鍥?锛氬乏鏃嬬ず鎰忓浘

鍥?锛氬彸鏃嬬ず鎰忓浘

鎻掑叆绀轰緥

鍋囪鎴戜滑鎻掑叆鐨勬柊鑺傜偣涓?/span>X

灏嗘柊鎻掑叆鐨勮妭鐐规爣璁颁负绾㈣壊
濡傛灉X鏄牴缁撶偣(root)锛屽垯鏍囪涓洪粦鑹?/span>
濡傛灉X鐨?parent 涓嶆槸榛戣壊锛屽悓鏃?X 涔熶笉鏄?root

3.1 濡傛灉 X 鐨?uncle (鍙斿彅) 鏄孩鑹?/span>

3.1.1 灏?parent 鍜?uncle 鏍囪涓洪粦鑹?/span>
3.1.2 灏?grand parent (绁栫埗) 鏍囪涓虹孩鑹?/span>
3.1.3 璁?X 鑺傜偣鐨勯鑹蹭笌 X 绁栫埗鐨勯鑹茬浉鍚岋紝鐒跺悗閲嶅姝ラ 2銆?

璇濅笉澶氳锛岀湅涓嬪浘6

璺熺潃涓婇潰鐨勫叕寮忚蛋:

灏嗘柊鎻掑叆鐨?X鑺傜偣鏍囪涓虹孩鑹?/span>
鍙戠幇 X鐨?parent (P) 鍚屾牱涓虹孩鑹诧紝杩欒繚鍙嶄簡绾㈤粦鏍戠殑绗笁鏉¤鍒欍€屼笉鑳芥湁涓や釜杩炵画鐩搁偦鐨勭孩鑹茶妭鐐广€?/span>
鍙戠幇X 鐨?uncle (U)鍚屾牱涓虹孩鑹?/span>
灏?P鍜?U鏍囪涓洪粦鑹?/span>
灏?/span>X鍜?/span>X 鐨?/span>grand parent (G)鏍囪涓虹浉鍚岀殑棰滆壊锛屽嵆绾㈣壊锛岀户缁噸澶嶅叕寮?2銆?
鍙戠幇 G鏄牴缁撶偣锛屾爣璁颁负榛戣壊
缁撴潫

鍒氬垰璇翠簡 X 鐨?uncle 鏄孩鑹茬殑鎯呭喌锛屾帴涓嬫潵瑕佽鏄粦鑹茬殑鎯呭喌

濡傛灉 X 鐨?parent 涓嶆槸榛戣壊锛屽悓鏃?X 涔熶笉鏄?root

3.2 濡傛灉 X 鐨?uncle (鍙斿彅) 鏄粦鑹诧紝鎴戜滑瑕佸垎鍥涚鎯呭喌澶勭悊

3.2.1 宸﹀乏 (P 鏄?G 鐨勫乏瀛╁瓙锛屽苟涓?X 鏄?P 鐨勫乏瀛╁瓙)
3.2.2 宸﹀彸 (P 鏄?G 鐨勫乏瀛╁瓙锛屽苟涓?X 鏄?P 鐨勫彸瀛╁瓙)
3.2.3 鍙冲彸 (鍜?3.2.1 闀滃儚杩囨潵锛屾伆濂界浉鍙?
3.2.4 鍙冲乏 (鍜?3.2.2 闀滃儚杩囨潵锛屾伆濂界浉鍙?

褰撳嚭鐜?uncle 鏄粦鑹茬殑鏃跺€欐垜浠涓€姝ヨ鑰冭檻鐨勬槸鏃嬭浆锛岃繖閲屽厛璇峰皬浼欎即涓嶈鍏虫敞绾㈤粦鏍戠殑绗?4 鏉¤鍒?/span>锛屼富瑕佹槸涓轰簡婕旂ず濡備綍鏃嬭浆鐨勶紝鏉ヤ竴鐐圭偣鐪嬶紝涓嶈鐪嬪浘灏辨厡锛屾湁瑙ｉ噴鐨?:

宸﹀乏鎯呭喌

杩欑鎯呭喌寰堢畝鍗曪紝鎯宠薄杩欐槸涓€鏍圭怀瀛愶紝鎵嬫彁璧?P 鑺傜偣锛岀劧鍚庡彉鑹插嵆鍙?鍙樿壊鍘熷垯渚濇嵁鐗规€?)

宸﹀彸鎯呭喌

宸︽棆: 浣?X 鐨勭埗鑺傜偣 P 琚?X 鍙栦唬锛屽悓鏃剁埗鑺傜偣 P 鎴愪负 X 鐨勫乏瀛╁瓙锛岀劧鍚庡啀搴旂敤宸﹀乏鎯呭喌

鍙冲彸鎯呭喌

涓?/span>宸﹀乏鎯呭喌涓€鏍凤紝鎯宠薄鎴愪竴鏍圭怀瀛?/span>

鍙冲乏鎯呭喌

鍙虫棆: 浣?X 鐨勭埗鑺傜偣 P 琚?X 鍙栦唬锛屽悓鏃剁埗鑺傜偣 P 鎴愪负 X 鐨勫彸瀛╁瓙锛岀劧鍚庡啀搴旂敤鍙冲彸鎯呭喌

褰掔撼鎬荤粨

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鐪嬬壒鎬?锛屾病鎻掑叆鏂拌妭鐐瑰墠锛岀鐖?/span>PP寰€涓嬶紝宸︽爲缁忚繃榛戣妭鐐硅矾寰勪负锛?/span>PP--->P锛夛紝鍙虫爲缁忚繃鐨勯粦鑺傜偣璺緞涓猴紙PP--->S锛夛紝宸﹀彸璺緞鐨勯粦鑹茶妭鐐规暟鍧囦负涓€涓紝骞宠　銆傛彃鍏ユ柊鑺傜偣鍙樿壊鍚庯紝宸︽爲璺緞锛?/span>PP--->P--->I锛夛紝鍙虫爲璺緞锛?/span>PP--->S锛夛紝宸﹀彸璺緞鐨勯粦鑹茶妭鐐规暟鍧囦负涓€涓紝骞宠　銆傛墍浠ュ彧鐢ㄥ浘鑹蹭笉鐢ㄦ棆杞紝濡備笅鍥?銆?/span>

鍦ㄨ繖涓眬閮ㄧ殑瀛愭爲涓紝褰撴彃鍏ヨ妭鐐?/span>I鐨勭埗浜插拰鍙斿彅S涓虹孩鑹叉椂锛屽彉鑹叉柟妗堝浐瀹氫负锛堢埗浜诧紝鍙斿彅鍙橀粦锛岀鐖讹紙鐖风埛锛?/span>鍙樼孩锛夛紙姣忔鍙樿壊鐗规€?锛岀壒鎬?閮戒細鏍￠獙锛屽湪杩欓噷绠€鍖栵級銆?/span>

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1锔忊儯鐨勬儏鍐碉細鍙互鐪嬪墠闈㈣鐨?/span>宸﹀乏鎯呭喌锛岄鍏堟牴鎹壒鎬?锛屽彉鑹诧紝p鍙樹负榛戣壊锛?/span>g鍙樹负绾㈣壊锛屽湪杩欎釜灞€閮ㄦ爲涓粦鑹茶妭鐐硅矾寰勪负锛氬乏g--->p--->x涓€涓粦鑹茶妭鐐癸紝鍙?/span>g--->u涓€涓粦鑹茶妭鐐癸紝杩欑鎯呭喌涓嶇鍚堢壒鎬?锛屾墍浠ョ幇鍦ㄥ眬閮ㄥ瓙鏍戜腑闇€瑕佹棆杞紝杩欐椂鐗规€?鍙樿壊鍚庣殑棰滆壊涓猴細绾紙x锛?/span>g锛夛紝榛戯紙p锛?/span>u锛?杩欐椂鍏抽敭鑺傜偣涓?/span>g鐖风埛杩欎釜鑺傜偣锛岄偅涔堜互杩欎釜鑺傜偣鍙虫棆锛堝鏋滃乏鏃嬪彲浠ヤ娇鐢ㄧ壒鎬?鏍￠獙涓嬶級锛屾棆杞箣鍚庯紝灞€閮ㄦ爲榛戣壊鑺傜偣璺緞涓猴細宸?/span>p--->x涓€涓粦鑹茶妭鐐癸紝鍙?/span>p--->g--->u浜屼釜榛戣壊鑺傜偣锛岀鍚堢壒鎬?锛屽眬閮ㄦ爲骞宠　锛屽洜涓哄眬閮ㄨ妭鐐圭殑椤剁偣杩樻槸榛戣壊锛屾墍浠ユ病鏈夌牬鍧忓眬閮ㄦ爲涔嬪鐨勫钩琛★紝鎵€浠ヤ笉鐢ㄦ牎楠屽眬閮ㄦ爲涔嬪鐨勬爲銆?/span>

鍏抽敭鑺傜偣鐨勫畾浣?/span>锛?/span>锛堟垜鐨勭悊瑙ｏ級褰撳叧閿妭鐐逛负绾㈣壊涓旂埗浜蹭篃鏄孩鑹诧紝鍦ㄦ病鍙樿壊涔嬪墠鍏抽敭鑺傜偣绉诲姩鍒扮埗浜茶妭鐐癸紝褰撳彉鑹蹭箣鍚庣Щ鍔ㄥ埌鐖风埛鑺傜偣锛屾柊鎻掑叆鐨勮妭鐐逛负鍏抽敭鑺傜偣銆?/span>

宸﹀彸鎯呭喌锛?/span>x鏄?/span>p鐨勫彸瀛愯妭鐐癸紝鍙樿壊涔嬪悗锛岀孩锛?/span>x锛?/span>g锛夛紝榛戯紙p锛?/span>u锛夛紝绗﹀悎鐗规€?锛?/span>g鐨勫乏瀛愭爲榛戣壊鑺傜偣璺緞涓?/span>g--->p--->x鍏变竴涓紝鍙冲瓙鏍戦粦鑹茶妭鐐硅矾寰勪负g--->u鍏变竴涓紝涓嶇鍚堢壒鎬?锛?/span>

鎵€浠ュ皾璇曟棆杞紝宸︽棆涓嶇鍚堢壒鎬?锛屽皾璇曞彸鏃?/span>g涓?/span>p鐨勫彸鑺傜偣x鍐茬獊锛屾棆杞箣鍚庡舰鎴愮殑鍥惧涓嬶紝鍐嶆鍙樿壊锛岀孩锛?/span>x锛?/span>p锛夛紝榛戯紙g锛?/span>u锛?/span>

鐢?/span>p鍚戜笅鐨勫乏瀛愭爲榛戣壊鑺傜偣璺緞p--->t10涓紝涓庢彃鍏ヤ箣鍓嶅皯浜嗕竴涓紝鍙冲瓙鏍戦粦鑹茶妭鐐硅矾寰勪负p--->g--->u鍏变袱涓紝鎵€浠ヤ笉绗﹀悎鐗规€?銆傞偅涔堝洖鍒版渶鍒濈殑鎯呭喌锛?/span>x鏄?/span>p鐨勫彸瀛愯妭鐐癸紝鍏堟棆杞紝鍏抽敭鑺傜偣p杩涜宸︽棆锛屾棆杞箣鍚庡彂鐜板眬閮ㄦ爲鍙樻垚浜?/span>宸﹀乏鎯呭喌锛屼互宸﹀乏鎯呭喌缁х画骞宠　灞€閮ㄦ爲锛?/span>

閭ｄ箞鍙虫棆鍛紝p鐨勫乏瀛愯妭鐐瑰洜涓?/span>p鏄孩鑹叉牴鎹壒鎬?锛岄偅涔堣鑺傜偣瑕佷箞鏄粦鑹茶涔堟槸NiL锛屾棆杞箣鍚?/span>p鐨勫彸瀛愭爲澶氫簡涓€涓粦鑹茶妭鐐广€?/span>

濡傛灉灞€閮ㄥ瓙鏍戞€庝箞鍙橀兘涓嶈兘骞宠　鎴栬€呭钩琛′篃鏄互鏀瑰彉灞€閮ㄦ爲涓庡閮ㄦ爲鐨勮繛鎺ョ偣涓哄墠鎻愶紝閭ｄ箞杩欐椂浠ヨ繛鎺ョ偣涓烘柊鐨勫叧閿妭鐐癸紝浣胯繛鎺ヨ妭鐐逛笌瀹冪殑涓昏鐩稿叧鑺傜偣缁勬垚涓€涓眬閮ㄦ爲锛屽啀娆＄殑骞宠　銆?/span>

鍓嶉潰璁茶В鐨勬柟娉曪紝鍙互鍦ㄦ彃鍏ョ殑鏃跺€欏垎涓轰互涓嬪嚑绉嶆儏鍐?/span>

鎯呮櫙4.2,4.3鐨勬儏鍐靛垎鍒槸锛屽乏宸︼紝宸﹀彸锛屽彸鍙筹紝鍙冲乏銆?/span>

缁冧範棰樹笌缁冧範缃戠珯锛?/span>

銆?0 70 32 34 13 56 32 56 21 3 62 4銆?/span>

缁冧範閾炬帴

[https://www.cs.usfca.edu/~galles/visualization/Algorithms.html]

绾㈤粦鏍戝垹闄わ細

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鑱旂郴鏂瑰紡锛?/span>

閭锛?/span>dongchao1860369@sina.com

鍙傝€冨紩鐢紙澶т浆鍗氬閾炬帴锛夛細

https://zhuanlan.zhihu.com/p/79980618https://zhuanlan.zhihu.com/p/79980618https://segmentfault.com/a/1190000012728513

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