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琛¢噺涓涓煡鎵劇畻娉曠殑鏃墮棿鏁堢巼鐨勬爣鍑嗘槸錛氬湪鏌ユ壘榪囩▼涓紝鍏抽敭瀛楃殑騫沖潎嬈℃暟錛岃繖涓爣鍑嗕負騫沖潎鏌ユ壘闀垮害ASL錛?/span>
2. 欏哄簭鏌ユ壘娉?/span>
1) 鍦ㄩ『搴忚〃涓婄殑鏌ユ壘錛堥潪絳夋鐜囨煡鎵撅級:鑻ョ瓑姒傜巼錛屽垯騫沖潎ASL涓猴紙n+1錛?2;鑻ラ潪絳夋鐜囷紝鍒欐眰鍑烘湡鏈?/span>
2) 鍦ㄧ嚎鎬ч摼琛ㄤ笂鐨勬煡鎵?/span>
3. 鎶樺崐鏌ユ壘
1) 鎶樺崐鏌ユ壘榪囩▼錛屽叧閿簭鍒楁湁搴忥紝鍒欎簩鍙夋帓搴忔爲涓瀹氾紝鍗沖垽瀹氭爲銆?/span>
2) 鑻ユ槸鍏抽敭鐮佹棤搴忥紝浠嶅彲鏋勯犱簩鍙夋帓搴忔爲錛岃繘鑰岃綆楁瘡涓叧閿爜鐨勫鉤鍧嘇SL銆?/span>
3) 鑻ユ槸鍏抽敭鐮佹棤搴忥紝浠嶅彲鏋勯犱簩鍙夋帓搴忔爲錛屽緩绔嬭繃紼嬩腑錛屽彲浠ヨ皟鏁翠負騫寵 浜屽弶鏍戙傝繘鑰岃綆楁瘡涓叧閿爜鐨勫鉤鍧嘇SL銆?/span>
4. B鏍?/span>
1) 綰挎х儲寮曪細鎵鏈夊瓙琛紝鍒嗗潡鏈夊簭錛屽悗涓涓瓙琛ㄧ殑鎵鏈夊叧閿瓧澶т簬鍓嶉潰涓涓瓙琛ㄤ腑鎵鏈夊厓绱犵殑鍏抽敭瀛椼傚彟澶栵紝鍦ㄥ緩绔嬩竴寮犵儲寮曡〃錛岀儲寮曢」璁板綍浜嗗悇瀛愯〃鐨勬渶澶у叧閿間互鍙婃墍鍦ㄧ殑浣嶇疆錛屽洜姝わ紝鍚勪釜绱㈠紩欏瑰湪绱㈠紩琛ㄤ腑鐨勫簭鍙蜂笌鍚勪釜瀛愯〃鐨勫潡鍙蜂竴涓瀵瑰簲銆傚绱㈠紩欏哄簭緇撴瀯榪涜鏌ユ壘鏃訛紝鍒嗕負涓ょ駭鏌ユ壘銆傚厛閫氳繃绱㈠紩欏圭‘瀹氬瓙琛紝鐒跺悗鍦ㄥ瓙琛ㄤ腑鏌ユ壘銆?/span>
2) 澶氱駭绱㈠紩鍜?/span>m鍙夋煡鎵炬爲錛氭湁澶氱駭绱㈠紩鏋勬垚涓涓猰鍙夋煡鎵炬爲錛屾爲涓殑姣忎竴涓垎鏀妭鐐硅〃紺虹儲寮曞潡錛屼粬鏈澶氬瓨鏀緈涓儲寮曞潡錛屾瘡涓儲寮曞潡鍒嗗埆緇欏嚭鍚勫瓙鏍戣妭鐐圭殑鏈澶у叧閿瓧鍜岃妭鐐瑰湴鍧銆?/span>
3) B鏍戜負浜屽弶鎺掑簭鏍?/span>
4) B-鏍戠殑姒傚康錛氭牴鑺傜偣鑷沖皯鏈?涓瓙鏍戯紱闈炴牴鐨勯潪涓粓绔帴鐐規湁m/2涓粨鐐癸紱鍚湁k涓粨鐐圭殑瀛愭爲縐嶆湁k-1涓叧閿瓧銆?/span>
5) B+鏍戠殑姒傚康錛欱+鏍戞槸-B鐨勪竴縐嶅彉褰紝瀹冧笌B鏍戠殑鍖哄埆鍦ㄤ簬鏈塳涓叧閿瓧鐨勭粨鐐瑰繀鐒舵湁K媯靛瓙鏍戯紝闈炲彾瀛愮粨鐐逛粎浠呭叿鏈夌儲寮曚綔鐢紝鑰岃窡璁板綍鏈夊叧鐨勫叧閿瓧閮藉湪鍙跺瓙緇撶偣涓?/span>璺烞鏍戠殑鏌ユ壘綾諱技錛屼絾鏄篃鏈変笉鍚屻傜敱浜庤窡璁板綍鏈夊叧鐨勪俊鎭瓨鏀懼湪鍙剁粨鐐逛腑錛屾煡鎵炬椂鑻ュ湪涓婂眰宸叉壘鍒板緟鏌ョ殑鍏抽敭鐮侊紝騫朵笉鍋滄錛岃屾槸緇х畫娌挎寚閽堝悜涓嬩竴鐩存煡鍒板彾緇撶偣灞傜殑鍏抽敭鐮併傛澶栵紝B+鏍戠殑鎵鏈夊彾緇撶偣鏋勬垚涓涓湁搴忛摼琛紝鍙互鎸夌収鍏抽敭鐮佹帓搴忕殑嬈″簭閬嶅巻鍏ㄩ儴璁板綍銆備笂闈袱縐嶆柟寮忕粨鍚堣搗鏉ワ紝浣垮緱B+鏍戦潪甯擱傚悎鑼冨洿媯绱€?/span>
5. 鏁e垪鏌ユ壘
1) 鏁e垪琛ㄧ殑姒傚康:琛ㄩ」鐨勫瓨鍌ㄤ綅緗笌琛ㄩ」鍏抽敭瀛椾箣闂寸‘绔嬩竴涓搴旂殑鍏崇郴鍑芥暟銆?/span>
2) 甯歌鏁e垪鍑芥暟錛氶櫎鐣欎綑鏁版硶銆?/span>
3) 瑙e喅鍐茬獊鐨勬柟娉曪細綰挎ф帰嫻嬫硶錛屼簩嬈℃帰嫻嬫硶錛屾媺閾炬硶
4) 鏁堢巼鍒嗘瀽錛氭煡鎵炬垚鍔熺殑騫沖潎鏌ユ壘闀垮害錛涙煡鎵懼け璐ョ殑騫沖潎鏌ユ壘闀垮害錛?/span>
1. 鏍堝拰闃熷垪鐨勬蹇?/span>
1) 鏍?鍙厑璁鎬竴绔繘琛屾彃鍏ュ拰鍒犻櫎鐨勭嚎鎬ц〃;鍏佽鎻掑叆鍜屽垹闄ょ殑涓绔彨鍋氭爤欏?涓嶅厑璁告彃鍏ュ拰鍒犻櫎鐨勪竴绔彨鍋氭爤搴?鍏堣繘鍚庡嚭
2) 闃熷垪:鍏佽鎻掑叆鐨勪竴绔負闃熼,鍏佽鍒犻櫎鐨勪竴绔負闃熷熬.鍏堣繘鍏堝嚭
2. 瀛樺偍緇撴瀯
1) 鏍堢殑欏哄簭瀛樺偍緇撴瀯:緇撴瀯浣?鏈夋暟緇勫拰欏舵寚閽?/span>
2) 鏍堢殑閾懼紡瀛樺偍緇撴瀯:鍗曢摼琛?/span>
3) 闃熷垪鐨勯『搴忓瓨鍌ㄧ粨鏋?緇撴瀯浣?鏁扮粍,棣栧熬鎸囬拡
4) 闃熷垪鐨勯摼寮忓瓨鍌ㄧ粨鏋?鍗曢摼琛?
5) 寰幆闃熷垪錛氶槦鍒椾負絀烘椂錛歳ear==front錛涢槦鍒楁弧鏃訛細(rear+1)%maxSize = front.錛堢壓鐗蹭簡涓涓瓨鍌ㄧ┖闂村崟鍏冿級
3. 搴旂敤
1) 鏍堝湪琛ㄨ揪寮忎腑鐨勫簲鐢?/span>
①銆鍓嶇紑琛ㄨ揪寮?(A+B)*C---->*C+AB銆 (娉㈠叞寮?;(榪愮畻絎﹀湪鍓?浠庡彸鍒板乏鎵弿)
②銆鍚庣紑琛ㄨ揪寮?(A+B)*C------>AB+C*.(榪愮畻絎﹀湪鍚庯紝浠庡乏鍒版湁鎵弿)
2) 鏍堥掑綊涓殑搴旂敤
3) 浣跨敤闃熷垪涓昏鏄負浜嗕繚瀛樹笅涓姝ョ殑澶勭悊姝ラ
4) 鐗規畩鐭╅樀鐨勫帇緙╁瓨鍌?/span>
①銆浜岀淮鏁扮粍瀵逛簬浜岀淮鐭╅樀瀵瑰簲錛屾暟緇勭殑涓嬫爣瀵瑰簲鐭╅樀鐨勪笅鏍嘇[m][n];
②銆浜岀淮鐭╅樀鐨勮浼樺厛瀛樺偍錛宎[i][j]瀵瑰簲鐨勫瓨鍌ㄤ綅緗負loc錛?錛?錛?錛坕*m+j錛?L
③銆涓嬩笁瑙掔煩闃佃浼樺厛瀛樺偍錛歛[i,j]鍦ㄦ暟緇凚涓殑瀛樺偍浣嶇疆涓?+2+3+……+i+j
④銆涓婁笁瑙掔煩闃佃浼樺厛瀛樺偍錛歛[i,j]鍦ㄦ暟緇凚涓殑瀛樺偍浣嶇疆涓簄+……+錛坣+1-i錛?j-i錛?/span>
1. 鍥劇殑鍩烘湰姒傚康
1) 鏈夊悜瀹屽叏鍥?/span>
2) 鏃犲悜瀹屽叏鍥?/span>
3) 璺緞闀垮害
4) 綆鍗曡礬寰?/span>
5) 榪為氬浘錛岃繛閫氬垎閲?/span>
6) 寮鴻繛閫氬浘錛屽己榪為氬垎閲?/span>
7) 鐢熸垚鏍戯紝鐢熸垚媯灄
2. 鍥劇殑瀛樺偍緇撴瀯
1) 閭繪帴鐭╅樀錛氬彲鏂逛究璁$畻鍏ュ害鍜屽嚭搴︼紱鍩轟簬姝ょ緇撴瀯鐨勫浘錛岄亶鍘嗙粨鏋滃敮涓銆?/span>
2) 閭繪帴琛細閫傜敤浜庣偣澶氳竟灝戠殑鎯呭喌錛涘熀浜庢縐嶇粨鏋勭殑鍥撅紝閬嶅巻涓嶅敮涓錛堥偦鎺ヨ〃涓嶅敮涓錛?/span>
3. 鍥劇殑閬嶅巻錛氶氳繃閬嶅巻錛屽彲浠ユ眰寰楀浘鐨勬墍鏈夎繛閫氬垎閲?/span>
1) 娣卞害浼樺厛閬嶅巻錛氱被浼間簬浜屽弶鏍戠殑鍏堝簭閬嶅巻
2) 騫垮害浼樺厛閬嶅巻錛氱被浼間簬浜屽弶鏍戠殑灞傛閬嶅巻
4. 鏈灝忕敓鎴愭爲
1) 鏅埄濮嗙畻娉曪紙浠庢煇鐐瑰紑濮嬶紝閫愭鎼滅儲錛屾坊鍔犺妭鐐癸紝錛?/span>
2) 鍏嬮瞾鏂崱灝旂畻娉?/span>
5. 鏈鐭礬寰?/span>
1) 榪澃鏂壒鎷夌畻娉?/span>
2) 浣涚綏閲屽痙綆楁硶
6. 鎷撴墤鎺掑簭錛氬浘鐨勬嫇鎵戞帓搴忓彲浠ユ帴瑙︿緷璧栧叧緋諱互鍙婂垽瀹氬浘涓槸鍚︽湁鐜?/span>
7. 鍏抽敭璺緞錛氶氳繃AOE錛屽彲浠ユ眰寰楀浘涓《鐐圭殑鏈鏃╁紑濮嬫椂闂達紝鏈鏅氬紑濮嬫椂闂達紝媧誨姩鐨勬渶鏃╁紑濮嬫椂闂達紝浠ュ強媧誨姩鐨勬渶鏅氬紑濮嬫椂闂淬?/span>
1. 鎺掑簭鐨勫熀鏈蹇?/span>
1) 鎺掑簭榪囩▼鍙互鏄墿鐞嗛噸鎺?涔熷彲浠ユ槸閫氳繃鎸囬拡,浣垮緱閫昏緫鏈夊簭.
2) 鍐呴儴鎺掑簭鍜屽鎺掑簭:鎵鏈夌殑璁板綍閮藉湪鍐呭瓨涓?榪欐牱鐨勬帓搴忎負鍐呴儴鎺掑簭;濡傛灉鎺掑簭鐨勮繃紼嬩腑瑕佷笉鏂殑榪涜鍐呭瓨涓庡瀛樼殑浜ゆ崲,榪欐牱鐨勬帓搴忎負澶栭儴鎺掑簭.
2. 鎻掑叆鎺掑簭:
1) 鐩存帴鎻掑叆鎺掑簭:紼沖畾鐨勬帓搴忕畻娉曪紝鏃墮棿澶嶆潅搴︼細鏈濂芥儏鍐?/span>O(n)錛涙渶宸儏鍐礝錛坣^2錛夛紱騫沖潎鎯呭喌涓篛錛坣^2錛?
2) 鎶樺崐鎻掑叆鎺掑簭錛氱ǔ瀹氱殑鎺掑簭綆楁硶
3) 甯屽皵鎺掑簭錛氫笉紼沖畾鐨勬帓搴忕畻娉曪紝鏃墮棿澶嶆潅搴︿負錛氭病鏈夋渶濂芥儏鍐碉紱鏈宸儏鍐?/span>O錛坣log2n錛夛紱騫沖潎鎯呭喌涓篛(nlog2n)銆?/span>
3. 浜ゆ崲鎺掑簭
1) 姘旀場鎺掑簭錛氱ǔ瀹氱殑鎺掑簭綆楁硶錛屾椂闂村鏉傚害涓?/span>:鏈濂芥儏鍐礝錛坣錛夛紱鏈宸儏鍐礝(n^2);騫沖潎鎯呭喌涓篛錛坣^2錛?
2) 蹇熸帓搴?/span>:涓嶇ǔ瀹氱殑鎺掑簭綆楁硶錛屾椂闂村鏉傚害涓猴細鏈濂界殑鎯呭喌O(nlog2n)錛涙渶宸儏鍐礝(n^2)錛屽鉤鍧囨儏鍐典負O(nlog2n)錛?/span>
4. 閫夋嫨鎺掑簭
1) 綆鍗曢夋嫨鎺掑簭錛氫笉紼沖畾鐨勬帓搴忥紝鏃墮棿澶嶆潅搴︿負錛氭渶濂芥儏鍐?/span>O(n^2);鏈宸儏鍐典負O錛坣^2錛?騫沖潎鎯呭喌涓篛錛坣^2錛?涓庡叧閿瓧鐨勫垵濮嬫帓鍒楁棤鍏熾?/span>
2) 鍫嗘帓搴?/span>:涓嶇ǔ瀹氱殑鎺掑簭錛屾椂闂村鏉傚害涓猴細鏈濂芥儏鍐礝錛坣log2n錛夛紱鏈宸儏鍐典負O錛坣log2n錛夛紱騫沖潎鎯呭喌O錛坣log2n錛夛紱
5. 浜岃礬褰掑茍鎺掑簭
紼沖畾鐨勬帓搴忥紝鏃墮棿澶嶆潅搴︿負錛氭渶濂芥儏鍐礝錛坣log2n錛夛紱鏈宸儏鍐典負O錛坣log2n錛夛紱騫沖潎鎯呭喌O錛坣log2n錛夛紱
6. 鍩烘暟鎺掑簭
紼沖畾鐨勬帓搴忥紝鏃墮棿澶嶆潅搴︿負錛氭渶濂芥儏鍐礝錛坉錛坣+rd錛夛級錛涙渶宸儏鍐典負O錛坉錛坣+rd錛夛級錛涘鉤鍧囨儏鍐礝錛坉錛坣+rd錛夛級錛?/span>
1. 涓庢爲鏈夊叧鐨勬蹇?/span>
1) 緇撶偣鐨勫害錛氱粨鐐規嫢鏈夌殑瀛愭爲鏁般?/span>
2) 鏍戠殑搴︼細鏍戜腑鎵鏈夌粨鐐圭殑搴︾殑鏈澶у箋?/span>
3) 緇撶偣鐨勫眰鏁幫細
4) 鏍戠殑娣卞害錛氭爲涓粨鐐圭殑鏈澶у眰鏁版垨鑰呯О涓烘爲鐨勯珮搴︽垨鑰呮繁搴︺?/span>
5) 鍙跺瓙緇撶偣錛氬害涓?鐨勭偣鎴栬呯粓绔妭鐐廣?/span>
6) 鍒嗘敮緇撶偣錛氬害澶т簬0鐨勭粨鐐廣?/span>
7) 媯灄錛歮媯典簰涓嶇浉浜ょ殑鏍戠殑闆嗗悎涓烘.鏋?/span>
8) 鏍戜笉鍏佽涓虹┖銆備絾鏄簩鍙夋爲鍏佽涓虹┖錛屼簩鍙夋爲涓嶆槸鏍戯紝騫朵笖浜屽弶鏍戞槸鏈夊簭鏍戯紝宸﹀瀛愬拰鍙沖瀛愭槸涓嶄竴鏍風殑銆?/span>
2. 浜屽弶鏍戞蹇碉細鏈夐檺涓厓绱犵殑闆嗗悎錛岃闆嗗悎鎴栬呬負絀恒佹垨鑰呮湁涓涓О涓烘牴鐨勫厓绱犱互鍙婁袱涓や笉鐩鎬氦鐨勩佸垎鍒О涓哄乏瀛愭爲鍜屽彸瀛愭爲鐨勭粍鎴愩?/span>
1) 浜屽弶鏍戠殑鎬ц川濡備笅錛?/span>
①銆浜屽弶鏍戠殑絎琲灞傦紝鍏辨湁2^錛坕-1錛変釜緇撶偣銆?/span>
②銆娣卞害涓簁浜屽弶鏍戞渶澶氭湁2^k-1涓粨鐐廣?/span>
③銆浜屽弶鏍戜腑錛岀粓绔妭鐐圭殑鏁扮洰涓簄0錛涘害涓?鐨勭粨鐐規暟鐩負n1錛屽害涓?鐨勭粨鐐逛負n2錛涘垯n0 = n2+1錛?/span>
鎹錛屽彲浠ュ紩鍑轟竴涓嬬粨璁?瀵逛簬n涓粨鐐圭殑瀹屽叏浜屽弶鏍戯細
a>,鑻涓哄鏁幫紝鍒欐爲涓彧鏈夊害涓?鍜屽害涓?鐨勭粨鐐廣傚叾涓害涓?鐨勭粨鐐規暟涓?nbsp; (n-1)/2錛涘害涓?鐨勭粨鐐規暟涓?n-1)/2+1錛?/span>
b>,鑻涓哄伓鏁幫紝鍒欐爲涓櫎浜嗗害涓?鍜屽害涓?鐨勭粨鐐圭粨鐐瑰錛岃繕鏈夊害涓?鐨勭粨鐐?涓?/span>
④銆濡傛灉鏈変竴媯祅涓粨鐐圭殑瀹屽叏浜屽弶鏍戯紝鑷笂鑷笅錛屽悓涓灞傝嚜宸﹀埌鍙寵繛緇粰緇撶偣緙栧彿錛屽垯鏈夊涓嬪叧緋伙細
a>,鑻=1錛屽垯緇撶偣涓篿涓烘牴緇撶偣錛岃嫢i>1錛屽垯緇撶偣i鐨勭埗鑺傜偣涓恒巌/2銆忥紱
b>,鑻?i<n,鍒欑粨鐐筰鐨勫乏瀛╁瓙緇撶偣涓?i錛?/span>
c>,鑻?i+1<n;鍒欑粨鐐筰鐨勫彸瀛╁瓙緇撶偣涓?i+1錛?/span>
d>,鑻ョ粨鐐筰涓哄鏁幫紝鍒欏乏瀛愭爲緇撶偣涓篿-1錛?/span>
e>,鑻ョ粨鐐筰涓哄伓鏁幫紝鍒欏彸瀛愭爲緇撶偣涓篿+1錛?/span>
f>,緇撶偣i鎵鍦ㄧ殑灞傛涓簂og2i+1錛?/span>
鐢辨鍙互寮曞叆濡備笅緇撹錛氬浜庡畬鍏ㄤ簩鍙夋爲緙栧彿涓篿鐨勭粨鐐規湁錛?/span>
1>,鑻<=n/2錛屽垯緙栧彿涓篿鐨勭粨鐐逛負鍒嗘敮緇撶偣錛屽惁鍒欎負鍙剁粨鐐?/span>
2>,鑻涓哄鏁幫紝鍒欐瘡涓垎鏀粨鐐歸兘鏈夊乏瀛愭爲鍜屽彸瀛愭爲錛涜嫢n涓哄伓鏁幫紝鍒欑紪鍙鋒渶澶х殑鍒嗘敮緇撶偣鍙湁宸﹀瓙鏍戙?/span>
⑤銆 鍏鋒湁n涓粨鐐圭殑瀹屽叏浜屽弶鏍戠殑娣卞害涓簂og2錛坣+1錛夛紙鍚戜笂鍙栨暣錛?/span>
2) 浜屽弶鏍戠殑瀛樺偍緇撴瀯
①銆浜屽弶鏍戠殑欏哄簭瀛樺偍緇撴瀯涓鑸傜敤浜庡畬鍏ㄤ簩鍙夋爲銆?/span>
②銆浜屽弶鏍戠殑閾懼紡瀛樺偍緇撴瀯錛屾湁浜屽弶閾捐〃鍜屼笁鍙夐摼琛ㄣ?/span>
3) 浜屽弶鏍戠殑閬嶅巻
①銆涓簭閫掑綊閬嶅巻
②銆鍏堝簭閫掑綊閬嶅巻
③銆鍚庡簭閫掑綊閬嶅巻
④銆涓簭闈為掑綊
⑤銆鍚庡簭闈為掑綊
⑥銆鍏堝簭闈為掑綊
⑦銆灞傛閬嶅巻
4) 綰跨儲浜屽弶鏍?/span>
3. 鏍戜笌媯灄
1) 鏍戠殑瀛樺偍緇撴瀯
2) 媯灄錛屾爲涓庝簩鍙夋爲鐨勮漿鎹?/span>
3) 媯灄涓庢爲鐨勯亶鍘?/span>
4. 鏍戠殑搴旂敤
1) 浜屽弶鎺掑簭鏍?/span>
2) 騫寵 浜屽弶鏍?/span>
3) 鍝堝か鏇兼爲
4) 鍫?/span>
1. 綰挎ц〃鐨勫畾涔夊拰鎿嶄綔
①銆瀛樺湪鍞竴鐨勪竴涓?#8220;縐頒負絎竴涓殑鍏冪礌“錛?/span>
②銆瀛樺湪鍞竴鐨勭О涓?#8221;鏈鍚庝竴涓?#8220;鐨勫厓绱狅紝
③銆闄ょ涓涓厓绱犲錛屽叾浠栫殑姣忎釜鍏冪礌鍙湁涓涓洿鎺ュ墠椹憋紱
④銆闄ゆ渶鍚庝竴涓厓绱犲錛岄泦鍚堜腑鐨勬瘡涓厓绱犲潎鍙湁涓涓洿鎺ュ悗緇э紱
⑤銆鏈鍚庝袱鐐癸紝浣撶幇浜嗙嚎鎬ц〃涓厓绱犱箣闂寸殑閫昏緫鍏崇郴銆?/span>
2. 綰挎ц〃鐨勫瓨鍌?/span>
①銆欏哄簭瀛樺偍
②銆閾懼紡瀛樺偍
3. 綰挎ц〃鐨勫簲鐢?/span>