暟鍒楋紝褰掑茍鎺掑簭鍒╃敤鍚堝茍鎿嶄綔鍦∣(nlogn)鐨勬椂闂村唴灝嗘暟鍒椾粠灝忓埌澶ф帓搴忋傚綊騫舵帓搴忕敤鐨勬槸鍒嗘不
(Divide and
Conquer)鐨勬濇兂銆傞鍏堟垜浠妸緇欏嚭鐨勬暟鍒楀鉤鍒嗕負宸﹀彸涓ゆ錛岀劧鍚庡涓ゆ鏁板垪鍒嗗埆榪涜鎺掑簭錛屾渶鍚庣敤鍒氭墠鐨勫悎騫剁畻娉曟妸榪欎袱孌碉紙宸茬粡鎺掕繃搴忕殑錛夋暟鍒楀悎騫朵負涓
涓暟鍒椼傛湁浜轟細闂?#8220;瀵瑰乏鍙充袱孌墊暟鍒楀垎鍒帓搴忔椂鐢ㄧ殑浠涔堟帓搴?#8221;涔堬紵絳旀鏄細鐢ㄥ綊騫舵帓搴忋備篃灝辨槸璇達紝鎴戜滑閫掑綊鍦版妸姣忎竴孌墊暟鍒楀張鍒嗘垚涓ゆ榪涜涓婅堪鎿嶄綔銆備綘涓嶉渶瑕?
鍏沖績瀹為檯涓婃槸鎬庝箞鎿嶄綔鐨勶紝鎴戜滑鐨勭▼搴忎唬鐮佸皢閫掑綊璋冪敤璇ヨ繃紼嬬洿鍒版暟鍒椾笉鑳藉啀鍒嗭紙鍙湁涓涓暟錛変負姝€?br> 鍒濈湅榪欎釜綆楁硶鏃舵湁浜轟細璇互涓烘椂闂村鏉傚害鐩?
褰撻珮銆傛垜浠笅闈㈢粰鍑虹殑涓涓浘灝嗙敤闈為掑綊鐨勭溂鍏夋潵鐪嬪綊騫舵帓搴忕殑瀹為檯鎿嶄綔榪囩▼錛屼緵澶у鍙傝冦傛垜浠彲浠ュ熷姪榪欎釜鍥捐瘉鏄庯紝褰掑茍鎺掑簭綆楁硶鐨勬椂闂村鏉傚害涓?
O(nlogn)銆?br>
[3] [1] [4] [1] [5] [9]
[2] [7]
\ / \ / \ / \ /
[1 3] [1 4] [5 9] [2
7]
\ / \ /
[1 1 3 4] [2 5 7 9]
\ /
[1 1 2 3 4 5 7 9]
涓婂浘涓殑姣忎竴涓?#8220; \ /
”琛ㄧず鐨勬槸涓婃枃鎵榪扮殑綰挎ф椂闂村悎騫舵搷浣溿備笂鍥劇敤浜?琛屾潵鍥捐В褰掑茍鎺掑簭銆傚鏋滄湁n涓暟錛岃〃紺烘垚涓婂浘鏄劇劧闇瑕丱(logn)琛屻傛瘡涓琛岀殑鍚堝茍鎿嶄綔澶嶆潅搴︽誨拰閮?
鏄疧(n)錛岄偅涔坙ogn琛岀殑鎬誨鏉傚害涓篛(nlogn)銆傝繖鐩稿綋浜庣敤閫掑綊鏍?wèi)鐨勬栆?guī)硶瀵瑰綊騫舵帓搴忕殑澶嶆潅搴﹁繘琛屼簡鍒嗘瀽銆傚亣璁撅紝褰掑茍鎺掑簭鐨勫鏉傚害涓?
T(n)錛孴(n)鐢變袱涓猅(n/2)鍜屼竴涓叧浜巒鐨勭嚎鎬ф椂闂寸粍鎴愶紝閭d箞T(n)=2*T(n/2)+O(n)銆備笉鏂睍寮榪欎釜寮忓瓙鎴戜滑鍙互鍚屾牱鍙互寰楀埌
T(n)=O(nlogn)鐨勭粨璁猴紝浣犲彲浠ヨ嚜宸辮瘯璇曘傚鏋滀綘鑳藉湪綰挎х殑鏃墮棿閲屾妸鍒嗗埆璁$畻鍑虹殑涓ょ粍涓嶅悓鏁版嵁鐨勭粨鏋滃悎騫跺湪涓璧鳳紝鏍規(guī)嵁
T(n)=2*T(n/2)+O(n)=O(nlogn)錛岄偅涔堟垜浠氨鍙互鏋勯燨(nlogn)鐨勫垎娌葷畻娉曘傝繖涓粨璁哄悗闈㈢粡甯哥敤銆傛垜浠皢鍦ㄨ綆楀嚑浣曢儴鍒嗕婦
涓澶у爢綾諱技鐨勪緥瀛愩?br> 濡傛灉浣犵涓嬈¤鍒拌繖涔堣寮傜殑綆楁硶錛屼綘鍙兘浼氬 榪欎釜 鎰熷叴瓚c?
鍒嗘不鏄掑綊鐨勪竴縐嶅簲鐢ㄣ傝繖鏄垜浠涓嬈℃帴瑙﹂掑綊榪愮畻銆備笅闈㈣鐨勫揩閫熸帓搴忎篃鏄敤鐨勯掑綊鐨勬濇兂銆傞掑綊紼嬪簭鐨勫鏉傚害鍒嗘瀽閫氬父鍜屼笂闈竴鏍鳳紝涓誨畾鐞?Master
Theory)鍙互綆鍖栬繖涓垎鏋愯繃紼嬨備富瀹氱悊鍜屾湰鏂囧唴瀹圭寰楀お榪滐紝鎴戜滑浠ュ悗涔熶笉浼氱敤瀹冿紝鍥犳鎴戜滑涓嶄粙緇嶅畠錛屽ぇ瀹跺彲浠ヨ嚜宸卞幓鏌ャ傛湁涓悕璇嶅湪榪欓噷鐨勮瘽鎵懼涔?fàn)璧?
鏂欏皢鍙樺緱闈炲父瀹規(guī)槗錛屾垜鏈鎬曠殑灝辨槸涓涓笢瑗夸笉鐭ラ亾鍙粈涔堝悕瀛楋紝鍗婂ぉ鎵句笉鍒拌祫鏂欍?br>
褰掑茍鎺掑簭鏈変竴涓湁瓚g殑鍓駭鍝併傚埄鐢ㄥ綊騫舵帓搴忚兘澶熷湪
O(nlogn)鐨勬椂闂撮噷璁$畻鍑虹粰瀹氬簭鍒楅噷閫嗗簭瀵圭殑涓暟銆備綘鍙互鐢ㄤ換浣曚竴縐嶅鉤琛′簩鍙夋爲(wèi)鏉ュ畬鎴愯繖涓搷浣滐紝浣嗙敤褰掑茍鎺掑簭緇熻閫嗗簭瀵規(guī)洿鏂逛究銆傛垜浠璁洪嗗簭瀵逛竴鑸?
鏄鐨勪竴涓帓鍒椾腑鐨勯嗗簭瀵癸紝鍥犳榪欓噷鎴戜滑鍋囪鎵鏈夋暟涓嶇浉鍚屻傚亣濡傛垜浠兂瑕佹暟1, 6, 3, 2, 5,
4涓湁澶氬皯涓嗗簭瀵癸紝鎴戜滑棣栧厛鎶婅繖涓暟鍒楀垎涓哄乏鍙充袱孌點傞偅涔堜竴涓嗗簭瀵瑰彧鍙兘鏈変笁縐嶆儏鍐碉細涓や釜鏁伴兘鍦ㄥ乏杈癸紝涓や釜鏁伴兘鍦ㄥ彸杈癸紝涓涓湪宸︿竴涓湪鍙熾傚湪宸﹀彸涓ゆ
鍒嗗埆澶勭悊瀹屽悗錛岀嚎鎬у悎騫剁殑榪囩▼涓垜浠彲浠ラ『渚跨畻鍑烘墍鏈夌涓夌鎯呭喌鐨勯嗗簭瀵規(guī)湁澶氬皯涓傛崲鍙ヨ瘽璇達紝鎴戜滑鑳藉湪綰挎х殑鏃墮棿閲岀粺璁″嚭A闃熷垪鐨勬煇涓暟姣擝闃熷垪鐨勬煇涓暟
澶ф湁澶氬皯縐嶆儏鍐點?br>
A闃熷垪錛? 3 6 A闃熷垪錛?s>1
3 6 A闃熷垪錛?s>1 3 6 A闃熷垪錛?s>1 3 6 A闃熷垪錛?s>1 3
6
B闃熷垪錛? 4 5 ==> B闃熷垪錛? 4 5 ==> B闃熷垪錛?s>2 4 5
==> B闃熷垪錛?s>2 4 5 ==> B闃熷垪錛?s>2 4 5 ……
杈?
鍑猴細 杈撳嚭錛? 杈撳嚭錛? 2 杈撳嚭錛? 2
3 杈撳嚭錛? 2 3 4
姣忎竴嬈′粠B闃熷垪鍙栧嚭涓涓暟鏃訛紝鎴戜滑灝辯煡閬撲簡鍦ˋ闃熷垪涓湁澶氬皯涓暟姣擝
闃熷垪鐨勮繖涓暟澶э紝瀹冪瓑浜嶢闃熷垪鐜板湪榪樺墿鐨勬暟鐨勪釜鏁般傛瘮濡傦紝褰撴垜浠粠B闃熷垪涓彇鍑?鏃訛紝鎴戜滑鍚屾椂鐭ラ亾浜咥闃熷垪鐨?鍜?涓や釜鏁版瘮2澶с傚湪鍚堝茍鎿嶄綔涓垜浠笉鏂洿
鏂癆闃熷垪涓繕鍓╁嚑涓暟錛屽湪姣忔浠嶣闃熷垪涓彇鍑轟竴涓暟鏃舵妸褰撳墠A闃熷垪鍓╃殑鏁扮洰鍔犺繘鏈緇堢瓟妗堥噷銆傝繖鏍鋒垜浠畻鍑轟簡鎵鏈?#8220;澶х殑鏁板湪鍓嶄竴鍗婏紝灝忕殑鏁板湪鍚庝竴鍗?#8221;鐨勬儏
鍐碉紝鍏朵綑鎯呭喌涓嬬殑閫嗗簭瀵瑰湪榪欎箣鍓嶅凡緇忚閫掑綊鍦扮畻榪囦簡銆?br>
============================鍗庝附鐨勫垎鍓?
綰?===========================
鍫嗘帓搴?Heap Sort)鍒╃敤浜嗗爢(Heap)榪欑鏁版嵁緇撴瀯錛?a target="_blank"> 浠涔堟槸鍫嗭紵 錛夈?
鍫嗙殑鎻掑叆鎿嶄綔鏄鉤鍧囧父鏁扮殑錛岃屽垹闄や竴涓牴鑺傜偣闇瑕佽姳璐筄(log
n)鐨勬椂闂淬傚洜姝わ紝瀹屾垚鍫嗘帓搴忛渶瑕佺嚎鎬ф椂闂村緩绔嬪爢錛堟妸鎵鏈夊厓绱犱緷嬈℃彃鍏ヤ竴涓爢錛夛紝鐒跺悗鐢ㄦ誨叡O(jiān)(nlogn)鐨勬椂闂翠笉鏂彇鍑烘渶灝忕殑閭d釜鏁般傚彧瑕佸爢浼氭悶錛屽爢
鎺掑簭灝變細鎼炪傚爢鍦ㄩ偅綃囨棩蹇楅噷鏈夎緇嗙殑璇存槑錛屽洜姝よ繖閲屼笉閲嶅璇翠簡銆?br>
============================鍗庝附鐨勫垎鍓?
綰?===========================
蹇熸帓搴?Quick
Sort)涔熷簲鐢ㄤ簡閫掑綊鐨勬濇兂銆傛垜浠兂瑕佹妸緇欏畾搴忓垪鍒嗘垚涓ゆ錛屽茍瀵硅繖涓ゆ鍒嗗埆榪涜鎺掑簭銆備竴縐嶄笉閿欑殑鎯蟲硶鏄紝閫夊彇涓涓暟浣滀負“鍏抽敭瀛?#8221;錛屽茍鎶婂叾瀹冩暟鍒嗗壊涓轟袱
閮ㄥ垎錛屾妸鎵鏈夊皬浜庡叧閿瓧鐨勬暟閮芥斁鍦ㄥ叧閿瓧鐨勫乏杈癸紝澶т簬鍏抽敭瀛楃殑閮芥斁鍦ㄥ彸杈癸紝鐒跺悗閫掑綊鍦板宸﹁竟鍜屽彸杈硅繘琛屾帓搴忋傛妸璇ュ尯闂村唴鐨勬墍鏈夋暟渚濇涓庡叧閿瓧姣旇緝錛屾垜浠氨
鍙互鍦ㄧ嚎鎬х殑鏃墮棿閲屽畬鎴愬垎鍓茬殑鎿嶄綔銆傚畬鎴愬垎鍓叉搷浣滄湁寰堝鏈夋妧宸фх殑瀹炵幇鏂規(guī)硶錛屾瘮濡傛渶甯哥敤鐨勪竴縐嶆槸瀹氫箟涓や釜鎸囬拡錛屼竴涓粠鍓嶅線鍚庢壘鎵懼埌姣斿叧閿瓧澶х殑錛屼竴涓粠鍚?
寰鍓嶆壘鍒版瘮鍏抽敭瀛楀皬鐨勶紝鐒跺悗涓や釜鎸囬拡瀵瑰簲鐨勫厓绱犱氦鎹綅緗茍緇х畫縐誨姩鎸囬拡閲嶅鍒氭墠鐨勮繃紼嬨傝繖鍙槸澶ц嚧鐨勬柟娉曪紝鍏蜂綋鐨勫疄鐜拌繕鏈夊緢澶氱粏鑺傞棶棰樸傚揩閫熸帓搴忔槸鎴戜滑鏈
甯哥敤鐨勪唬鐮佷箣涓錛岀綉涓婄殑蹇熸帓搴忎唬鐮佷簲鑺卞叓闂紝鍚勭璇█錛屽悇縐嶉鏍肩殑閮芥湁銆傚ぇ瀹跺彲浠ラ殢渚挎壘涓涓潵鐪嬬湅錛屾垜璇磋繃浜嗘垜浠綆楁硶浣嗕笉璁插浣曞疄鐜般侼OIp寰堢畝
鍗曪紝寰堝浜篘OIp鍓嶅氨鑳屼簡涓涓揩閫熸帓搴忎唬鐮佸氨涓婃垬鍦轟簡銆傚綋鏃舵垜鎶婂揩閫熸帓搴忚儗瀹屼簡錛屾姄绱ф椂闂磋繕欏轟究鑳屼簡涓涓嬪巻鍙詫紝鍏嶅緱鏅氫笂鍚啓鍙堜笉鍙婃牸銆?br> 涓?
鍍忓綊騫舵帓搴忥紝蹇熸帓搴忕殑鏃墮棿澶嶆潅搴﹀緢闅捐綆椼傛垜浠彲浠ョ湅鍒幫紝褰掑茍鎺掑簭鐨勫鏉傚害鏈鍧忔儏鍐典笅涔熸槸O(nlogn)鐨勶紝鑰屽揩閫熸帓搴忕殑鏈鍧忔儏鍐墊槸O(n^2)鐨勩?
濡傛灉姣忎竴嬈¢夌殑鍏抽敭瀛楅兘鏄綋鍓嶅尯闂撮噷鏈澶э紙鎴栨渶灝忥級鐨勬暟錛岄偅涔堣繖鏍峰皢浣垮緱姣忎竴嬈$殑瑙勬ā鍙噺灝忎竴涓暟錛岃繖鍜屾彃鍏ユ帓搴忋侀夋嫨鎺掑簭絳夊鉤鏂圭駭鎺掑簭娌℃湁鍖哄埆銆傝繖縐嶆儏
鍐典笉鏄笉鍙兘鍙戠敓銆傚鏋滀綘姣忔閫夋嫨鍏抽敭瀛楅兘鏄夋嫨鐨勮鍖洪棿鐨勭涓涓暟錛岃岀粰浣犵殑鏁版嵁鎭板ソ鍙堟槸宸茬粡鏈夊簭鐨勶紝閭d綘鐨勫揩閫熸帓搴忓氨瀹岃泲浜嗐傛樉鐒訛紝鏈濂芥儏鍐墊槸姣忎竴嬈?
閫夌殑鏁版濂藉氨鏄腑浣嶆暟錛岃繖灝嗘妸璇ュ尯闂村鉤鍒嗕負涓ゆ錛屽鏉傚害鍜屽墠闈㈣璁虹殑褰掑茍鎺掑簭涓妯′竴鏍楓傛牴鎹繖涓鐐癸紝蹇熸帓搴忔湁涓浜涘父鐢ㄧ殑浼樺寲銆傛瘮濡傦紝鎴戜滑緇忓父浠庢暟鍒椾腑闅?
鏈哄彇涓涓暟褰撲綔鏄叧閿瓧錛堣屼笉鏄瘡嬈℃繪槸鍙栧浐瀹氫綅緗笂鐨勬暟錛夛紝浠庤屽敖鍙兘閬垮厤鏌愪簺鐗規(guī)畩鐨勬暟鎹墍瀵艱嚧鐨勪綆鏁堛傛洿濂界殑鍋氭硶鏄殢鏈哄彇涓変釜鏁板茍閫夋嫨榪欎笁涓暟鐨勪腑浣?
鏁頒綔涓哄叧閿瓧銆傝屽涓変釜鏁扮殑闅忔満鍙栧煎弽鑰屽皢鑺辮垂鏇村鐨勬椂闂達紝鍥犳鎴戜滑鐨勮繖涓変釜鏁板彲浠ュ垎鍒彇鏁板垪鐨勫ご涓涓暟銆佹湯涓涓暟鍜屾涓棿閭d釜鏁般傚彟澶栵紝褰撻掑綊鍒頒簡涓瀹?
娣卞害鍙戠幇褰撳墠鍖洪棿閲岀殑鏁板彧鏈夊嚑涓垨鍗佸嚑涓椂錛岀戶緇掑綊涓嬪幓鍙嶈岃垂鏃訛紝涓嶅榪斿洖鎻掑叆鎺掑簭鍚庣殑緇撴灉銆傝繖縐嶆柟娉曞悓鏃墮伩鍏嶄簡褰撴暟瀛楀お灝戞椂閫掑綊鎿嶄綔鍑洪敊鐨勫彲鑳姐?br>
涓?
闈㈡垜浠瘉鏄庯紝蹇熸帓搴忕畻娉曠殑騫沖潎澶嶆潅搴︿負O(nlogn)銆備笉鍚岀殑涔︿笂鏈変笉鍚岀殑瑙i噴鏂規(guī)硶錛岃繖閲屾垜閫夌敤綆楁硶瀵艱涓婄殑璁叉硶銆傚畠鏇存湁鎶宸фт竴浜涳紝鏇存湁瓚d竴浜涳紝闇
瑕佽漿鍑犱釜寮墠鑳芥兂鏄庣櫧銆?br> 鐪嬩竴鐪嬪揩閫熸帓搴忕殑浠g爜銆傛濡傛垜浠彁鍒拌繃鐨勯偅縐嶅垎鍓叉柟娉曪紝紼嬪簭鍦ㄧ粡榪囪嫢騫叉涓庡叧閿瓧鐨勬瘮杈冨悗鎵嶈繘琛屼竴嬈′氦鎹紝鍥犳姣?
杈冪殑嬈℃暟姣斾氦鎹㈡鏁版洿澶氥傛垜浠氳繃璇佹槑涓嬈″揩閫熸帓搴忎腑鍏冪礌涔嬮棿鐨勬瘮杈冩鏁板鉤鍧囦負O(nlogn)鏉ヨ鏄庡揩閫熸帓搴忕畻娉曠殑騫沖潎澶嶆潅搴︺傝瘉鏄庣殑鍏抽敭鍦ㄤ簬錛屾垜浠渶
瑕佺畻鍑烘煇涓や釜鍏冪礌鍦ㄦ暣涓畻娉曡繃紼嬩腑榪涜榪囨瘮杈冪殑姒傜巼銆?br> 鎴戜滑涓句竴涓緥瀛愩傚亣濡傜粰鍑轟簡1鍒?0榪?0涓暟錛岀涓嬈¢夋嫨鍏抽敭瀛?灝嗗畠浠垎鎴愪簡
{1,2,3,4,5,6}鍜寋8,9,10}涓ら儴鍒嗭紝閫掑綊宸﹁竟鏃舵垜浠夋嫨浜?浣滀負鍏抽敭瀛楋紝浣垮緱宸﹂儴鍒嗗張琚垎鍓蹭負{1,2}鍜寋4,5,6}銆傛垜浠湅鍒幫紝
鏁板瓧7涓庡叾瀹冩墍鏈夋暟閮芥瘮杈冭繃涓嬈★紝榪欐牱鎵嶈兘瀹炵幇鍒嗗壊鎿嶄綔銆傚悓鏍峰湴錛?鍒?榪?涓暟閮介渶瑕佷笌3榪涜涓嬈℃瘮杈冿紙闄や簡瀹冩湰韜箣澶栵級銆傜劧鑰岋紝3鍜?鍐充笉鍙兘鐩鎬簰姣?
杈冭繃錛?鍜?涔熶笉鍙兘榪涜榪囨瘮杈冿紝鍥犱負絎竴嬈″嚭鐜板湪3鍜?錛?鍜?涔嬮棿鐨勫叧閿瓧鎶婂畠浠垎鍓插紑浜嗐備篃灝辨槸璇達紝涓や釜鏁癆(i)鍜孉(j)姣旇緝榪囷紝褰撲笖浠呭綋絎竴
涓弧瓚矨(i)<=x<=A(j)鐨勫叧閿瓧x鎭板ソ灝辨槸A(i)鎴朅(j)
錛堝亣璁続(i)姣擜(j)灝忥級銆傛垜浠О鎺掑簭鍚庣i灝忕殑鏁頒負Z(i)錛屽亣璁緄<j錛岄偅涔堢涓嬈″嚭鐜板湪Z(i)鍜孼(j)涔嬮棿鐨勫叧閿瓧鎭板ソ灝辨槸Z(i)
鎴朲(j)鐨勬鐜囦負2/(j-i+1)錛岃繖鏄洜涓哄綋Z(i)鍜孼(j)涔嬮棿榪樹笉鏇炬湁榪囧叧閿瓧鏃訛紝Z(i)鍜孼(j)澶勪簬鍚屼竴涓緟鍒嗗壊鐨勫尯闂達紝涓嶇榪欎釜鍖洪棿
鏈夊澶э紝涓嶇閫掑綊鍒板摢閲屼簡錛屽叧閿瓧鐨勯夋嫨鎬繪槸闅忔満鐨勩傛垜浠緱鍒幫紝Z(i)鍜孼(j)鍦ㄤ竴嬈″揩閫熸帓搴忎腑鏇劇粡姣旇緝榪囩殑姒傜巼涓?/(j-i+1)銆?br> 鐜?
鍦ㄦ湁鍥涗釜鏁幫紝2,3,5,7銆傛帓搴忔椂錛岀浉閭?cè)潥勪袱涓暟鑲畾閮借姣旇緝杩囧Q?鍜?銆?鍜?閮芥湁2/3鐨勬鐜囪姣旇緝榪囷紝2鍜?涔嬮棿琚瘮杈冭繃鏈?/4鐨勫彲鑳姐備篃灝辨槸
璇達紝濡傛灉瀵硅繖鍥涗釜鏁板仛12嬈″揩閫熸帓搴忥紝閭d箞2鍜?銆?鍜?銆?鍜?涔嬮棿涓鍏辨瘮杈冧簡12*3=36嬈★紝2鍜?銆?鍜?涔嬮棿鎬誨叡姣旇緝浜?*2=16嬈★紝2鍜?
涔嬮棿騫沖潎姣旇緝浜?嬈°傞偅涔堬紝12嬈℃帓搴忎腑鎬葷殑姣旇緝嬈℃暟鏈熸湜鍊間負36+16+6=58銆傛垜浠彲浠ヨ綆楀嚭鍗曟鐨勫揩閫熸帓搴忓鉤鍧囨瘮杈冧簡澶氬皯嬈★細58/12=29
/6銆傚叾瀹烇紝瀹冨氨絳変簬6欏規(guī)鐜囦箣鍜岋紝1+1+1+2/3+2/3+2/4=29/6銆傝繖鍏跺疄鏄笌鏈熸湜鍊肩浉鍏崇殑涓涓叕寮忋?br> 鍚屾牱鍦幫紝濡傛灉鏈塶
涓暟錛岄偅涔堝揩閫熸帓搴忓鉤鍧囬渶瑕佺殑姣旇緝嬈℃暟鍙互鍐欐垚涓嬮潰鐨勫紡瀛愩備護k=j-i錛屾垜浠兘澶熸渶緇堝緱鍒版瘮杈冩鏁扮殑鏈熸湜鍊間負O(nlogn)銆?br> 
榪?
閲岀敤鍒頒簡涓涓煡璇嗭細1+1/2+1/3+…+1/n涓巐og n澧為暱閫熷害鐩稿悓錛屽嵆Σ(1/n)=Θ(log n)銆傚畠鐨勮瘉鏄庢斁鍦ㄦ湰鏂囩殑鏈鍚庛?br>
鍦?
涓夌O(nlogn)鐨勬帓搴忕畻娉曚腑錛屽揩閫熸帓搴忕殑鐞嗚澶嶆潅搴︽渶涓嶇悊鎯籌紝闄や簡瀹冧互澶栦粖澶╄鐨勫彟澶栦袱縐嶇畻娉曢兘鏄互鏈鍧忔儏鍐礝(nlogn)鐨勫鏉傚害榪涜鎺掑簭銆備絾
瀹炶返涓婄湅蹇熸帓搴忔晥鐜囨渶楂橈紙涓嶇劧涓哄暐鍙揩閫熸帓搴忓憿錛夛紝鍘熷洜鍦ㄤ簬蹇熸帓搴忕殑浠g爜姣斿叾瀹冨悓澶嶆潅搴︾殑綆楁硶鏇寸畝媧侊紝甯告暟鏃墮棿鏇村皬銆?br>
蹇熸帓
搴忎篃鏈変竴涓湁瓚g殑鍓駭鍝侊細蹇熼夋嫨緇欏嚭鐨勪竴浜涙暟涓k灝忕殑鏁般備竴縐嶇畝鍗曠殑鏂規(guī)硶鏄嬌鐢ㄤ笂榪頒換涓縐峅(nlogn)鐨勭畻娉曞榪欎簺鏁拌繘琛屾帓搴忓茍榪斿洖鎺掑簭鍚庢暟緇勭殑
絎琸涓厓绱犮傚揩閫熼夋嫨(Quick
Select)綆楁硶鍙互鍦ㄥ鉤鍧嘜(n)鐨勬椂闂村畬鎴愯繖涓鎿嶄綔銆傚畠鐨勬渶鍧忔儏鍐靛悓蹇熸帓搴忎竴鏍鳳紝涔熸槸O(n^2)銆傚湪姣忎竴嬈″垎鍓插悗錛屾垜浠兘鍙互鐭ラ亾姣斿叧閿瓧灝忕殑
鏁版湁澶氬皯涓紝浠庤岀‘瀹氫簡鍏抽敭瀛楀湪鎵鏈夋暟涓槸絎嚑灝忕殑銆傛垜浠亣璁懼叧閿瓧鏄m灝忋傚鏋渒=m錛岄偅涔堟垜浠氨鎵懼埌浜嗙瓟妗堚斺旂k灝忓厓绱犲嵆璇ュ叧閿瓧銆傚惁鍒欙紝鎴戜滑閫?
褰掑湴璁$畻宸﹁竟鎴栬呭彸杈癸細褰搆<m鏃訛紝鎴戜滑閫掑綊鍦板鎵懼乏杈圭殑鍏冪礌涓k灝忕殑錛涘綋k>m鏃訛紝鎴戜滑閫掑綊鍦板鎵懼彸杈圭殑鍏冪礌涓k-m灝忕殑鏁般傜敱浜庢垜浠?
涓嶈冭檻鎵鏈夌殑鏁扮殑欏哄簭錛屽彧闇瑕侀掑綊鍏朵腑鐨勪竴杈癸紝鍥犳澶嶆潅搴﹀ぇ澶ч檷浣庛傚鏉傚害騫沖潎綰挎э紝鎴戜滑涓嶅啀鍏蜂綋璇佷簡銆?br> 榪樻湁涓縐嶇畻娉曞彲浠ュ湪鏈鍧廜(n)
鐨勬椂闂撮噷鎵懼嚭絎琸灝忓厓绱犮傞偅鏄垜瑙佽繃鐨勬墍鏈夌畻娉曚腑鏈娌℃湁瀹炵敤浠峰肩殑綆楁硶銆傞偅涓狾(n)鍙湁鐞嗚浠峰箋?br>
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鍗庝附鐨勫垎鍓茬嚎============================
鎴戜滑鍓嶉潰璇佹槑榪囷紝浠呬粎渚濋潬浜ゆ崲鐩擱偦鍏冪礌鐨勬搷浣滐紝澶嶆潅搴﹀彧
鑳借揪鍒癘(n^2)銆備簬鏄紝浜轟滑灝濊瘯浜ゆ崲璺濈鏇磋繙鐨勫厓绱犮傚綋浜轟滑鍙戠幇O(nlogn)鐨勬帓搴忕畻娉曚技涔庡凡緇忔槸鏋侀檺鐨勬椂鍊欙紝鍙堟槸浠涔堝埗綰︿簡澶嶆潅搴︾殑涓嬬晫鍛紵鎴?
浠皢瑕佽璁虹殑鏄洿搴曞眰鐨勪笢瑗褲傛垜浠粛鐒跺亣璁炬墍鏈夌殑鏁伴兘涓嶇浉絳夈?br> 鎴戜滑鎬繪槸涓嶆柇鍦ㄦ暟涓庢暟涔嬮棿榪涜姣旇緝銆備綘鍙互璇曡瘯錛屽彧鐢?嬈℃瘮杈冪粷瀵逛笉鍙兘緇?
4涓暟鎺掑嚭欏哄簭銆傛瘡澶氳繘琛屼竴嬈℃瘮杈冩垜浠氨鍙堝鐭ラ亾浜嗕竴涓ぇ灝忓叧緋伙紝浠?嬈℃瘮杈冧腑涓鍏卞彲浠ヨ幏鐭?涓ぇ灝忓叧緋匯?涓ぇ灝忓叧緋誨叡鏈?^4=16縐嶇粍鍚堟柟寮忥紝鑰?
涓暟鐨勯『搴忎竴鍏辨湁4!=24縐嶃備篃灝辨槸璇達紝4嬈℃瘮杈冨彲鑳藉嚭鐜扮殑緇撴灉鏁扮洰涓嶈凍浠ュ尯鍒?4縐嶅彲鑳界殑欏哄簭銆傛洿涓鑸湴錛岀粰浣爊涓暟鍙綘鎺掑簭錛屽彲鑳界殑絳旀鍏辨湁n!
涓紝k嬈℃瘮杈冨彧鑳藉尯鍒?^k縐嶅彲鑳斤紝浜庢槸鍙湁2^k>=n!鏃舵墠鏈夊彲鑳芥帓鍑洪『搴忋傜瓑鍙蜂袱杈瑰彇瀵規(guī)暟錛屼簬鏄紝緇檔涓暟鎺掑簭鑷沖皯闇瑕乴og2(n!)嬈°?
娉ㄦ剰錛屾垜浠茍娌℃湁璇存槑涓瀹氳兘閫氳繃log2(n!)嬈℃瘮杈冩帓鍑洪『搴忋傝櫧鐒?^5=32瓚呰繃浜?!錛屼絾榪欎笉瓚充互璇存槑5嬈℃瘮杈冧竴瀹氳凍澶熴傚浣曠敤5嬈℃瘮杈冪‘瀹?涓?
鏁扮殑澶у皬鍏崇郴榪橀渶瑕佽繘涓姝ョ爺絀躲傜涓嬈′緥澶栧彂鐢熷湪n=12鐨勬椂鍊欙紝铏界劧2^29>12!錛屼絾鐜板凡璇佹槑緇?2涓暟鎺掑簭鏈灝戦渶瑕?0嬈℃瘮杈冦傛垜浠彲浠ヨ瘉
鏄巐og(n!)鐨勫闀塊熷害涓巒logn鐩稿悓錛屽嵆log(n!)=Θ(nlogn)銆傝繖鏄帓搴忔墍闇瑕佺殑鏈灝戠殑姣旇緝嬈℃暟錛屽畠緇欏嚭浜嗘帓搴忓鏉傚害鐨勪竴涓笅鐣屻?
log(n!)=Θ(nlogn)鐨勮瘉鏄庝篃闄勫湪鏈枃鏈鍚庛?br> 榪欑瘒鏃ュ織 鐨勭
涓夐涓瘉鏄巐og2(N)鏄渶浼樻椂鐢ㄥ埌浜嗗嚑涔庣浉鍚岀殑鏂規(guī)硶銆傞偅縐?#8220;鐢ㄥぉ騫崇О鍑洪噸閲忎笉鍚岀殑閭d釜鐞冭嚦灝戣縐板嚑嬈?#8221;涓綾婚鐩篃鍙互鐢ㄨ繖縐嶆柟娉曟潵瑙e喅銆備簨瀹炰笂錛岃繖閲?
鏈変竴鏁村鐨勭悊璁猴紝瀹冨彨鍋氫俊鎭銆備俊鎭鏄敱棣欏啘(Shannon)鎻愬嚭鐨勩備粬鐢ㄥ鏁版潵琛ㄧず淇℃伅閲忥紝鐢ㄧ喌鏉ヨ〃紺哄彲鑳界殑鎯呭喌鐨勯殢鏈烘э紝閫氳繃榪愮畻鍙互鐭ラ亾浣犵洰鍓?
寰楀埌鐨勪俊鎭兘澶熸庢牱褰卞搷鏈緇堢粨鏋滅殑紜畾銆傚鏋滄垜浠殑淇℃伅閲忔槸浠?涓哄簳鐨勶紝閭d俊鎭灝卞彉鎴愪俊鎭浜嗐備粠鏍規(guī)湰涓婅錛岃綆楁満鐨勪竴鍒囦俊鎭氨鏄互2涓哄簳鐨勪俊鎭噺
(bits=binary digits)錛屽洜姝ゆ垜浠父璇撮鍐滄槸鏁板瓧閫氫俊涔嬬埗銆備俊鎭鍜岀儹鍔涘鍏崇郴瀵嗗垏錛屾瘮濡傜喌鐨勬蹇墊槸鐩存帴
浠庣儹鍔涘鐨勭喌瀹氫箟寮曠敵榪囨潵鐨勩傚拰榪欎釜鏈夊叧鐨勪笢瑗垮凡緇忎弗閲嶅亸棰樹簡錛岃繖閲屼笉璇翠簡錛屾湁鍏磋叮鍙互鍘葷湅銆婁俊鎭涓庣紪鐮佺悊璁恒嬨傛垜瀵硅繖涓篃寰堟湁鍏磋叮錛屽崐鎳備笉鎳傜殑錛屽緢鎯?
浜嗚В鏇村鐨勪笢瑗匡紝鏈夊叴瓚g殑鍚屽織涓嶅Θ鍔犲叆璁ㄨ銆傜墿鐞嗗鐪熺殑寰堢濂囷紝鍒╃敤鐗╃悊瀛﹀彲浠ヨВ鍐沖緢澶氱函鏁板闂錛屾垜鏈夋椂闂寸殑璇濆彲浠ヤ婦涓浜涗緥瀛愩傛垜浠栧鐨勪負鍟ヨ閫夋枃縐?
鍛€?br> 鍚庨潰灝嗕粙緇嶇殑涓夌鎺掑簭鏄嚎鎬ф椂闂村鏉傚害錛屽洜涓猴紝瀹冧滑鎺掑簭鏃舵牴鏈笉鏄氳繃浜掔浉姣旇緝鏉ョ‘瀹氬ぇ灝忓叧緋葷殑銆?br>
闄?
1錛?#931;(1/n)=Θ(log n)鐨勮瘉鏄?br> 棣栧厛鎴戜滑璇佹槑錛?#931;(1/n)=O(log
n)銆傚湪寮忓瓙1+1/2+1/3+1/4+1/5+…涓紝鎴戜滑鎶?/3鍙樻垚1/2錛屼嬌寰椾袱涓?/2鍔犺搗鏉ュ噾鎴愪竴涓?錛涘啀鎶?/5,1/6鍜?/7鍏ㄩ儴鍙樻垚
1/4錛岃繖鏍峰洓涓?/4鍔犺搗鏉ュ張鏄竴涓?銆傛垜浠妸鎵鏈?/2^k鐨勫悗闈?^k-1欏瑰叏閮ㄦ墿澶т負1/2^k錛屼嬌寰楄繖2^k涓垎寮忓姞璧鋒潵鏄竴涓?銆傜幇
鍦紝1+1/2+…+1/n閲岄潰浜х敓浜嗗嚑涓?鍛紵鎴戜滑鍙渶瑕佺湅灝忎簬n鐨勬暟鏈夊灝戜釜2鐨勫箓鍗沖彲銆傛樉鐒訛紝緇忚繃鏁扮殑鎵╁ぇ鍚庡師寮忓悇欏規(guī)誨拰涓簂og
n銆侽(logn)鏄?#931;(1/n)鐨勫鏉傚害涓婄晫銆?br> 鐒跺悗鎴戜滑璇佹槑錛?#931;(1/n)=Ω(log
n)銆傚湪寮忓瓙1+1/2+1/3+1/4+1/5+…涓紝鎴戜滑鎶?/3鍙樻垚1/4錛屼嬌寰椾袱涓?/4鍔犺搗鏉ュ噾鎴愪竴涓?/2錛涘啀鎶?/5,1/6鍜?/7鍏ㄩ儴
鍙樻垚1/8錛岃繖鏍峰洓涓?/8鍔犺搗鏉ュ張鏄竴涓?/2銆傛垜浠妸鎵鏈?/2^k鐨勫墠闈?^k-1欏瑰叏閮ㄧ緝?yōu)畯湄?/2^k錛屼嬌寰楄繖2^k涓垎寮忓姞璧鋒潵鏄竴涓?
/2銆傜幇鍦紝1+1/2+…+1/n閲岄潰浜х敓浜嗗嚑涓?/2鍛紵鎴戜滑鍙渶瑕佺湅灝忎簬n鐨勬暟鏈夊灝戜釜2鐨勫箓鍗沖彲銆傛樉鐒訛紝緇忚繃鏁扮殑緙╁皬鍚庡師寮忓悇欏規(guī)誨拰涓?
/2*logn銆?#937;(logn)鏄?#931;(1/n)鐨勫鏉傚害涓嬬晫銆?br>
闄?錛歭og(n!)=Θ(nlogn)鐨勮瘉鏄?br> 棣?
鍏堟垜浠瘉鏄庯紝log(n!)=O(nlogn)銆傛樉鐒秐!<n^n錛屼袱杈瑰彇瀵規(guī)暟鎴戜滑寰楀埌l(fā)og(n!)<log(n^n)錛岃?
log(n^n)灝辯瓑浜巒logn銆傚洜姝わ紝O(nlogn)鏄痩og(n!)鐨勫鏉傚害涓婄晫銆?br> 鐒跺悗鎴戜滑璇?
鏄庯紝log(n!)=Ω(nlogn)銆俷!=n(n-1)(n-2)(n-3)….1錛屾妸鍓嶉潰涓鍗婄殑鍥犲瓙鍏ㄩ儴緙╁皬鍒皀/2錛屽悗闈竴鍗婂洜瀛愬叏閮ㄨ垗鍘伙紝鏄劇劧
鏈塶!>(n/2)^(n/2)銆備袱杈瑰彇瀵規(guī)暟錛宭og(n!)>(n/2)log(n/2)錛屽悗鑰呭嵆Ω(nlogn)銆傚洜
姝わ紝Ω(nlogn)鏄痩og(n!)鐨勫鏉傚害涓嬬晫銆?br>
浠婂ぉ鍐欏埌榪欓噷浜嗭紝澶у甯繖鏍″鍝?br>Matrix67鍘熷垱
杞創(chuàng)璇鋒敞鏄庡嚭
澶?br>浠庨浂寮濮嬪綆楁硶錛氬崄縐嶆帓搴忕畻娉曚粙緇嶏紙涓嬶級
閭d箞錛屾湁浠涔堟柟娉曞彲浠ヤ笉鐢ㄦ瘮杈冨氨鑳芥帓
鍑洪『搴忓憿錛熷熷姪Hash琛ㄧ殑鎬濇兂錛屽鏁頒漢閮借兘鎯沖嚭榪欐牱涓縐嶆帓搴忕畻娉曟潵銆?br> 鎴戜滑鍋囪緇欏嚭鐨勬暟瀛楅兘鍦ㄤ竴瀹氳寖鍥翠腑錛岄偅涔堟垜浠氨鍙互寮涓涓寖鍥寸浉鍚?
鐨勬暟緇勶紝璁板綍榪欎釜鏁板瓧鏄惁鍑虹幇榪囥傜敱浜庢暟瀛楁湁鍙兘鏈夐噸澶嶏紝鍥犳Hash琛ㄧ殑姒傚康闇瑕佹墿灞曪紝鎴戜滑闇瑕佹妸鏁扮粍綾誨瀷鏀規(guī)垚鏁村瀷錛岀敤鏉ヨ〃紺烘瘡涓暟鍑虹幇鐨勬鏁般?br> 鐪?
榪欐牱涓涓緥瀛愶紝鍋囧鎴戜滑瑕佸鏁板垪3 1 4 1 5 9 2 6 5 3 5
9榪涜鎺掑簭銆傜敱浜庣粰瀹氭暟瀛楁瘡涓涓兘灝忎簬10錛屽洜姝ゆ垜浠紑涓涓?鍒?鐨勬暣鍨嬫暟緇凾[i]錛岃褰曟瘡涓涓暟鍑虹幇浜嗗嚑嬈°傝鍒頒竴涓暟瀛梮錛屽氨鎶婂搴旂殑T[x]鍔?
涓銆?br>
A[]= 3, 1, 4, 1, 5, 9, 2, 6,
5, 3, 5, 9
+---+---+---+---+---+---+---+---+---+---+
鏁?
瀛?i錛?| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+---+---+---+---+---+---+---+---+---+---+
鍑虹幇嬈℃暟T[i]錛?| 0 | 2 | 1 | 2 |
1 | 3 | 1 | 0 | 0 | 2 |
+---+---+---+---+---+---+---+---+---+---+
鏈鍚庯紝鎴戜滑鐢ㄤ竴涓寚閽堜粠鍓?
寰鍚庢壂鎻忎竴閬嶏紝鎸夌収嬈″簭杈撳嚭0鍒?錛屾瘡涓暟鍑虹幇浜嗗嚑嬈″氨杈撳嚭鍑犱釜銆傚亣濡傜粰瀹氱殑鏁版槸n涓ぇ灝忎笉瓚呰繃m鐨勮嚜鐒舵暟錛屾樉鐒惰繖涓畻娉曠殑澶嶆潅搴︽槸O(m+n)鐨勩?br>
鎴?
鏇劇粡浠ヤ負錛岃繖灝辨槸綰挎ф椂闂存帓搴忎簡銆傚悗鏉ユ垜鍙戠幇鎴戦敊浜嗐傚啀鍚庢潵錛屾垜鍙戠幇鎴戞浘鐘殑閿欒鏄竴涓櫘閬嶇殑閿欒銆傚緢澶氫漢閮戒互涓轟笂闈㈢殑榪欎釜綆楁硶灝辨槸浼犺涓殑璁℃暟鎺掑簭銆傞棶
棰樺嚭鍦ㄥ摢閲屼簡錛熶負浠涔堝畠涓嶆槸綰挎ф椂闂寸殑鎺掑簭綆楁硶錛熷師鍥犳槸錛岃繖涓畻娉曟牴鏈笉鏄帓搴忕畻娉曪紝瀹冩牴鏈病鏈夊鍘熸暟鎹繘琛屾帓搴忋?br>
闂?
棰樹竴錛氫負浠涔堣涓婅堪綆楁硶娌℃湁瀵規(guī)暟鎹繘琛屾帓搴忥紵
STOP! You
should think for a while.
鎴戜滑鐝湁寰堝MM銆傚拰韜珮鐩稿樊澶繙鐨凪M鍦ㄤ竴璧瘋偗瀹氬緢鍒壄錛?
鎺ヤ釜鍚婚兘瑕佸集鑵版墠琛岋紙 灝忕尗 鐭浜嗭級銆備負姝わ紝鎴戝笇鏈涚粰鎴戜滑鐝殑MM鐨勮韓楂樻帓搴忋傛垜浠彮MM鐨勮韓楂橈紝
鍐嶇璋變篃娌℃湁瓚呰繃2綾崇殑錛岃繖寰堥傚悎鐢ㄦ垜浠垰鎵嶇殑綆楁硶銆傛垜浠湪榛戞澘涓婄敾涓涓?00鍒?00鐨勬暟緇勶紝MM渚濇鑷洕韜珮錛屾垜璐熻矗鐢?#8220;姝?#8221;瀛楃粺璁′漢鏁般傜粺璁″嚭鏉?
浜嗭紝浠庡皬鍒板ぇ渚濇涓?41, 143, 143, 147, 152, 153,
…銆傝繖綆楀摢闂ㄥ瓙鎺掑簭錛熷氨涓鎺掓暟瀛楀鎴戞湁浠涔堢敤錛屾垜瑕佺煡閬撶殑鏄摢涓狹M鏈夊楂樸傛垜浠粎浠呮妸鍏冪礌鐨勫睘鎬у間粠灝忓埌澶у垪浜嗗嚭鏉ワ紝浣嗘垜浠病鏈夊鍏冪礌鏈韓榪涜鎺掑簭銆備篃
灝辨槸璇達紝鎴戜滑闇瑕佺煡閬撹緭鍑虹粨鏋滅殑姣忎釜鏁板煎搴斿師鏁版嵁鐨勫摢涓涓厓绱犮備笅鏂囨彁鍒扮殑“鎺掑簭綆楁硶鐨勭ǔ瀹氭?#8221;涔熷拰灞炴у間笌瀹為檯鍏冪礌鐨勫尯鍒湁鍏熾?br>
闂?
棰樹簩錛氭庢牱灝嗙嚎鎬ф椂闂存帓搴忓悗鐨勮緭鍑虹粨鏋滆繕鍘熶負鍘熸暟鎹腑鐨勫厓绱狅紵
STOP!
You should think for a while.
鍚屾牱鍊熷姪Hash琛ㄧ殑鎬濇兂錛屾垜浠珛鍗蟲兂鍒頒簡綾諱技浜?
寮鏁e垪鐨勬柟娉曘傛垜浠敤閾捐〃鎶婂睘鎬у肩浉鍚岀殑鍏冪礌涓茶搗鏉ワ紝鎸傚湪瀵瑰簲鐨凾[i]涓娿傛瘡嬈¤鍒頒竴涓暟錛屽湪澧炲姞T[i]鐨勫悓鏃舵垜浠妸榪欎釜鍏冪礌鏀捐繘T[i]寤朵幾鍑哄幓鐨?
閾捐〃閲屻傝繖鏍鳳紝杈撳嚭緇撴灉鏃舵垜浠彲浠ユ柟渚垮湴鑾峰緱鍘熸暟鎹腑鐨勬墍鏈夊睘鎬у間負i鐨勫厓绱犮?br>
A[]= 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9
+---+---+---+---+---+---+---+---+---+---+
鏁板瓧 i錛?| 0 | 1 | 2 | 3
| 4 | 5 | 6 | 7 | 8 | 9 |
+---+---+---+---+---+---+---+---+---+---+
鍑虹幇嬈℃暟T[i]錛?| 0 | 2 | 1 | 2 |
1 | 3 | 1 | 0 | 0 | 2 |
+---+o--+-o-+-o-+-o-+-o-+--o+---+---+-o-+
| |
| | | | |
+--+ +-+ | |
+-+ +---+ |
| | A[1] | | |
A[6]
A[2] A[7] | A[3] A[5] A[8] |
| | | A[12]
A[4] A[10] A[9]
|
A[11]
褰?
璞″湴璇達紝鎴戜滑鍦ㄥ湴涓婃憜10涓《錛屾瘡涓《緙栦竴涓彿錛岀劧鍚庢妸鏁版嵁鍒嗛棬鍒被鏀懼湪鑷繁鎵灞炵殑妗墮噷銆傝繖縐嶆帓搴忕畻娉曞彨鍋氭《寮忔帓搴?Bucket
Sort)銆傛湰鏂囨渶鍚庝綘灝嗙湅鍒版《寮忔帓搴忕殑鍙︿竴涓敤閫斻?br> 閾捐〃鍐欒搗鏉ユ瘮杈冮夯鐑︼紝涓鑸垜浠笉浣跨敤瀹冦傛垜浠湁鏇寸畝鍗曠殑鏂規(guī)硶銆?br>
闂?
棰樹笁錛氬悓鏍鋒槸杈撳嚭鍏冪礌鏈韓錛屼綘鑳芥兂鍑轟笉鐢ㄩ摼琛ㄧ殑鍏跺畠綆楁硶涔堬紵
STOP!
You should think for a while.
A[]= 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9
+---+---+---+---+---+---+---+---+---+---+
鏁板瓧 i錛?| 0 | 1 | 2 | 3
| 4 | 5 | 6 | 7 | 8 | 9 |
+---+---+---+---+---+---+---+---+---+---+
鍑虹幇嬈℃暟T[i]錛?| 0 | 2 | 1 | 2 |
1 | 3 | 1 | 0 | 0 | 2 |
+---+---+---+---+---+---+---+---+---+---+
淇敼鍚庣殑T[i]錛?| 0 | 2 | 3 | 5 |
6 | 9 | 10| 10| 10| 12|
+---+---+---+---+---+---+---+---+---+---+
鎵鏈夋暟閮借鍏ュ悗錛屾垜浠慨鏀?
T[i]鏁扮粍鐨勫鹼紝浣垮緱T[i]琛ㄧず鏁板瓧i鍙兘鐨勬帓鍚嶇殑鏈澶у箋傛瘮濡傦紝1鏈宸帓鍚嶇浜岋紝3鏈榪滃彲浠ユ帓鍒扮浜斻俆鏁扮粍鐨勬渶鍚庝竴涓暟搴旇絳変簬杈撳叆鏁版嵁鐨勬暟瀛椾釜
鏁般備慨鏀筎鏁扮粍鐨勬搷浣滃彲浠ョ敤涓嬈$嚎鎬х殑鎵弿绱姞瀹屾垚銆?br> 鎴戜滑榪橀渶瑕佸噯澶囦竴涓緭鍑烘暟緇勩傜劧鍚庯紝鎴戜滑浠庡悗寰鍓嶆壂鎻廇鏁扮粍錛屼緷鐓鏁扮粍鐨勬寚紺轟緷嬈?
鎶婂師鏁版嵁鐨勫厓绱犵洿鎺ユ斁鍒拌緭鍑烘暟緇勪腑錛屽悓鏃禩[i]鐨勫煎噺涓銆備箣鎵浠ヤ粠鍚庡線鍓嶆壂鎻廇鏁扮粍錛屾槸鍥犱負榪欐牱杈撳嚭緇撴灉鎵嶆槸紼沖畾鐨勩傛垜浠涓涓帓搴忕畻娉曟槸紼沖畾鐨?
(Stable)錛屽綋綆楁硶婊¤凍榪欐牱鐨勬ц川錛氬睘鎬у肩浉鍚岀殑鍏冪礌錛屾帓搴忓悗鍓嶅悗浣嶇疆涓嶅彉錛屾湰鏉ュ湪鍓嶉潰鐨勭幇鍦ㄤ粛鐒跺湪鍓嶉潰銆備笉瑕佽寰楁帓搴忕畻娉曟槸鍚﹀叿鏈夌ǔ瀹氭т技涔庡叧緋?
涓嶅ぇ錛屾帓搴忕殑紼沖畾鎬у湪涓嬫枃鐨勬煇涓棶棰樹腑灝嗗彉寰楅潪甯擱噸瑕併備綘鍙互鍊掑洖鍘葷湅鐪嬪墠闈㈣鐨勪竷縐嶆帓搴忕畻娉曞摢浜涙槸紼沖畾鐨勩?br> 渚嬪瓙涓紝A鏁扮粍鏈鍚庝竴涓暟9
鎵瀵瑰簲鐨凾[9]=12錛屾垜浠洿鎺ユ妸9鏀懼湪寰呰緭鍑哄簭鍒椾腑鐨勭12涓綅緗紝鐒跺悗T[9]鍙樻垚11錛堣繖鏍蜂笅涓嬈″啀鍑虹幇9鏃跺氨搴旇鏀懼湪絎?1浣嶏級銆?br>
A[]= 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9 <--
T[i]=
0, 2, 3, 5, 6, 9, 10, 10, 10, 11
Ans
= _ _ _ _ _ _ _ _ _ _ _ 9
鎺ヤ笅鏉ョ殑鍑犳濡備笅錛?br>
A[]= 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5 <--
T[i]=
0, 2, 3, 5, 6, 8, 10, 10, 10, 11
Ans
= _ _ _ _ _ _ _ _ 5 _ _ 9
A[]= 3, 1, 4, 1, 5, 9, 2, 6, 5, 3
<--
T[i]= 0, 2, 3, 4, 6, 8, 10,
10, 10, 11
Ans = _ _ _ _ 3 _ _ _ 5 _ _ 9
A[]= 3, 1, 4, 1, 5,
9, 2, 6, 5 <--
T[i]= 0, 2, 3, 4, 6, 7,
10, 10, 10, 11
Ans = _ _ _ _ 3 _ _ 5 5 _ _ 9
榪欑綆楁硶鍙?
鍋氳鏁版帓搴?Counting Sort)銆傛紜у拰澶嶆潅搴﹂兘鏄樉鐒剁殑銆?br>
闂鍥涳細緇欏畾鏁扮殑鏁版嵁鑼冨洿澶т簡璇ユ庝箞
鍔烇紵
STOP! You should think for a
while.
鍓嶉潰鐨勭畻娉曞彧鏈夊湪鏁版嵁鐨勮寖鍥翠笉澶ф椂鎵嶅彲琛岋紝濡傛灉緇欏畾鐨勬暟鍦ㄩ暱鏁磋寖鍥村唴鐨勮瘽錛岃繖涓畻娉曟槸涓嶅彲琛岀殑錛屽洜涓?
浣犲紑涓嶄笅榪欎箞澶х殑鏁扮粍銆俁adix鎺掑簭(Radix Sort)瑙e喅浜嗚繖涓毦棰樸?br> 鏄ㄥぉ鎴戞病浜嬬炕浜嗕竴涓嬪垵涓紙9鐝級鏃剁殑鍚屽褰曪紝鍥炲繂浜嗕竴涓?
榪囧幓銆傛垜鎶婃瘮杈冩劅鍏磋叮鐨凪M鐨勭敓鏃ュ垪鍦ㄤ笅闈紙緇濆鐪熷疄錛夈傚鏋滃垪琛ㄤ腑鐨勫摢涓狹M鏈夊垢鐪嬪埌浜嗚繖綃囨棩蹇楋紙鍑犱箮涓嶅彲鑳斤級錛屽乏杈圭殑Support鏍忔湁鎴戠殑鐢?shù)瀛愯仈绯?
鏂瑰紡錛屾垜鎯崇煡閬撲綘浠庝箞鏍蜂簡銆傛帓鍚嶄笉鍒嗗厛鍚庛?br>
榪欏氨鏄垜鐨勬暟鎹簡銆傜幇鍦紝鎴戣緇欒繖浜涙暟鎺掑簭銆傚亣濡傛垜鐨勭數(shù)鑴戝彧鑳藉紑鍑?..99鐨勬暟緇勶紝閭h鏁版帓搴忕畻娉曟渶澶氬涓や綅鏁拌繘琛屾帓搴忋傛垜灝辨妸
姣忎釜鍏綅鏁頒袱浣嶄袱浣嶅湴鍒嗘垚鍥涙錛堝浘1錛夛紝鍒嗗埆榪涜鍥涙璁℃暟鎺掑簭銆傚湴鐞冧漢閮界煡閬撴湀浠界浉鍚屾椂搴旇鐪嬪摢涓鏃ワ紝鍥犳鎴戜滑鐪嬫湀浠界殑澶у皬鏃跺簲璇ヤ簨鍏堜繚璇佹棩宸茬粡鏈夊簭銆傛崲
鍙ヨ瘽璇達紝鎴戜滑鍏堝“鏈涓嶉噸瑕?#8221;鐨勯儴鍒嗚繘琛屾帓搴忋傛垜浠厛瀵規(guī)墍鏈夋暟鐨勬渶鍚庝袱浣嶈繘琛屼竴嬈¤鏁版帓搴忥紙鍥?錛夈傛敞鎰忚瀵?鏈?6鍙風(fēng)殑MM鍜?鏈?6鍙風(fēng)殑MM錛屾湰嬈℃帓
搴忎腑瀹冧滑鐨勫睘鎬у肩浉鍚岋紝鐢變簬璁℃暟鎺掑簭鏄ǔ瀹氱殑錛屽洜姝?鏈堜喚閭d釜鎺掑畬鍚庝緷鐒跺湪1鏈堜喚閭d釜鐨勫墠澶淬傛帴涓嬫潵鎴戜滑瀵圭櫨浣嶅拰鍗冧綅榪涜鎺掑簭錛堝浘3錛夈備綘鍙互鐪嬪埌涓や釜
26鏃ョ殑MM鍦ㄨ繖涓嬈℃帓搴忎腑鍒嗗嚭浜嗗ぇ灝忥紝鑰屾湀浠界浉鍚岀殑MM渚濈劧淇濇寔鏃ユ暟鏈夊簭錛堝洜涓鴻鏁版帓搴忔槸紼沖畾鐨勶級銆傛渶鍚庢垜浠騫翠喚鎺掑簭錛堝浘4錛夛紝瀹屾垚鏁翠釜綆楁硶銆傚ぇ瀹墮兘
鏄法涓栫邯鐨勫ソ鍎跨錛屽洜姝ゆ病鏈夊浘5浜嗐?br>

榪?
縐嶇畻娉曟樉鐒舵槸姝g‘鐨勩傚畠鐨勫鏉傚害涓鑸啓鎴怬(d*(n+m))錛屽叾涓璶琛ㄧずn涓暟錛宮鏄垜寮鐨勬暟緇勫ぇ灝忥紙鏈緥涓璵=100錛夛紝d鏄竴涓父鏁板洜瀛愶紙鏈緥涓?
d=4錛夈傛垜浠涓哄畠涔熸槸綰挎х殑銆?br>
闂浜旓細榪欐牱鐨勬帓搴忔柟娉曡繕鏈変粈涔堣嚧鍛界殑緙洪櫡錛?/strong>
STOP! You should think for a while.
鍗?
浣挎暟鎹湁30浣嶏紝鎴戜滑涔熷彲浠ョ敤d=5鎴?鐨凴adix綆楁硶榪涜鎺掑簭銆備絾錛岃鏄粰瀹氱殑鏁版嵁鏈夋棤絀峰浣嶆庝箞鍔烇紵鏈変漢璇達紝榪欏彲鑳戒箞銆傝繖鏄彲鑳界殑錛屾瘮濡傜粰瀹氱殑鏁版嵁
鏄皬鏁幫紙鏇村噯紜湴璇達紝瀹炴暟錛夈傚熀浜庢瘮杈冪殑鎺掑簭鍙互鍖哄垎355/113鍜?#960;鍝?
涓ぇ錛屼絾浣犱笉鐭ラ亾Radix鎺掑簭闇瑕佺簿紜埌鍝竴浣嶃傝繖涓嬫儴浜嗭紝瀹炴暟鐨勫嚭鐜版妸璨屼技楂樼鎶鐨勭嚎鎬ф椂闂存帓搴忔墦鍥炰簡鍐滀笟鏃朵唬銆傝繖鏃訛紝妗舵帓搴忓啀搴﹀嚭灞憋紝鎸芥晳浜嗙嚎鎬ф椂
闂存帓搴忔?zhèn)叉儴鐨勫懡杩愩?br>
闂鍏細濡備綍瀵瑰疄鏁拌繘琛岀嚎鎬ф椂闂存帓搴忥紵
STOP! You should think for a while.
鎴?
浠妸闂綆鍖栦竴涓嬶紝緇欏嚭鐨勬墍鏈夋暟閮芥槸0鍒?涔嬮棿鐨勫皬鏁般傚鏋滀笉鏄紝涔熷彲浠ユ妸鎵鏈夋暟鍚屾椂闄や互涓涓ぇ鏁存暟浠庤岃漿鍖栦負榪欑褰㈠紡銆傛垜浠緷鐒惰绔嬭嫢騫蹭釜妗訛紝姣斿錛屼互
灝忔暟鐐瑰悗闈竴浣嶆暟涓轟緷鎹鎵鏈夋暟榪涜鍒掑垎銆傛垜浠粛鐒剁敤閾捐〃鎶婂悓涓綾葷殑鏁頒覆鍦ㄤ竴璧鳳紝涓嶅悓鐨勬槸錛屾瘡涓涓摼琛ㄩ兘鏄湁搴忕殑銆備篃灝辨槸璇達紝姣忎竴嬈¤鍒頒竴涓柊鐨勬暟閮借榪?
琛屼竴嬈℃彃鍏ユ帓搴忋傜湅鎴戜滑鐨勪緥瀛愶細
A[]=
0.12345, 0.111, 0.618, 0.9, 0.99999
+---+---+---+---+---+---+---+---+---+---+
鍗佸垎浣嶏細 | 0 | 1 | 2 | 3 |
4 | 5 | 6 | 7 | 8 | 9 |
+---+-o-+---+---+---+---+-o-+---+---+-o-+
| | |
A[2]=0.111 A[3]=0.618 A[4]=0.9
| |
A[1]=0.12345 A[5]=0.99999
鍋囧鍐嶄笅涓涓鍏ョ殑鏁版槸
0.122222錛岃繖涓暟闇瑕佹彃鍏ュ埌鍗佸垎浣嶄負1鐨勯偅涓摼琛ㄩ噷閫傚綋鐨勪綅緗傛垜浠渶瑕侀亶鍘嗚閾捐〃鐩村埌鎵懼埌絎竴涓瘮0.122222澶х殑鏁幫紝鍦ㄤ緥瀛愪腑鍒欏簲璇ユ彃鍏?
鍒伴摼琛ㄤ腑A[2]鍜孉[1]涔嬮棿銆傛渶鍚庯紝鎴戜滑鎸夐『搴忛亶鍘嗘墍鏈夐摼琛紝渚濇杈撳嚭姣忎釜閾捐〃涓殑姣忎釜鏁般?br> 榪欎釜綆楁硶鏄劇劧鏄紜殑錛屼絾澶嶆潅搴︽樉鐒朵笉鏄?
綰挎с備簨瀹炰笂錛岃繖縐嶇畻娉曟渶鍧忔儏鍐典笅鏄疧(n^2)鐨勶紝鍥犱負褰撴墍鏈夋暟鐨勫崄鍒嗕綅閮界浉鍚屾椂綆楁硶灝辨槸涓涓彃鍏ユ帓搴忋傚拰鍘熸潵涓鏍鳳紝鎴戜滑涓嬮潰瑕佽綆楃畻娉曠殑騫沖潎鏃墮棿澶嶆潅
搴︼紝鎴戜滑甯屾湜榪欑綆楁硶鐨勫鉤鍧囧鏉傚害鏄嚎鎬х殑銆?br> 榪欐綆楀鉤鍧囧鏉傚害鎴戜滑鐢ㄦ渶絎ㄧ殑鍔炴硶銆傛垜浠皢綆楀嚭鎵鏈夊彲鑳藉嚭鐜扮殑鎯呭喌鐨勬繪椂闂村鏉傚害錛岄櫎浠ユ葷殑
鎯呭喌鏁幫紝寰楀埌騫沖潎鐨勫鏉傚害鏄灝戙?br> 姣忎釜鏁伴兘鍙兘灞炰簬10涓《涓殑涓涓紝n涓暟鎬葷殑鎯呭喌鏈?0^n縐嶃傝繖涓兼槸鎴戜滑搴炲ぇ鐨勭畻寮忕殑鍒嗘瘝閮ㄥ垎銆?
濡傛灉涓涓《閲屾湁K涓厓绱狅紝閭d箞鍙笌榪欎釜妗舵湁鍏崇殑鎿嶄綔鏈塐(K^2)嬈★紝瀹冨氨鏄竴嬈℃彃鍏ユ帓搴忕殑鎿嶄綔嬈℃暟銆備笅闈㈣綆楋紝鍦?0^n縐嶆儏鍐典腑錛孠0=1鏈夊灝戠鎯?
鍐點侹0=1琛ㄧず錛宯涓暟涓彧鏈変竴涓暟鍦?鍙鋒《錛屽叾浣檔-1涓暟鐨勫崄鍒嗕綅灝卞彧鑳藉湪1鍒?涓夋嫨銆傞偅涔圞0=1鐨勬儏鍐墊湁C(n,1)*9^(n-1)錛岃屾瘡
涓狵0=1鐨勬儏鍐靛湪0鍙鋒《涓皢浜х敓1^2鐨勫鏉傚害銆傜被浼煎湴錛孠i=p鐨勬儏鍐墊暟涓篊(n,p)*9^(n-p)錛屽鏉傚害鎬昏涓篊(n,p)*9^(n-
p)*p^2銆傛灇涓炬墍鏈塊鐨勪笅鏍囧拰p鍊鹼紝绱姞璧鋒潵錛岃繖涓畻寮忓ぇ瀹跺簲璇ヨ兘鍐欏嚭鏉ヤ簡錛屼絾鏄繖涓?#8230;…鎬庝箞綆楀晩銆傚埆鎬曪紝鎴戜滑鏄悶璁$畻鏈虹殑錛屾嬁鍑虹偣鍜孧O涓嶄竴鏍風(fēng)殑涓?
瑗挎潵銆備簬鏄紝Mathematica 5.0闅嗛噸鐧誨満錛屾垜鍋氭暟瀛︿綔涓氬叏闈犲畠銆傚畠?yōu)畣甯垜浠寲绠榪欎釜澶嶆潅鐨勫紡瀛愩?br>
鎴?
浠仐鎲懼湴鍙戠幇錛岃櫧鐒跺父鏁板洜瀛愬緢灝忥紙鍙湁0.1錛夛紝浣嗙畻娉曠殑騫沖潎澶嶆潅搴︿粛鐒舵槸騫蟲柟鐨勩傜瓑涓涓嬶紝1/10鐨勯偅涓?0鏄垜浠《鐨勪釜鏁板悧錛熼偅涔堟垜浠負浠涔堜笉鎶婃《鐨?
涓暟寮勫ぇ鐐癸紵鎴戜滑騫茶剢鐢╩鏉ヨ〃紺烘《鐨勪釜鏁幫紝閲嶆柊璁$畻涓嬈★細
鍖?
綆鍑烘潵錛屾搷浣滄鏁頒負O(n+n^2/m)銆傚彂鐜頒簡涔堬紝濡傛灉m=Θ(n)鐨勮瘽錛屽鉤鍧囧鏉傚害灝卞彉鎴愪簡O(n)銆備篃灝辨槸璇達紝褰撴《鐨勪釜鏁扮瓑浜庤緭鍏ユ暟鎹殑涓暟鏃訛紝綆?
娉曟槸騫沖潎綰挎х殑銆?br> 鎴戜滑灝嗗湪Hash琛ㄥ紑鏁e垪鐨勪粙緇嶄腑閲嶆柊鎻愬埌榪欎釜緇撹銆?br>
涓旀參錛岃繕鏈変竴涓棶棰樸?0涓《浠ュ崄鍒嗕綅鐨?
鏁板瓧褰掔被錛岄偅涔坣涓《鐢ㄤ粈涔堟柟娉曟潵鍒嗙被鍛紵娉ㄦ剰錛屽垎綾葷殑鏂規(guī)硶闇瑕佹弧瓚籌紝涓錛屼竴涓暟鍒嗗埌姣忎釜妗墮噷鐨勬鐜囩浉鍚岋紙榪欐牱鎵嶆湁鎴戜滑涓婇潰鐨勭粨璁猴級錛涗簩錛屾墍鏈夋《閲屽綰沖厓
绱犵殑鑼冨洿蹇呴』鏄繛緇殑銆傛牴鎹繖涓や釜鏉′歡錛屾垜浠湁鍔炴硶鎶婃墍鏈夋暟鎭板ソ鍒嗕負n綾匯傛垜浠殑杈撳叆鏁版嵁涓嶆槸閮藉湪0鍒?涔嬮棿涔堬紵鍙渶瑕佺湅榪欎簺鏁頒箻浠鐨勬暣鏁伴儴鍒嗘槸澶氬皯灝?
琛屼簡錛岃鍒頒竴涓暟鍚庝箻浠鍙栨暣寰楀嚑灝辨彃鍏ュ埌鍑犲彿妗墮噷銆傝繖鏈川涓婄浉褰撲簬鎶婂尯闂碵0,1)騫沖潎鍒嗘垚n浠姐?br>
闂涓冿細鏈?
娌℃湁澶嶆潅搴︿綆浜庣嚎鎬х殑鎺掑簭綆楁硶
STOP! You should
think for a while.
鎴戜滑浠嶰(n^2)璧板悜O(nlogn)錛屽張浠嶰(nlogn)璧板悜綰挎э紝
姣忎竴嬈℃垜浠兘璁ㄨ浜嗗鏉傚害涓嬮檺鐨勯棶棰橈紝鏍規(guī)嵁璁ㄨ鐨勭粨鏋滄彁鍑轟簡鏇翠紭鐨勭畻娉曘傝繖嬈℃葷畻涓嶈浜嗭紝涓嶅彲鑳芥湁姣旂嚎鎬ц繕蹇殑綆楁硶浜嗭紝鍥犱負鈥斺斾綘璇誨叆銆佽緭鍑烘暟鎹嚦灝戝氨闇
瑕佺嚎鎬х殑鏃墮棿銆傛帓搴忕畻娉曚箣鏃呭湪綰挎ф椂闂村鏉傚害榪欎竴绔欑粓姝簡錛屾墍鏈夊崄縐嶆帓搴忕畻娉曞埌榪欓噷浠嬬粛瀹屾瘯浜嗐?br>
鏂囩珷鏈夎秺鍐欒秺闀?
鐨勮秼鍔夸簡錛屾垜媯鏌ヨ搗鏉ヤ篃瓚婃潵瓚婄瘡浜嗐傛垜鍙堢湅浜嗕笁閬嶏紝搴旇娌¢棶棰樹簡銆傜兢浼楃殑鐪肩潧鏄洩浜殑錛屾伋璇峰ぇ瀹跺府鎴戞壘閿欍?br>
鍘誨勾騫村簳鍐欑殑鍏充簬浣嶈繍綆?/a>鐨勬棩蹇楁槸榪欎釜Blog閲屽皯鏁板ぇ鍙楁榪庣殑鏂囩珷涔嬩竴錛屽緢澶氫漢閮藉笇鏈涙垜鑳戒笉鏂畬鍠勯偅綃囨枃绔犮傚悗鏉ユ垜鐪嬪埌浜嗕笉灝戝叾
瀹冪殑璧勬枡錛屽涔?fàn)鍒颁簡鏇村鍏充簬浣崢q愮畻鐨勭煡璇嗭紝鏈変簡閲嶆柊鏁寸悊浣嶈繍綆楁妧宸х殑鎯蟲硶銆備粠浠婂ぉ璧鋒垜灝卞紑濮嬪啓榪欎竴緋誨垪浣嶈繍綆楄瑙f枃绔狅紝涓庡叾璇存槸鍘熸潵閭g瘒鏂囩珷鐨?
follow-up錛屼笉濡傝鏄竴涓猺emake銆傚綋鐒墮鍏堟垜榪樻槸浠庢渶鍩虹鐨勪笢瑗胯璧楓?br>
浠涔堟槸浣嶈繍綆楋紵
紼嬪簭涓殑鎵鏈夋暟鍦ㄨ
綆楁満鍐呭瓨涓兘鏄互浜岃繘鍒剁殑褰㈠紡鍌ㄥ瓨鐨勩備綅榪愮畻璇寸┛浜嗭紝灝辨槸鐩存帴瀵規(guī)暣鏁板湪鍐呭瓨涓殑浜岃繘鍒朵綅榪涜鎿嶄綔銆傛瘮濡傦紝and榪愮畻鏈潵鏄竴涓昏緫榪愮畻絎︼紝浣嗘暣鏁頒笌鏁存暟涔?
闂翠篃鍙互榪涜and榪愮畻銆備婦涓緥瀛愶紝6鐨勪簩榪涘埗鏄?10錛?1鐨勪簩榪涘埗鏄?011錛岄偅涔? and
11鐨勭粨鏋滃氨鏄?錛屽畠鏄簩榪涘埗瀵瑰簲浣嶈繘琛岄昏緫榪愮畻鐨勭粨鏋滐紙0琛ㄧずFalse錛?琛ㄧずTrue錛岀┖浣嶉兘褰?澶勭悊錛夛細
110
AND
1011
----------
0010 --> 2
鐢變簬浣嶈繍綆楃洿鎺ュ鍐呭瓨鏁版嵁榪涜鎿嶄綔錛屼笉闇瑕佽漿鎴?
鍗佽繘鍒訛紝鍥犳澶勭悊閫熷害闈炲父蹇傚綋鐒舵湁浜轟細璇達紝榪欎釜蹇簡鏈変粈涔堢敤錛岃綆? and
11娌℃湁浠涔堝疄闄呮剰涔夊晩銆傝繖涓緋誨垪鐨勬枃绔犲氨灝嗗憡璇変綘錛屼綅榪愮畻鍒板簳鍙互騫蹭粈涔堬紝鏈変簺浠涔堢粡鍏稿簲鐢紝浠ュ強濡備綍鐢ㄤ綅榪愮畻浼樺寲浣犵殑紼嬪簭銆?br>
Pascal
鍜孋涓殑浣嶈繍綆楃鍙?br> 涓嬮潰鐨刟鍜宐閮芥槸鏁存暟綾誨瀷錛屽垯錛?br>C璇█ | Pascal璇█
-------+-------------
a
& b | a and b
a | b | a or b
a ^ b | a xor b
~a
| not a
a << b | a shl b
a >> b | a shr b
娉?
鎰廋涓殑閫昏緫榪愮畻鍜屼綅榪愮畻絎﹀彿鏄笉鍚岀殑銆?20|1314=1834錛屼絾520||1314=1錛屽洜涓洪昏緫榪愮畻鏃?20鍜?314閮界浉褰撲簬True銆傚悓鏍?
鐨勶紝!a鍜寏a涔熸槸鏈夊尯鍒殑銆?br>
鍚勭浣嶈繍綆楃殑浣跨敤
=== 1. and榪愮畻 ===
and榪愮畻閫?
甯哥敤浜庝簩榪涘埗鍙栦綅鎿嶄綔錛屼緥濡備竴涓暟 and
1鐨勭粨鏋滃氨鏄彇浜岃繘鍒剁殑鏈鏈綅銆傝繖鍙互鐢ㄦ潵鍒ゆ柇涓涓暣鏁扮殑濂囧伓錛屼簩榪涘埗鐨勬渶鏈綅涓?琛ㄧず璇ユ暟涓哄伓鏁幫紝鏈鏈綅涓?琛ㄧず璇ユ暟涓哄鏁?
===
2. or榪愮畻 ===
or榪愮畻閫氬父鐢ㄤ簬浜岃繘鍒剁壒瀹氫綅涓婄殑鏃犳潯浠惰祴鍊鹼紝渚嬪涓涓暟or
1鐨勭粨鏋滃氨鏄妸浜岃繘鍒舵渶鏈綅寮鴻鍙樻垚1銆傚鏋滈渶瑕佹妸浜岃繘鍒舵渶鏈綅鍙樻垚0錛屽榪欎釜鏁皁r
1涔嬪悗鍐嶅噺涓灝卞彲浠ヤ簡錛屽叾瀹為檯鎰忎箟灝辨槸鎶婅繖涓暟寮鴻鍙樻垚鏈鎺ヨ繎鐨勫伓鏁般?br>
=== 3. xor榪愮畻 ===
xor
榪愮畻閫氬父鐢ㄤ簬瀵逛簩榪涘埗鐨勭壒瀹氫竴浣嶈繘琛屽彇鍙嶆搷浣滐紝鍥犱負寮傛垨鍙互榪欐牱瀹氫箟錛?鍜?寮傛垨0閮戒笉鍙橈紝寮傛垨1鍒欏彇鍙嶃?br> xor榪愮畻鐨勯嗚繍綆楁槸瀹冩湰韜紝
涔熷氨鏄涓ゆ寮傛垨鍚屼竴涓暟鏈鍚庣粨鏋滀笉鍙橈紝鍗?a xor b) xor b =
a銆倄or榪愮畻鍙互鐢ㄤ簬綆鍗曠殑鍔犲瘑錛屾瘮濡傛垜鎯沖鎴慚M璇?314520錛屼絾鎬曞埆浜虹煡閬擄紝浜庢槸鍙屾柟綰﹀畾鎷挎垜鐨勭敓鏃?9880516浣滀負瀵嗛挜銆?314520
xor 19880516 = 20665500錛屾垜灝辨妸20665500鍛婅瘔MM銆侻M鍐嶆璁$畻20665500 xor
19880516鐨勫鹼紝寰楀埌1314520錛屼簬鏄ス灝辨槑鐧戒簡鎴戠殑浼佸浘銆?br> 涓嬮潰鎴戜滑鐪嬪彟澶栦竴涓笢瑗褲傚畾涔変袱涓鍙?鍜孈錛堟垜鎬庝箞鎵句笉鍒伴偅涓湀
閲屾湁涓弶鐨勫瓧絎︼級錛岃繖涓や釜絎﹀彿浜掍負閫嗚繍綆楋紝涔熷氨鏄(x # y) @ y = x銆傜幇鍦ㄤ緷嬈℃墽琛屼笅闈笁鏉″懡浠わ紝緇撴灉鏄粈涔堬紵x
<- x # y
y <- x @ y
x <- x @ y
鎵ц浜嗙涓鍙ュ悗x鍙樻垚浜唜
# y銆傞偅涔堢浜屽彞瀹炶川灝辨槸y <- x # y @ y錛岀敱浜?鍜孈浜掍負閫嗚繍綆楋紝閭d箞姝ゆ椂鐨剏鍙樻垚浜嗗師鏉ョ殑x銆傜涓夊彞涓瓁瀹為檯涓婅璧嬪間負(x #
y) @ x錛屽鏋?榪愮畻鍏鋒湁浜ゆ崲寰嬶紝閭d箞璧嬪煎悗x灝卞彉鎴愭渶鍒濈殑y浜嗐傝繖涓夊彞璇濈殑緇撴灉鏄紝x鍜寉鐨勪綅緗簰鎹簡銆?br> 鍔犳硶鍜屽噺娉曚簰涓洪嗚繍綆楋紝
騫朵笖鍔犳硶婊¤凍浜ゆ崲寰嬨傛妸#鎹㈡垚+錛屾妸@鎹㈡垚-錛屾垜浠彲浠ュ啓鍑轟竴涓笉闇瑕佷復(fù)鏃跺彉閲忕殑swap榪囩▼(Pascal)銆?br>procedure
swap(var a,b:longint);
begin
a:=a + b;
b:=a - b;
a:=a - b;
end;
濂戒簡錛屽垰鎵嶄笉鏄xor鐨勯嗚繍綆楁槸瀹冩湰韜悧錛熶簬鏄垜浠氨鏈変簡涓涓湅璧鋒潵闈炲父璇″紓鐨?
swap榪囩▼錛?br>procedure swap(var a,b:longint);
begin
a:=a
xor b;
b:=a xor b;
a:=a xor b;
end;
===
4. not榪愮畻 ===
not榪愮畻鐨勫畾涔夋槸鎶婂唴瀛樹腑鐨?鍜?鍏ㄩ儴鍙栧弽銆備嬌鐢╪ot榪愮畻鏃惰鏍煎灝忓績錛屼綘闇瑕佹敞鎰忔暣鏁扮被鍨嬫湁娌℃湁絎﹀彿銆?
濡傛灉not鐨勫璞℃槸鏃犵鍙鋒暣鏁幫紙涓嶈兘琛ㄧず璐熸暟錛夛紝閭d箞寰楀埌鐨勫煎氨鏄畠涓庤綾誨瀷涓婄晫鐨勫樊錛屽洜涓烘棤絎﹀彿綾誨瀷鐨勬暟鏄敤$0000鍒?FFFF渚濇琛ㄧず鐨勩備笅闈㈢殑
涓や釜紼嬪簭錛堜粎璇█涓嶅悓錛夊潎榪斿洖65435銆?br>var
a:word;
begin
a:=100;
a:=not a;
writeln(a);
end.#include
<stdio.h>
int main()
{
unsigned short a=100;
a
= ~a;
printf( "%d\n", a );
return 0;
}
濡?
鏋渘ot鐨勫璞℃槸鏈夌鍙風(fēng)殑鏁存暟錛屾儏鍐靛氨涓嶄竴鏍蜂簡錛岀◢鍚庢垜浠細鍦?#8220;鏁存暟綾誨瀷鐨勫偍瀛?#8221;灝忚妭涓彁鍒般?br>
=== 5. shl榪愮畻 ===
a
shl
b灝辮〃紺烘妸a杞負浜岃繘鍒跺悗宸︾Щb浣嶏紙鍦ㄥ悗闈㈡坊b涓?錛夈備緥濡?00鐨勪簩榪涘埗涓?100100錛岃?10010000杞垚鍗佽繘鍒舵槸400錛岄偅涔?00
shl 2 = 400銆傚彲浠ョ湅鍑猴紝a shl b鐨勫煎疄闄呬笂灝辨槸a涔樹互2鐨刡嬈℃柟錛屽洜涓哄湪浜岃繘鍒舵暟鍚庢坊涓涓?灝辯浉褰撲簬璇ユ暟涔樹互2銆?br> 閫氬父
璁や負a shl 1姣攁 * 2鏇村揩錛屽洜涓哄墠鑰呮槸鏇村簳灞備竴浜涚殑鎿嶄綔銆傚洜姝ょ▼搴忎腑涔樹互2鐨勬搷浣滆灝介噺鐢ㄥ乏縐諱竴浣嶆潵浠f浛銆?br> 瀹氫箟涓浜涘父閲忓彲鑳戒細
鐢ㄥ埌shl榪愮畻銆備綘鍙互鏂逛究鍦扮敤1 shl 16 -
1鏉ヨ〃紺?5535銆傚緢澶氱畻娉曞拰鏁版嵁緇撴瀯瑕佹眰鏁版嵁瑙勬ā蹇呴』鏄?鐨勫箓錛屾鏃跺彲浠ョ敤shl鏉ュ畾涔塎ax_N絳夊父閲忋?br>
=== 6.
shr榪愮畻 ===
鍜宻hl鐩鎬技錛宎 shr
b琛ㄧず浜岃繘鍒跺彸縐籦浣嶏紙鍘繪帀鏈玝浣嶏級錛岀浉褰撲簬a闄や互2鐨刡嬈℃柟錛堝彇鏁達級銆傛垜浠篃緇忓父鐢╯hr 1鏉ヤ唬鏇縟iv
2錛屾瘮濡備簩鍒嗘煡鎵俱佸爢鐨勬彃鍏ユ搷浣滅瓑絳夈傛兂鍔炴硶鐢╯hr浠f浛闄ゆ硶榪愮畻鍙互浣跨▼搴忔晥鐜囧ぇ澶ф彁楂樸傛渶澶у叕綰︽暟鐨勪簩榪涘埗綆楁硶鐢ㄩ櫎浠?鎿嶄綔鏉ヤ唬鏇挎參寰楀嚭濂囩殑mod榪?
綆楋紝鏁堢巼鍙互鎻愰珮60%銆?br>
浣嶈繍綆楃殑綆鍗曞簲鐢?br> 鏈夋椂鎴戜滑鐨勭▼搴忛渶瑕佷竴涓妯′笉澶х殑Hash琛ㄦ潵璁板綍鐘舵併傛瘮濡傦紝鍋氭暟
鐙椂鎴戜滑闇瑕?7涓狧ash琛ㄦ潵緇熻姣忎竴琛屻佹瘡涓鍒楀拰姣忎竴涓皬涔?jié)瀹牸閲屽凡缁忔湁鍝簺鏁颁簡銆傛鏃訛紝鎴戜滑鍙互鐢?7涓皬浜?^9鐨勬暣鏁拌繘琛岃褰曘備緥濡傦紝涓涓彧濉?
浜?鍜?鐨勫皬涔?jié)瀹牸灏辩敤鏁板?8琛ㄧず錛堜簩榪涘埗涓?00010010錛夛紝鑰屾煇涓琛岀殑鐘舵佷負511鍒欒〃紺鴻繖涓琛屽凡緇忓~婊°傞渶瑕佹敼鍙樼姸鎬佹椂鎴戜滑涓嶉渶瑕佹妸榪欎釜鏁拌漿
鎴愪簩榪涘埗淇敼鍚庡啀杞洖鍘伙紝鑰屾槸鐩存帴榪涜浣嶆搷浣溿傚湪鎼滅儲鏃訛紝鎶婄姸鎬佽〃紺烘垚鏁存暟鍙互鏇村ソ鍦拌繘琛屽垽閲嶇瓑鎿嶄綔銆?a target="_blank">榪欓亾棰?/a>鏄湪鎼滅儲涓嬌鐢ㄤ綅榪愮畻鍔犻熺殑緇忓吀渚嬪瓙銆備互鍚庢垜浠細鐪嬪埌鏇村鐨勪緥瀛愩?br> 涓嬮潰鍒椾婦浜嗕竴浜涘父瑙佺殑
浜岃繘鍒朵綅鐨勫彉鎹㈡搷浣溿?br>
鍔熻兘 | 紺轟緥 | 浣嶈繍綆?br>----------------------+---------------------------+--------------------
鍘?
鎺夋渶鍚庝竴浣?nbsp; | (101101->10110) | x shr 1
鍦ㄦ渶鍚庡姞涓涓?
0 | (101101->1011010) | x shl 1
鍦ㄦ渶鍚庡姞涓涓? |
(101101->1011011) | x shl 1+1
鎶婃渶鍚庝竴浣嶅彉鎴? |
(101100->101101) | x or 1
鎶婃渶鍚庝竴浣嶅彉鎴? |
(101101->101100) | x or 1-1
鏈鍚庝竴浣嶅彇鍙?nbsp; |
(101101->101100) | x xor 1
鎶婂彸鏁扮k浣嶅彉鎴? |
(101001->101101,k=3) | x or (1 shl (k-1))
鎶婂彸鏁扮k浣嶅彉鎴? |
(101101->101001,k=3) | x and not (1 shl (k-1))
鍙蟲暟絎琸浣嶅彇
鍙?nbsp; | (101001->101101,k=3) | x xor (1 shl (k-1))
鍙栨湯涓?
浣?nbsp; | (1101101->101) | x and 7
鍙栨湯k
浣?nbsp; | (1101101->1101,k=5) | x and (1 shl k-1)
鍙栧彸
鏁扮k浣?nbsp; | (1101101->1,k=4) | x shr (k-1) and 1
鎶婃湯k
浣嶅彉鎴? | (101001->101111,k=4) | x or (1 shl k-1)
鏈玨浣嶅彇
鍙?nbsp; | (101001->100110,k=4) | x xor (1 shl k-1)
鎶婂彸杈硅繛
緇殑1鍙樻垚0 | (100101111->100100000) | x and (x+1)
鎶婂彸璧風(fēng)涓涓?鍙樻垚
1 | (100101111->100111111) | x or (x+1)
鎶婂彸杈硅繛緇殑0鍙樻垚1 |
(11011000->11011111) | x or (x-1)
鍙栧彸杈硅繛緇殑1 |
(100101111->1111) | (x xor (x+1)) shr 1
鍘繪帀鍙寵搗絎竴涓?鐨勫乏杈?|
(100101000->1000) | x and (x xor (x-1))
鏈鍚庤繖涓涓湪鏍?wèi)鐘舵暟缁?
涓細鐢ㄥ埌銆?br>
Pascal鍜孋涓殑16榪涘埗琛ㄧず
Pascal涓渶瑕佸湪16榪涘埗鏁板墠鍔?絎﹀彿琛ㄧず錛孋涓渶瑕佸湪鍓嶉潰鍔?
0x鏉ヨ〃紺恒傝繖涓互鍚庢垜浠細緇忓父鐢ㄥ埌銆?br>
鏁存暟綾誨瀷鐨勫偍瀛?br> 鎴戜滑鍓嶉潰鎵璇寸殑浣嶈繍綆楅兘娌℃湁娑夊強璐熸暟錛岄兘鍋囪榪欎簺榪愮畻鏄湪
unsigned/word綾誨瀷錛堝彧鑳借〃紺烘鏁扮殑鏁村瀷錛変笂榪涜鎿嶄綔銆備絾璁$畻鏈哄浣曞鐞嗘湁姝h礋絎﹀彿鐨勬暣鏁扮被鍨嬪憿錛熶笅闈袱涓▼搴忛兘鏄冨療16浣嶆暣鏁扮殑鍌ㄥ瓨鏂瑰紡
錛堝彧鏄璦涓嶅悓錛夈?br>var
a,b:integer;
begin
a:=$0000;
b:=$0001;
write(a,' ',b,' ');
a:=$FFFE;
b:=$FFFF;
write(a,' ',b,' ');
a:=$7FFF;
b:=$8000;
writeln(a,'
',b);
end.#include <stdio.h>
int main()
{
short
int a, b;
a = 0×0000;
b = 0×0001;
printf( "%d %d
", a, b );
a = 0xFFFE;
b = 0xFFFF;
printf( "%d %d
", a, b );
a = 0×7FFF;
b = 0×8000;
printf( "%d
%d\n", a, b );
return 0;
}
涓や釜紼嬪簭鐨勮緭鍑哄潎涓? 1 -2 -1
32767
-32768銆傚叾涓墠涓や釜鏁版槸鍐呭瓨鍊兼渶灝忕殑鏃跺欙紝涓棿涓や釜鏁板垯鏄唴瀛樺兼渶澶х殑鏃跺欙紝鏈鍚庤緭鍑虹殑涓や釜鏁版槸姝f暟涓庤礋鏁扮殑鍒嗙晫澶勩傜敱姝や綘鍙互娓呮鍦扮湅鍒拌綆楁満鏄?
濡備綍鍌ㄥ瓨涓涓暣鏁扮殑錛氳綆楁満鐢?0000鍒?7FFF渚濇琛ㄧず0鍒?2767鐨勬暟錛屽墿涓嬬殑$8000鍒?FFFF渚濇琛ㄧず-32768鍒?1鐨勬暟銆?2浣?
鏈夌鍙鋒暣鏁扮殑鍌ㄥ瓨鏂瑰紡涔熸槸綾諱技鐨勩傜◢鍔犳敞鎰忎綘浼氬彂鐜幫紝浜岃繘鍒剁殑絎竴浣嶆槸鐢ㄦ潵琛ㄧず姝h礋鍙風(fēng)殑錛?琛ㄧず姝o紝1琛ㄧず璐熴傝繖閲屾湁涓涓棶棰橈細0鏈潵鏃笉鏄鏁幫紝涔熶笉鏄?
璐熸暟錛屼絾瀹冨崰鐢ㄤ簡$0000鐨勪綅緗紝鍥犳鏈夌鍙風(fēng)殑鏁存暟綾誨瀷鑼冨洿涓鏁頒釜鏁版瘮璐熸暟灝戜竴涓傚涓涓湁絎﹀彿鐨勬暟榪涜not榪愮畻鍚庯紝鏈楂樹綅鐨勫彉鍖栧皢瀵艱嚧姝h礋棰犲掞紝
騫朵笖鏁扮殑緇濆鍊間細宸?銆備篃灝辨槸璇達紝not a瀹為檯涓婄瓑浜?a-1銆傝繖縐嶆暣鏁板偍瀛樻柟寮忓彨鍋?#8220;琛ョ爜”銆?br>
鏈鍚庤繕鏈変袱鍙ヨ瘽
Matrix67
鍘熷垱
杞創(chuàng)璇鋒敞鏄庡嚭澶?br>
浣?
榪愮畻綆浠嬪強瀹炵敤鎶宸э紙浜岋級錛氳繘闃剁瘒(1)
浜岃繘鍒朵腑鐨?鏈夊鏁頒釜榪樻槸鍋舵暟涓?br> 鎴戜滑鍙互鐢ㄤ笅闈㈢殑浠g爜鏉ヨ綆?
涓涓?2浣嶆暣鏁扮殑浜岃繘鍒朵腑1鐨勪釜鏁扮殑濂囧伓鎬э紝褰撹緭鍏ユ暟鎹殑浜岃繘鍒惰〃紺洪噷鏈夊伓鏁頒釜鏁板瓧1鏃剁▼搴忚緭鍑?錛屾湁濂囨暟涓垯杈撳嚭1銆備緥濡傦紝1314520鐨勪簩榪涘埗
101000000111011011000涓湁9涓?錛屽垯x=1314520鏃剁▼搴忚緭鍑?銆?br>var
i,x,c:longint;
begin
readln(x);
c:=0;
for i:=1 to
32 do
begin
c:=c + x and 1;
x:=x shr 1;
end;
writeln( c and 1 );
end.
浣嗚繖鏍風(fēng)殑鏁堢巼騫朵笉楂橈紝浣嶈繍綆楃殑紲炲涔嬪榪?
娌℃湁浣撶幇鍑烘潵銆?br> 鍚屾牱鏄垽鏂簩榪涘埗涓?鐨勪釜鏁扮殑濂囧伓鎬э紝涓嬮潰榪欐浠g爜灝卞己浜嗐備綘鑳界湅鍑鴻繖涓唬鐮佺殑鍘熺悊鍚楋紵var
x:longint;
begin
readln(x);
x:=x xor (x shr 1);
x:=x xor (x shr 2);
x:=x xor (x shr 4);
x:=x xor (x shr 8);
x:=x xor (x shr 16);
writeln(x and 1);
end.
涓轟簡璇存槑
涓婇潰榪欐浠g爜鐨勫師鐞嗭紝鎴戜滑榪樻槸鎷?314520鍑烘潵璇翠簨銆?314520鐨勪簩榪涘埗涓?01000000111011011000錛岀涓嬈″紓鎴栨搷浣滅殑緇撴灉濡?
涓嬶細
00000000000101000000111011011000
XOR 0000000000010100000011101101100
---------------------------------------
00000000000111100000100110110100
寰?
鍒扮殑緇撴灉鏄竴涓柊鐨勪簩榪涘埗鏁幫紝鍏朵腑鍙寵搗絎琲浣嶄笂鐨勬暟琛ㄧず鍘熸暟涓i鍜宨+1浣嶄笂鏈夊鏁頒釜1榪樻槸鍋舵暟涓?銆傛瘮濡傦紝鏈鍙寵竟閭d釜0琛ㄧず鍘熸暟鏈袱浣嶆湁鍋舵暟涓?錛屽彸
璧風(fēng)3浣嶄笂鐨?灝辮〃紺哄師鏁扮殑榪欎釜浣嶇疆鍜屽墠涓涓綅緗腑鏈夊鏁頒釜1銆傚榪欎釜鏁拌繘琛岀浜屾寮傛垨鐨勭粨鏋滃涓嬶細
00000000000111100000100110110100
XOR
000000000001111000001001101101
---------------------------------------
00000000000110011000101111011001
緇?
鏋滈噷鐨勬瘡涓?琛ㄧず鍘熸暟鐨勮浣嶇疆鍙婂叾鍓嶉潰涓変釜浣嶇疆涓叡鏈夊鏁頒釜1錛屾瘡涓?灝辮〃紺哄師鏁板搴旂殑鍥涗釜浣嶇疆涓婂叡鍋舵暟涓?銆備竴鐩村仛鍒扮浜旀寮傛垨緇撴潫鍚庯紝寰楀埌鐨勪簩榪涘埗鏁?
鐨勬渶鏈綅灝辮〃紺烘暣涓?2浣嶆暟閲屾湁澶氬皯涓?錛岃繖灝辨槸鎴戜滑鏈緇堟兂瑕佺殑絳旀銆?br>
璁$畻浜岃繘鍒朵腑鐨?鐨勪釜鏁?br> 鍚屾牱鍋囪x鏄竴涓?
32浣嶆暣鏁般傜粡榪囦笅闈簲嬈¤祴鍊煎悗錛寈鐨勫煎氨鏄師鏁扮殑浜岃繘鍒惰〃紺轟腑鏁板瓧1鐨勪釜鏁般傛瘮濡傦紝鍒濆鏃秞涓?314520錛堢綉鍙嬫姄鐙傦細鑳戒笉鑳芥崲涓涓暟鍟婏級錛岄偅涔堟渶鍚?
x灝卞彉鎴愪簡9錛屽畠琛ㄧず1314520鐨勪簩榪涘埗涓湁9涓?銆?br>x := (x and $55555555) + ((x shr 1)
and $55555555);
x := (x and $33333333) + ((x shr 2) and $33333333);
x := (x and $0F0F0F0F) + ((x shr 4) and $0F0F0F0F);
x := (x and
$00FF00FF) + ((x shr 8) and $00FF00FF);
x := (x and $0000FFFF) +
((x shr 16) and $0000FFFF);
涓轟簡渚夸簬瑙h錛屾垜浠笅闈粎璇存槑榪欎釜紼嬪簭鏄浣曞涓涓?浣嶆暣鏁拌繘
琛屽鐞嗙殑銆傛垜浠嬁鏁板瓧211錛堟垜浠彮鏌怣M鐨勭敓鏃ワ級鏉ュ紑鍒銆?11鐨勪簩榪涘埗涓?1010011銆?br>
+---+---+---+---+---+---+---+---+
|
1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | <---鍘熸暟
+---+---+---+---+---+---+---+---+
| 1
0 | 0 1 | 0 0 | 1 0 | <---絎竴嬈¤繍綆楀悗
+-------+-------+-------+-------+
| 0
0 1 1 | 0 0 1 0 | <---絎簩嬈¤繍綆楀悗
+---------------+---------------+
| 0
0 0 0 0 1 0 1 | <---絎笁嬈¤繍綆楀悗錛屽緱鏁頒負5
+-------------------------------+
鏁?
涓▼搴忔槸涓涓垎娌葷殑鎬濇兂銆傜涓嬈℃垜浠妸姣忕浉閭?cè)潥勪袱浣嶅姞钃v鏉ワ紝寰楀埌姣忎袱浣嶉噷1鐨勪釜鏁幫紝姣斿鍓嶄袱浣?0灝辮〃紺哄師鏁扮殑鍓嶄袱浣嶆湁2涓?銆傜浜屾鎴戜滑緇х畫涓や袱鐩?
鍔狅紝10+01=11錛?0+10=10錛屽緱鍒扮殑緇撴灉鏄?0110010錛屽畠琛ㄧず鍘熸暟鍓?浣嶆湁3涓?錛屾湯4浣嶆湁2涓?銆傛渶鍚庝竴嬈℃垜浠妸0011鍜?010
鍔犺搗鏉ワ紝寰楀埌鐨勫氨鏄暣涓簩榪涘埗涓?鐨勪釜鏁般傜▼搴忎腑宸у鍦頒嬌鐢ㄥ彇浣嶅拰鍙崇Щ錛屾瘮濡傜浜岃涓?33333333鐨勪簩榪涘埗涓?0110011001100….錛岀敤
瀹冨拰x鍋歛nd榪愮畻灝辯浉褰撲簬浠?涓哄崟浣嶉棿闅斿彇鏁般俿hr鐨勪綔鐢ㄥ氨鏄鍔犳硶榪愮畻鐨勭浉鍚屾暟浣嶅榻愩?br>
浜屽垎鏌ユ壘32浣嶆暣鏁扮殑鍓嶅0涓暟
榪?
閲岀敤鐨凜璇█錛屾垜鐩存帴Copy鐨凥acker's
Delight涓婄殑浠g爜銆傝繖孌典唬鐮佸啓鎴怌瑕佸ソ鐪嬩簺錛屽啓鎴怭ascal鐨勮瘽浼氬嚭鐜板緢澶歜egin鍜宔nd錛屾悶寰椾唬鐮佸緢闅劇湅銆傜▼搴忔濇兂鏄簩鍒嗘煡鎵撅紝搴旇寰堢畝
鍗曪紝鎴戝氨涓嶇粏璇翠簡銆?br>int nlz(unsigned x)
{
int n;
if (x
== 0) return(32);
n = 1;
if ((x >> 16) == 0) {n = n
+16; x = x <<16;}
if ((x >> 24) == 0) {n = n + 8; x = x
<< 8;}
if ((x >> 28) == 0) {n = n + 4; x = x <<
4;}
if ((x >> 30) == 0) {n = n + 2; x = x << 2;}
n = n - (x >> 31);
return n;
}
鍙敤浣嶈繍綆楁潵鍙?
緇濆鍊?br> 榪欐槸涓涓潪甯告湁瓚g殑闂銆傚ぇ瀹跺厛鑷繁鎯蟲兂鍚э紝Ctrl+A鏄劇ず絳旀銆?br> 絳旀錛氬亣璁緓涓?2浣嶆暣鏁幫紝鍒檟 xor
(not (x shr 31) + 1) + x shr 31鐨勭粨鏋滄槸x鐨勭粷瀵瑰?br> x shr
31鏄簩榪涘埗鐨勬渶楂樹綅錛屽畠鐢ㄦ潵琛ㄧずx鐨勭鍙楓傚鏋滃畠涓?錛坸涓烘錛夛紝鍒檔ot (x shr 31) +
1絳変簬$00000000錛屽紓鎴栦換浣曟暟緇撴灉閮戒笉鍙橈紱濡傛灉鏈楂樹綅涓?錛坸涓鴻礋錛夛紝鍒檔ot (x shr 31) +
1絳変簬$FFFFFFFF錛寈寮傛垨瀹冪浉褰撲簬鎵鏈夋暟浣嶅彇鍙嶏紝寮傛垨瀹屽悗鍐嶅姞涓銆?br>
楂樹綆浣嶄氦鎹?br> 榪欎釜棰?/a>瀹為檯涓婃槸鎴戝嚭鐨勶紝鍋氫負瀛︽牎鍐呴儴NOIp妯℃嫙璧涚殑絎竴棰樸傞鐩槸榪欐牱錛?br>
緇欏嚭涓涓皬浜?^32鐨勬鏁存暟銆傝繖涓暟鍙互鐢ㄤ竴涓?2浣嶇殑浜岃繘鍒舵暟琛ㄧず錛堜笉瓚?2浣嶇敤0琛ヨ凍錛夈傛垜浠О榪欎釜浜岃繘
鍒舵暟鐨勫墠16浣嶄負“楂樹綅”錛屽悗16浣嶄負“浣庝綅”銆傚皢瀹冪殑楂樹綆浣嶄氦鎹紝鎴戜滑鍙互寰楀埌涓涓柊鐨勬暟銆傝瘯闂繖涓柊鐨勬暟鏄灝戯紙鐢ㄥ崄榪涘埗琛ㄧず錛夈?br>銆銆渚嬪錛?
鏁?314520鐢ㄤ簩榪涘埗琛ㄧず涓?000 0000 0001 0100 0000 1110 1101
1000錛堟坊鍔犱簡11涓墠瀵?琛ヨ凍涓?2浣嶏級錛屽叾涓墠16浣嶄負楂樹綅錛屽嵆0000 0000 0001 0100錛涘悗16浣嶄負浣庝綅錛屽嵆0000 1110
1101 1000銆傚皢瀹冪殑楂樹綆浣嶈繘琛屼氦鎹紝鎴戜滑寰楀埌浜嗕竴涓柊鐨勪簩榪涘埗鏁?000 1110 1101 1000 0000 0000 0001
0100銆傚畠鍗蟲槸鍗佽繘鍒剁殑249036820銆?
褰撴椂鍑犱箮娌℃湁浜烘兂鍒扮敤涓鍙ヤ綅鎿嶄綔鏉ヤ唬鏇垮啑闀跨殑紼嬪簭銆備嬌鐢ㄤ綅榪愮畻鐨勮瘽涓ゅ彞璇濆氨瀹屼簡銆?br>var
n:dword;
begin
readln( n );
writeln( (n shr 16) or
(n shl 16) );
end.
鑰屼簨瀹炰笂錛孭ascal鏈変竴涓郴緇熷嚱鏁皊wap鐩存帴灝卞彲浠ョ敤銆?br>
浜?
榪涘埗閫嗗簭
涓嬮潰鐨勭▼搴忚鍏ヤ竴涓?2浣嶆暣鏁板茍杈撳嚭瀹冪殑浜岃繘鍒跺掑簭鍚庢墍琛ㄧず鐨勬暟銆?br> 杈撳叆錛?
1314520 錛堜簩榪涘埗涓?0000000000101000000111011011000錛?br> 杈撳嚭錛?
460335104 錛堜簩榪涘埗涓?0011011011100000010100000000000錛?br>var
x:dword;
begin
readln(x);
x := (x and $55555555) shl 1
or (x and $AAAAAAAA) shr 1;
x := (x and $33333333) shl 2 or (x
and $CCCCCCCC) shr 2;
x := (x and $0F0F0F0F) shl 4 or (x and
$F0F0F0F0) shr 4;
x := (x and $00FF00FF) shl 8 or (x and
$FF00FF00) shr 8;
x := (x and $0000FFFF) shl 16 or (x and
$FFFF0000) shr 16;
writeln(x);
end.
瀹冪殑鍘熺悊鍜屽垰鎵嶆眰浜岃繘鍒朵腑1
鐨勪釜鏁伴偅涓緥棰樻槸澶ц嚧鐩稿悓鐨勩傜▼搴忛鍏堜氦鎹㈡瘡鐩擱偦涓や綅涓婄殑鏁幫紝浠ュ悗鎶婁簰鐩鎬氦鎹㈣繃鐨勬暟鐪嬫垚涓涓暣浣擄紝緇х畫榪涜浠?浣嶄負鍗曚綅銆佷互4浣嶄負鍗曚綅鐨勫乏鍙沖鎹㈡搷浣溿傛垜
浠啀嬈$敤8浣嶆暣鏁?11鏉ユ紨紺虹▼搴忔墽琛岃繃紼嬶細
+---+---+---+---+---+---+---+---+
| 1 | 1 | 0
| 1 | 0 | 0 | 1 | 1 | <---鍘熸暟
+---+---+---+---+---+---+---+---+
| 1
1 | 1 0 | 0 0 | 1 1 | <---絎竴嬈¤繍綆楀悗
+-------+-------+-------+-------+
| 1
0 1 1 | 1 1 0 0 | <---絎簩嬈¤繍綆楀悗
+---------------+---------------+
| 1
1 0 0 1 0 1 1 | <---絎笁嬈¤繍綆楀悗
+-------------------------------+
Copyright
涔熷緢寮?br>writeln('Matrix' , 42 XOR 105 , '鍘熷垱錛岃漿璐磋娉ㄦ槑鍑哄');
n鐨囧悗闂浣嶈繍綆楃増
n鐨囧悗闂鏄暐鎴戝氨涓嶈浜嗗惂錛屽緙栫▼鐨勮偗瀹氶兘瑙佽繃銆備笅闈?
鐨勫崄澶氳浠g爜鏄痭鐨囧悗闂鐨勪竴涓珮鏁堜綅榪愮畻紼嬪簭錛岀湅鍒拌繃鐨勪漢閮藉じ瀹冪墰銆傚垵濮嬫椂錛寀pperlim:=(1 shl
n)-1銆備富紼嬪簭璋冪敤test(0,0,0)鍚巗um鐨勫煎氨鏄痭鐨囧悗鎬葷殑瑙f暟銆傛嬁榪欎釜鍘諱氦USACO錛?.3s錛屾毚鐖姐?br>procedure
test(row,ld,rd:longint);
var
pos,p:longint;
begin
{
1} if row<>upperlim then
{ 2} begin
{ 3}
pos:=upperlim and not (row or ld or rd);
{ 4} while pos<>0
do
{ 5} begin
{ 6} p:=pos and -pos;
{
7} pos:=pos-p;
{ 8} test(row+p,(ld+p)shl 1,(rd+p)shr
1);
{ 9} end;
{10} end
{11} else inc(sum);
end;
涔?
涓鐪嬩技涔庡畬鍏ㄦ懜涓嶇潃澶磋剳錛屽疄闄呬笂鏁翠釜紼嬪簭鏄潪甯稿鏄撶悊瑙g殑銆傝繖閲岃繕鏄緩璁ぇ瀹惰嚜宸卞崟姝ヨ繍琛屼竴鎺㈢┒绔燂紝瀹炲湪娌$爺絀跺嚭鏉ュ啀鐪嬩笅闈㈢殑瑙h銆?br>

鍜?
鏅氱畻娉曚竴鏍鳳紝榪欐槸涓涓掑綊榪囩▼錛岀▼搴忎竴琛屼竴琛屽湴瀵繪壘鍙互鏀劇殗鍚庣殑鍦版柟銆傝繃紼嬪甫涓変釜鍙傛暟錛宺ow銆乴d鍜宺d錛屽垎鍒〃紺哄湪綰靛垪鍜屼袱涓瑙掔嚎鏂瑰悜鐨勯檺鍒舵潯浠?
涓嬭繖涓琛岀殑鍝簺鍦版柟涓嶈兘鏀俱傛垜浠互6×6鐨勬鐩樹負渚嬶紝鐪嬬湅紼嬪簭鏄庝箞宸ヤ綔鐨勩傚亣璁劇幇鍦ㄥ凡緇忛掑綊鍒扮鍥涘眰錛屽墠涓夊眰鏀劇殑瀛愬凡緇忔爣鍦ㄥ乏鍥句笂浜嗐傜孩鑹層佽摑鑹插拰緇胯壊
鐨勭嚎鍒嗗埆琛ㄧず涓変釜鏂瑰悜涓婃湁鍐茬獊鐨勪綅緗紝浣嶄簬璇ヨ涓婄殑鍐茬獊浣嶇疆灝辯敤row銆乴d鍜宺d涓殑1鏉ヨ〃紺恒傛妸瀹冧滑涓変釜騫惰搗鏉ワ紝寰楀埌璇ヨ鎵鏈夌殑紱佷綅錛屽彇鍙嶅悗灝卞緱鍒版墍
鏈夊彲浠ユ斁鐨勪綅緗紙鐢╬os鏉ヨ〃紺猴級銆傚墠闈㈣榪?a鐩稿綋浜巒ot a + 1錛岃繖閲岀殑浠g爜絎?琛屽氨鐩稿綋浜巔os and (not pos +
1)錛屽叾緇撴灉鏄彇鍑烘渶鍙寵竟鐨勯偅涓?銆傝繖鏍鳳紝p灝辮〃紺鴻琛岀殑鏌愪釜鍙互鏀懼瓙鐨勪綅緗紝鎶婂畠浠巔os涓Щ闄ゅ茍閫掑綊璋冪敤test榪囩▼銆傛敞鎰忛掑綊璋冪敤鏃朵笁涓弬鏁扮殑鍙?
鍖栵紝姣忎釜鍙傛暟閮藉姞涓婁簡涓涓浣嶏紝浣嗕袱涓瑙掔嚎鏂瑰悜鐨勭浣嶅涓嬩竴琛岀殑褰卞搷闇瑕佸鉤縐諱竴浣嶃傛渶鍚庯紝濡傛灉閫掑綊鍒版煇涓椂鍊欏彂鐜皉ow=111111浜嗭紝璇存槑鍏釜鐨囧悗
鍏ㄦ斁榪涘幓浜嗭紝姝ゆ椂紼嬪簭浠庣1琛岃煩鍒扮11琛岋紝鎵懼埌鐨勮В鐨勪釜鏁板姞涓銆?br>
~~~~====~~~~===== 鍗庝附鐨勫垎鍓茬嚎
=====~~~~====~~~~
Gray鐮?br> 鍋囧鎴戞湁4涓綔鍦ㄧ殑GF錛屾垜闇瑕佸喅瀹氭渶緇堝埌搴曞拰璋佸湪涓璧楓備竴涓畝鍗曠殑鍔炴硶
灝辨槸錛屼緷嬈″拰姣忎釜MM浜ゅ線涓孌墊椂闂達紝鏈鍚庨夋嫨緇欐垜甯︽潵鐨?#8220;婊℃剰搴?#8221;鏈澶х殑MM銆備絾鐪嬩簡dd鐗涚殑鐞嗚鍚庯紝
浜嬫儏寮濮嬪彉寰楀鏉備簡錛氭垜鍙互閫夋嫨鍜屽涓狹M鍦ㄤ竴璧楓傝繖鏍鳳紝闇瑕佽冩牳鐨勭姸鎬佸彉鎴愪簡2^4=16縐嶏紙褰撶劧鍖呮嫭0000榪欎竴鐘舵侊紝鍥犱負鎴戞湁鍙兘鏄幓鐠冿級銆傜幇鍦ㄧ殑
闂灝辨槸錛屾垜搴旇鐢ㄤ粈涔堥『搴忔潵閬嶅巻榪?6縐嶇姸鎬佸憿錛?br> 浼犵粺鐨勫仛娉曟槸錛岀敤浜岃繘鍒舵暟鐨勯『搴忔潵閬嶅巻鎵鏈夊彲鑳界殑緇勫悎銆備篃灝辨槸璇達紝鎴戦渶瑕佷互
0000->0001->0010->0011->0100->…->1111榪欐牱鐨勯『搴忓姣忕鐘舵佽繘琛屾祴璇曘傝繖涓?
欏哄簭寰堜笉縐戝錛屽緢澶氭椂鍊欑姸鎬佺殑杞Щ閮藉緢鑰楁椂銆傛瘮濡備粠0111鍒?000鏃舵垜闇瑕佹殏鏃剁敥鎺夊綋鍓嶆墍鏈夌殑3涓狹M錛岀劧鍚庡幓鎶婄4涓狹M銆傚悓鏃舵敼鍙樻墍鏈塎M涓庢垜鐨?
鍏崇郴鏄竴浠朵綍絳夊法澶х殑宸ョ▼鍟娿傚洜姝わ紝鎴戝笇鏈涚煡閬擄紝鏄惁鏈変竴縐嶆柟娉曞彲浠ヤ嬌寰楋紝浠庢病鏈塎M榪欎竴鐘舵佸嚭鍙戯紝姣忔鍙敼鍙樻垜鍜屼竴涓狹M鐨勫叧緋伙紙榪芥垨鑰呯敥錛夛紝15嬈℃搷
浣滃悗鎭板ソ閬嶅巻瀹屾墍鏈夊彲鑳界殑緇勫悎錛堟渶緇堢姸鎬佷笉涓瀹氭槸1111錛夈傚ぇ瀹惰嚜宸卞厛璇曚竴璇曠湅琛屼笉琛屻?br> 瑙e喅榪欎釜闂鐨勬柟娉曞緢宸у銆傛垜浠潵璇存槑錛屽亣濡傛垜
浠凡緇忕煡閬撲簡n=2鏃剁殑鍚堟硶閬嶅巻欏哄簭錛屾垜浠浣曞緱鍒皀=3鐨勯亶鍘嗛『搴忋傛樉鐒訛紝n=2鐨勯亶鍘嗛『搴忓涓嬶細
00
01
11
10
浣?
鍙兘宸茬粡鎯沖埌浜嗗浣曟妸涓婇潰鐨勯亶鍘嗛『搴忔墿灞曞埌n=3鐨勬儏鍐點俷=3鏃朵竴鍏辨湁8縐嶇姸鎬侊紝鍏朵腑鍓嶉潰4涓妸n=2鐨勯亶鍘嗛『搴忕収鎼笅鏉ワ紝鐒跺悗鎶婂畠浠縐扮炕鎶樹笅鍘誨茍鍦?
鏈鍓嶉潰鍔犱笂1浣滀負鍚庨潰4涓姸鎬侊細
000
001
011
010 ↑
--------
110 ↓
111
101
100
鐢?
榪欑鏂規(guī)硶寰楀埌鐨勯亶鍘嗛『搴忔樉鐒剁鍚堣姹傘傞鍏堬紝涓婇潰8涓姸鎬佹伆濂芥槸n=3鏃剁殑鎵鏈?縐嶇粍鍚堬紝鍥犱負瀹冧滑鏄湪n=2鐨勫叏閮ㄥ洓縐嶇粍鍚堢殑鍩虹涓婅冭檻閫変笉閫夌3涓厓绱?
鎵寰楀埌鐨勩傜劧鍚庢垜浠湅鍒幫紝鍚庨潰涓鍗婄殑鐘舵佸簲璇ュ拰鍓嶉潰涓鍗婁竴鏍鋒弧瓚?#8220;鐩擱偦鐘舵侀棿浠呬竴浣嶄笉鍚?#8221;鐨勯檺鍒訛紝鑰?#8220;闀滈潰”澶勫垯鏄渶鍓嶉潰閭d竴浣嶆暟涓嶅悓銆傚啀嬈$炕鎶樹笁闃墮亶鍘?
欏哄簭錛屾垜浠氨寰楀埌浜嗗垰鎵嶇殑闂鐨勭瓟妗堬細
0000
0001
0011
0010
0110
0111
0101
0100
1100
1101
1111
1110
1010
1011
1001
1000
榪?
縐嶉亶鍘嗛『搴忎綔涓轟竴縐嶇紪鐮佹柟寮忓瓨鍦紝鍙仛Gray鐮侊紙鍐欎釜涓枃璁╄湗铔涙潵鎶擄細鏍奸浄鐮侊級銆傚畠鐨勫簲鐢ㄨ寖鍥村緢騫褲傛瘮濡傦紝n闃剁殑Gray鐮佺浉褰撲簬鍦╪緇寸珛鏂逛綋涓婄殑
Hamilton鍥炶礬錛屽洜涓烘部鐫绔嬫柟浣撲笂鐨勮竟璧頒竴姝ワ紝n緇村潗鏍囦腑鍙細鏈変竴涓兼敼鍙樸傚啀姣斿錛孏ray鐮佸拰Hanoi濉旈棶棰樼瓑浠楓侴ray鐮佹敼鍙樼殑鏄鍑犱釜
鏁幫紝Hanoi濉斿氨璇ョЩ鍔ㄥ摢涓洏瀛愩傛瘮濡傦紝3闃剁殑Gray鐮佹瘡嬈℃敼鍙樼殑鍏冪礌鎵鍦ㄤ綅緗緷嬈′負1-2-1-3-1-2-1錛岃繖姝eソ鏄?闃禜anoi濉旀瘡嬈$Щ鍔?
鐩樺瓙緙栧彿銆傚鏋滄垜浠彲浠ュ揩閫熸眰鍑篏ray鐮佺殑絎琻涓暟鏄灝戯紝鎴戜滑灝卞彲浠ヨ緭鍑轟換鎰忔鏁板悗Hanoi濉旂殑縐誨姩姝ラ銆傜幇鍦ㄦ垜鍛婅瘔浣狅紝Gray鐮佺殑絎琻涓暟錛堜粠
0綆楄搗錛夋槸n xor (n shr 1)錛屼綘鑳芥兂鍑烘潵榪欐槸涓轟粈涔堝悧錛熷厛鑷繁鎯蟲兂鍚с?br>
涓嬮潰鎴戜滑鎶婁簩榪涘埗鏁板拰Gray鐮侀兘鍐欏湪涓?
闈紝鍙互鐪嬪埌宸﹁竟鐨勬暟寮傛垨鑷韓鍙崇Щ鐨勭粨鏋滃氨絳変簬鍙寵竟鐨勬暟銆?br>
浜岃繘鍒舵暟 Gray鐮?br> 000 000
001 001
010 011
011 010
100
110
101 111
110 101
111 100
浠?
浜岃繘鍒舵暟鐨勮搴︾湅錛?#8220;闀滃儚”浣嶇疆涓婄殑鏁板嵆鏄鍘熸暟榪涜not榪愮畻鍚庣殑緇撴灉銆傛瘮濡傦紝絎?涓暟010鍜屽掓暟絎?涓暟101鐨勬瘡涓浣嶉兘姝eソ鐩稿弽銆傚亣璁捐繖涓や釜鏁板垎
鍒負x鍜寉錛岄偅涔坸 xor (x shr 1)鍜寉 xor (y shr
1)鐨勭粨鏋滃彧鏈変竴鐐逛笉鍚岋細鍚庤呯殑棣栦綅鏄?錛屽墠鑰呯殑棣栦綅鏄?銆傝岃繖姝eソ鏄疓ray鐮佺殑鐢熸垚鏂規(guī)硶銆傝繖灝辮鏄庝簡錛孏ray鐮佺殑絎琻涓暟紜疄鏄痭 xor (n
shr 1)銆?br>
浠婂勾鍥涙湀浠?a target="_blank">mashuo緇?
鎴戠湅浜?a target="_blank">榪欓亾棰?/a>錛屾槸浜岀淮鎰忎箟涓婄殑Gray鐮併傞鐩ぇ鎰忔槸璇達紝鎶?鍒?^(n+m)-1鐨勬暟鍐欐垚2^n *
2^m鐨勭煩闃碉紝浣垮緱浣嶇疆鐩擱偦涓ゆ暟鐨勪簩榪涘埗琛ㄧず鍙湁涓浣嶄箣宸傜瓟妗堝叾瀹炲緢綆鍗曪紝鎵鏈夋暟閮芥槸鐢眒浣嶇殑Gray鐮佸拰n浣岹ray鐮佹嫾鎺ヨ屾垚錛岄渶瑕佺敤宸︾Щ鎿嶄綔鍜?
or榪愮畻瀹屾垚銆傚畬鏁寸殑浠g爜濡備笅錛?br>var
x,y,m,n,u:longint;
begin
readln(m,n);
for x:=0 to 1 shl m-1 do begin
u:=(x xor (x
shr 1)) shl n; //杈撳嚭鏁扮殑宸﹁竟鏄竴涓猰浣嶇殑Gray鐮?br> for y:=0 to 1 shl n-1 do
write(u or (y xor (y shr 1)),' '); //騫朵笂涓涓猲浣岹ray鐮?br> writeln;
end;
end.
Matrix67鍘熷垱
杞創(chuàng)璇鋒敞鏄庡嚭澶?/p>
浣嶈繍綆楃畝浠嬪強瀹炵敤鎶宸э紙鍥涳級錛氬疄鎴樼瘒
涓嬮潰
鍒嗕韓鐨勬槸鎴戣嚜宸卞啓鐨勪笁涓唬鐮侊紝閲岄潰鏈変簺棰樼洰涔熸槸鎴戣嚜宸卞嚭鐨勩傝繖浜涗唬鐮侀兘鏄湪鎴戠殑Pascal鏃朵唬鍐欑殑錛屾仌涓嶆彁渚汣璇█浜嗐備唬鐮佸啓寰楀茍涓嶅ソ錛屾垜鍙槸鎯沖憡璇夊ぇ
瀹朵綅榪愮畻鍦ㄥ疄鎴樹腑鐨勫簲鐢紝鍖呮嫭浜嗘悳绱㈠拰鐘舵佸帇緙〥P鏂歸潰鐨勯鐩傚叾瀹炲ぇ瀹跺彲浠ュ湪緗戜笂鎵懼埌鏇村鐢ㄤ綅榪愮畻浼樺寲鐨勯鐩紝榪欓噷鏁寸悊鍑轟竴浜涜嚜宸卞啓鐨勪唬鐮侊紝鍙槸涓轟簡鍘?
鍒涚郴鍒楁枃绔犵殑瀹屾暣鎬с傝繖涓緋誨垪鏂囩珷鍒拌繖閲屽氨緇撴潫浜嗭紝甯屾湜澶у鑳芥湁鎵鏀惰幏銆?br> Matrix67鍘熷垱錛岃漿璐磋娉ㄦ槑鍑哄銆?br>
Problem : 璐硅В鐨勫紑鍏?br>
棰樼洰鏉ユ簮
06
騫碞OIp妯℃嫙璧涳紙涓錛?by Matrix67 絎洓棰?br>
闂鎻忚堪
浣犵帺榪?#8220;鎷夌伅”娓告垙鍚楋紵25鐩忕伅鎺掓垚涓涓?×5鐨勬柟
褰€傛瘡涓涓伅閮芥湁涓涓紑鍏籌紝娓告垙鑰呭彲浠ユ敼鍙樺畠鐨勭姸鎬併傛瘡涓姝ワ紝娓告垙鑰呭彲浠ユ敼鍙樻煇涓涓伅鐨勭姸鎬併傛父鎴忚呮敼鍙樹竴涓伅鐨勭姸鎬佷細浜х敓榪為攣鍙嶅簲錛氬拰榪欎釜鐏笂涓嬪乏鍙崇浉
閭?cè)潥勭伅涔熻鐩稿簲鍦版敼鍙樺叾鐘舵併?br> 鎴戜滑鐢ㄦ暟瀛?#8220;1”琛ㄧず涓鐩忓紑鐫鐨勭伅錛岀敤鏁板瓧“0”琛ㄧず鍏崇潃鐨勭伅銆備笅闈㈣繖縐嶇姸鎬?br>
10111
01101
10111
10000
11011
鍦?
鏀瑰彉浜嗘渶宸︿笂瑙掔殑鐏殑鐘舵佸悗灝嗗彉鎴愶細
01111
11101
10111
10000
11011
鍐?
鏀瑰彉瀹冩涓棿鐨勭伅鍚庣姸鎬佸皢鍙樻垚錛?br>
01111
11001
11001
10100
11011
緇?
瀹氫竴浜涙父鎴忕殑鍒濆鐘舵侊紝緙栧啓紼嬪簭鍒ゆ柇娓告垙鑰呮槸鍚﹀彲鑳藉湪6姝ヤ互鍐呬嬌鎵鏈夌殑鐏兘鍙樹寒銆?br>
杈撳叆鏍煎紡
絎竴琛屾湁涓涓鏁存暟n錛屼唬琛ㄦ暟
鎹腑鍏辨湁n涓緟瑙e喅鐨勬父鎴忓垵濮嬬姸鎬併?br> 浠ヤ笅鑻ュ共琛屾暟鎹垎涓簄緇勶紝姣忕粍鏁版嵁鏈?琛岋紝姣忚5涓瓧絎︺傛瘡緇勬暟鎹弿榪頒簡涓涓父鎴忕殑鍒濆鐘舵併傚悇緇勬暟
鎹棿鐢ㄤ竴涓┖琛屽垎闅斻?br> 瀵逛簬30%鐨勬暟鎹紝n<=5錛?br> 瀵逛簬100%鐨勬暟鎹紝n<=500銆?br>
杈?
鍑烘牸寮?br> 杈撳嚭鏁版嵁涓鍏辨湁n琛岋紝姣忚鏈変竴涓皬浜庣瓑浜?鐨勬暣鏁幫紝瀹冭〃紺哄浜庤緭鍏ユ暟鎹腑瀵瑰簲鐨勬父鎴忕姸鎬佹渶灝戦渶瑕佸嚑姝ユ墠鑳戒嬌鎵鏈夌伅鍙樹寒銆?br> 瀵?
浜庢煇涓涓父鎴忓垵濮嬬姸鎬侊紝鑻?姝ヤ互鍐呮棤娉曚嬌鎵鏈夌伅鍙樹寒錛岃杈撳嚭“-1”銆?br>
鏍蜂緥杈撳叆
3
00111
01011
10001
11010
11100
11101
11101
11110
11111
11111
01111
11111
11111
11111
11111
鏍?
渚嬭緭鍑?br>3
2
-1
紼嬪簭浠g爜const
BigPrime=3214567;
MaxStep=6;
type
pointer=^rec;
rec=record
v:longint;
step:integer;
next:pointer;
end;
var
total:longint;
hash:array[0..BigPrime-1]of pointer;
q:array[1..400000]of rec;
function
update(a:longint;p:integer):longint;
begin
a:=a xor (1 shl p);
if p mod 5<>0 then a:=a xor (1 shl (p-1));
if (p+1) mod
5<>0 then a:=a xor (1 shl (p+1));
if p<20 then a:=a xor
(1 shl (p+5));
if p>4 then a:=a xor (1 shl (p-5));
exit(a);
end;
function find(a:longint;step:integer):boolean;
var
now:pointer;
begin
now:=hash[a mod BigPrime];
while
now<>nil do
begin
if now^.v=a then exit(true);
now:=now^.next;
end;
new(now);
now^.v:=a;
now^.step:=step;
now^.next:=hash[a mod BigPrime];
hash[a mod BigPrime]:=now;
total:=total+1;
exit(false);
end;
procedure solve;
var
p:integer;
close:longint=0;
open:longint=1;
begin
find(1 shl 25-1,0);
q[1].v:=1 shl 25-1;
q[1].step:=0;
repeat
inc(close);
for p:=0 to 24 do
if
not find(update(q[close].v,p),q[close].step+1) and
(q[close].step+1<MaxStep) then
begin
open:=open+1;
q[open].v:=update(q[close].v,p);
q[open].step:=q[close].step+1;
end;
until close>=open;
end;
procedure
print(a:longint);
var
now:pointer;
begin
now:=hash[a
mod BigPrime];
while now<>nil do
begin
if
now^.v=a then
begin
writeln(now^.step);
exit;
end;
now:=now^.next;
end;
writeln(-1);
end;
procedure main;
var
ch:char;
i,j,n:integer;
t:longint;
begin
readln(n);
for i:=1
to n do
begin
t:=0;
for j:=1 to 25 do
begin
read(ch);
t:=t*2+ord(ch)-48;
if j mod 5=0 then
readln;
end;
print(t);
if i<n then readln;
end;
end;
begin
solve;
main;
end.
======================= 鎬?
鎰熺殑鍒嗗壊綰?nbsp; =======================
Problem : garden / 鍜孧M閫涜姳鍥?br>
棰樼洰鏉ユ簮
07騫碝atrix67鐢熸棩閭璇瘋禌 絎?
鍥涢
闂鎻忚堪
鑺卞洯璁捐寮鴻皟錛岀畝鍗曞氨鏄編銆侻atrix67甯稿幓鐨勮姳鍥湁鐫闈炲父綆鍗曠殑甯冨眬錛氳姳鍥殑鎵鏈夋櫙鐐圭殑浣嶇疆閮芥槸“瀵?
榻?#8221;浜嗙殑錛岃繖浜涙櫙鐐瑰彲浠ョ湅浣滄槸騫抽潰鍧愭爣涓婄殑鏍肩偣銆傜浉閭?cè)潥勬櫙鐐逛箣闂存湁灏忚矾鐩笜q烇紝榪欎簺灝忚礬鍏ㄩ儴騫寵浜庡潗鏍囪醬銆傛櫙鐐瑰拰灝忚礬緇勬垚浜嗕竴涓?#8220;涓嶅畬鏁寸殑緗戞牸”銆?br> 涓
涓吀鍨嬬殑鑺卞洯甯冨眬濡傚乏鍥炬墍紺恒傝姳鍥竷灞鍦?琛?鍒楃殑緗戞牸涓婏紝鑺卞洯鐨?6涓櫙鐐圭殑浣嶇疆鐢ㄧ孩鑹叉爣娉ㄥ湪浜嗗浘涓傞粦鑹茬嚎鏉¤〃紺烘櫙鐐歸棿鐨勫皬璺紝鍏朵綑鐏拌壊閮ㄥ垎瀹為檯騫朵笉
瀛樺湪銆?br> 
Matrix67
鐨勭敓鏃ラ偅澶╋紝浠栬甯︾潃浠栫殑MM鍦ㄨ姳鍥噷娓哥帺銆侻atrix67涓嶄細甯M涓ゆ緇忚繃鍚屼竴涓櫙鐐癸紝鍥犳姣忎釜鏅偣鏈澶氳娓歌涓嬈°備粬鍜屼粬鐨凪M杈硅蛋杈硅亰錛屼粬浠槸
濡傛鐨勬姇鍏ヤ互鑷翠簬浠栦滑浠庝笉浼?#8220;涓誨姩鍦版嫄寮?#8221;銆備篃灝辨槸璇達紝闄ら潪鍓嶆柟宸叉病鏈夋櫙鐐規(guī)垨鏄墠鏂圭殑鏅偣宸茬粡璁塊棶榪囷紝鍚﹀垯浠栦滑浼氫竴鐩村線鍓嶈蛋涓嬪幓銆傚綋鍓嶆柟鏅偣涓嶅瓨鍦ㄦ垨宸叉父
瑙堣繃鏃訛紝Matrix67浼氬甫MM鍙﹂変竴涓柟鍚戠戶緇墠榪涖傜敱浜庢櫙鐐逛釜鏁版湁闄愶紝璁塊棶榪囩殑鏅偣灝嗚秺鏉ヨ秺澶氾紝榪熸棭浼氬嚭鐜頒笉鑳藉啀璧扮殑鎯呭喌錛堝嵆鍥涗釜鏂瑰悜涓婄殑鐩擱偦鏅偣
閮借闂繃浜嗭級錛屾鏃朵粬浠皢緇撴潫鑺卞洯鐨勬父瑙堛侻atrix67甯屾湜鐭ラ亾浠ヨ繖縐嶆柟寮忔父瑙堣姳鍥槸鍚︽湁鍙兘閬嶅巻鎵鏈夌殑鏅偣銆侻atrix67鍙互閫夋嫨浠庝換鎰忎竴涓櫙
鐐瑰紑濮嬫父瑙堬紝浠ヤ換鎰忎竴涓櫙鐐圭粨鏉熴?br> 鍦ㄤ笂鍥炬墍紺虹殑鑺卞洯甯冨眬涓紝涓縐嶅彲鑳界殑娓歌鏂瑰紡濡傚彸鍥炬墍紺恒傝繖縐嶆祻瑙堟柟寮忎粠(1,2)鍑哄彂錛屼互(2,4)
緇撴潫錛岀粡榪囨瘡涓櫙鐐規(guī)伆濂戒竴嬈°?br>
杈撳叆鏍煎紡
絎竴琛岃緭鍏ヤ袱涓敤絀烘牸闅斿紑鐨勬鏁存暟m鍜宯錛岃〃紺鴻姳鍥甯冨眬鍦╩琛宯鍒楃殑緗戞牸涓娿?br> 浠?
涓媘琛屾瘡琛宯涓瓧絎︼紝瀛楃“0”琛ㄧず璇ヤ綅緗病鏈夋櫙鐐癸紝瀛楃“1”琛ㄧず瀵瑰簲浣嶇疆鏈夋櫙鐐廣傝繖浜涙暟瀛椾箣闂存病鏈夌┖鏍箋?br>
杈撳嚭鏍煎紡
浣?
鐨勭▼搴忛渶瑕佸鎵炬弧瓚?#8220;涓嶄富鍔ㄦ嫄寮?#8221;鎬ц川涓旈亶鍘嗘墍鏈夋櫙鐐圭殑娓歌璺嚎銆?br> 濡傛灉娌℃湁榪欐牱鐨勬父瑙堣礬綰匡紝璇瘋緭鍑轟竴琛?#8220;Impossible”錛堜笉甯﹀紩
鍙鳳紝娉ㄦ剰澶у皬鍐欙級銆?br> 濡傛灉瀛樺湪娓歌璺嚎錛岃渚濇杈撳嚭浣犵殑鏂規(guī)涓闂殑鏅偣鐨勫潗鏍囷紝姣忚杈撳嚭涓涓傚潗鏍囩殑琛ㄧず鏍煎紡涓?#8220;(x,y)”錛屼唬琛ㄧx
琛岀y鍒椼?br> 濡傛灉鏈夊縐嶆柟妗堬紝浣犲彧闇瑕佽緭鍑哄叾涓竴縐嶅嵆鍙傝瘎嫻嬬郴緇熷彲浠ュ垽鏂綘鐨勬柟妗堢殑姝g‘鎬с?br>
鏍蜂緥杈撳叆
6 4
1100
1001
1111
1100
1110
1110
鏍?
渚嬭緭鍑?br>(1,2)
(1,1)
(2,1)
(3,1)
(4,1)
(5,1)
(6,1)
(6,2)
(6,3)
(5,3)
(5,2)
(4,2)
(3,2)
(3,3)
(3,4)
(2,4)
鏁?
鎹妯?br> 瀵逛簬30%鐨勬暟鎹紝n,m<=5錛?br> 瀵逛簬100%鐨勬暟鎹紝n,m<=10銆?
紼嬪簭浠g爜錛?br>program garden;
const
dir:array[1..4,1..2]of integer=
((1,0),(0,1),(-1,0),(0,-1));
type
arr=array[1..10]of integer;
rec=record x,y:integer;end;
var
map:array[0..11,0..11]of boolean;
ans:array[1..100]of rec;
n,m,max:integer;
step:integer=1;
state:arr;
procedure
readp;
var
i,j:integer;
ch:char;
begin
readln(m,n);
for i:=1 to n do
begin
for j:=1 to m
do
begin
read(ch);
map[i,j]:=(ch='1');
inc(max,ord( map[i,j] ))
end;
readln;
end;
end;
procedure
writep;
var
i:integer;
begin
for i:=1 to step do
writeln(
'(' , ans[i].x , ',' , ans[i].y , ')' );
end;
procedure
solve(x,y:integer);
var
tx,ty,d:integer;
step_cache:integer;
state_cache:arr;
begin
step_cache:=step;
state_cache:=state;
if step=max then
begin
writep;
exit;
end;
for d:=1 to 4
do
begin
tx:=x+dir[d,1];
ty:=y+dir[d,2];
while
map[tx,ty] and ( not state[tx] and(1 shl (ty-1) )>0) do
begin
inc(step);
ans[step].x:=tx;
ans[step].y:=ty;
state[tx]:=state[tx] or ( 1 shl (ty-1) );
tx:=tx+dir[d,1];
ty:=ty+dir[d,2];
end;
tx:=tx-dir[d,1];
ty:=ty-dir[d,2];
if
(tx<>x) or (ty<>y) then solve(tx,ty);
state:=state_cache;
step:=step_cache;
end;
end;
{====main====}
var
i,j:integer;
begin
assign(input,'garden.in');
reset(input);
assign(output,'garden.out');
rewrite(output);
readp;
for i:=1 to n do
for j:=1 to m do
if map[i,j] then
begin
ans[1].x:=i;
ans[1].y:=j;
state[i]:=1
shl (j-1);
solve(i,j);
state[i]:=0;
end;
close(input);
close(output);
end.
======================= 鎬?
鎰熺殑鍒嗗壊綰?nbsp; =======================
Problem : cowfood / 鐜夌背鍦?br>
棰樼洰鏉ユ簮
USACO鏈堣禌
闂?
棰樻弿榪?br> 鍐滃か綰︾堪璐拱浜嗕竴澶勮偉娌冪殑鐭╁艦鐗у満錛屽垎鎴怣*N(1<=M<=12;
1<=N<=12)涓牸瀛愩備粬鎯沖湪閭i噷鐨勪竴浜涙牸瀛愪腑縐嶆緹庡懗鐨勭帀綾熾傞仐鎲劇殑鏄紝鏈変簺鏍煎瓙鍖哄煙鐨勫湡鍦版槸璐槧鐨勶紝涓嶈兘鑰曠銆?br> 綺炬槑
鐨勭害緲扮煡閬撳ザ鐗涗滑榪涢鏃朵笉鍠滄鍜屽埆鐨勭墰鐩擱偦錛屾墍浠ヤ竴鏃﹀湪涓涓牸瀛愪腑縐嶆鐜夌背錛岄偅涔堜粬灝變笉浼氬湪鐩擱偦鐨勬牸瀛愪腑縐嶆錛屽嵆娌℃湁涓や釜琚変腑鐨勬牸瀛愭嫢鏈夊叕鍏辮竟銆備粬榪樻病
鏈夋渶緇堢‘瀹氬摢浜涙牸瀛愯閫夋嫨縐嶆鐜夌背銆?br> 浣滀負涓涓濇兂寮鏄庣殑浜猴紝鍐滃か綰︾堪甯屾湜鑰冭檻鎵鏈夊彲琛岀殑閫夋嫨鏍煎瓙縐嶆鏂規(guī)銆傜敱浜庡お寮鏄庯紝浠栬繕鑰冭檻涓涓牸瀛?
閮戒笉閫夋嫨鐨勭妞嶆柟妗堬紒璇峰府鍔╁啘澶害緲扮‘瀹氱妞嶆柟妗堟繪暟銆?br>
杈撳叆鏍煎紡:
絎竴琛岋細涓や釜鐢ㄧ┖鏍煎垎闅旂殑鏁存暟M鍜孨
絎?
浜岃鍒扮M+1琛岋細絎琲+1琛屾弿榪扮墽鍦虹i琛屾瘡涓牸瀛愮殑鎯呭喌錛孨涓敤絀烘牸鍒嗛殧鐨勬暣鏁幫紝琛ㄧず榪欎釜鏍煎瓙鏄惁鍙互縐嶆錛?琛ㄧず鑲ユ矁鐨勩侀傚悎縐嶆錛?琛ㄧず璐槧鐨勩?
涓嶅彲縐嶆錛?br>
杈撳嚭鏍煎紡
涓涓暣鏁幫紝鍐滃か綰︾堪鍙夋嫨鐨勬柟妗堟繪暟闄や互 100,000,000 鐨勪綑鏁?br>
鏍蜂緥杈撳叆
2
3
1 1 1
0 1 0
鏍蜂緥杈撳嚭
9
鏍蜂緥璇存槑
緇欏彲浠ョ妞嶇帀綾崇殑鏍煎瓙緙?
鍙鳳細
1 2 3
4
鍙?
縐嶄竴涓牸瀛愮殑鏂規(guī)鏈夊洓縐?1,2,3鎴?)錛岀妞嶄袱涓牸瀛愮殑鏂規(guī)鏈変笁縐?13,14鎴?4)錛岀妞嶄笁涓牸瀛愮殑鏂規(guī)鏈変竴縐?134)錛岃繕鏈変竴縐嶄粈涔堟牸瀛愰兘涓?
縐嶃?br> 4+3+1+1=9銆?br>
鏁版嵁瑙勬ā
瀵逛簬30%鐨勬暟鎹紝N,M<=4錛?br> 瀵逛簬
100%鐨勬暟鎹紝N,M<=12銆?
紼嬪簭浠g爜錛?br>program cowfood;
const
d=100000000;
MaxN=12;
var
f:array[0..MaxN,1..2000]of
longint;
w:array[1..2000,1..2000]of boolean;
st:array[0..2000]of integer;
map:array[0..MaxN]of integer;
m,n:integer;
function Impossible(a:integer):boolean;
var
i:integer;
flag:boolean=false;
begin
for i:=1 to MaxN do
begin
if flag and (a and 1=1) then exit(true);
flag:=(a
and 1=1);
a:=a shr 1;
end;
exit(false);
end;
function
Conflict(a,b:integer):boolean;
var
i:integer;
begin
for i:=1 to MaxN do
begin
if (a and 1=1) and (b and 1=1)
then exit(true);
a:=a shr 1;
b:=b shr 1;
end;
exit(false);
end;
function CanPlace(a,b:integer):boolean;
begin
exit(a or b=b);
end;
procedure FindSt;
var
i:integer;
begin
for i:=0 to 1 shl MaxN-1 do
if not
Impossible(i) then
begin
inc(st[0]);
st[st[0]]:=i;
end;
end;
procedure Init;
var
i,j:integer;
begin
for i:=1 to st[0] do
for j:=i to
st[0] do
if not Conflict(st[i],st[j]) then
begin
w[i,j]:=true;
w[j,i]:=true;
end;
end;
procedure
Readp;
var
i,j,t,v:integer;
begin
readln(m,n);
for i:=1 to m do
begin
v:=0;
for j:=1 to n do
begin
read(t);
v:=v*2+t;
end;
map[i]:=v;
readln;
end;
end;
procedure Solve;
var
i,j,k:integer;
begin
f[0,1]:=1;
map[0]:=1 shl n-1;
for i:=1 to m do
for
j:=1 to st[0] do
if not CanPlace(st[j],map[i]) then f[i,j]:=-1
else
for k:=1 to st[0] do if (f[i-1,k]<>-1) and w[j,k]
then
f[i,j]:=(f[i,j]+f[i-1,k]) mod d;
end;
procedure
Writep;
var
j:integer;
ans:longint=0;
begin
for
j:=1 to st[0] do
if f[m,j]<>-1 then ans:=(ans+f[m,j])
mod d;
writeln(ans);
end;
begin
assign(input,'cowfood.in');
reset(input);
assign(output,'cowfood.out');
rewrite(output);
FindSt;
Init;
Readp;
Solve;
Writep;
close(input);
close(output);
end.