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<h1 class="article_title">紼嬪簭璁捐涓殑璁＄畻澶嶇敤</h1>
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<div class="article_main"><div id="MyContent"><p>浠庢枑娉㈤偅濂戞暟鍒楄璧?/p><p>銆�銆�鎴戞兂鍑犱箮姣忎竴涓▼搴忓憳瀵規枑娉㈤偅濂戯紙Fibonacci錛夋暟鍒楅兘涓嶄細闄岀敓錛屽湪寰堝鏁欑涔︽垨鏂囩珷涓秹鍙婂埌閫掑綊鎴栬綆楀鏉傛�х殑鍦版柟閮戒細灝嗚綆楁枑娉㈤偅濂戞暟鍒楃殑紼嬪簭浣滀負緇忓吀紺轟緥銆傚鏋滅幇鍦ㄨ浣犱互鏈�蹇殑閫熷害鐢–#鍐欏嚭涓�涓綆楁枑娉㈤偅濂戞暟鍒楃n涓暟鐨勫嚱鏁幫紙涓嶈�冭檻鍙傛暟灝忎簬1鎴栫粨鏋滄孩鍑虹瓑寮傚父鎯呭喌錛夛紝鎴戜笉鐭ヤ綘鐨勭▼搴忔槸鍚︿細鍜屼笅鍒椾唬鐮佺被浼鹼細</p><p>public static ulong Fib(ulong n)</p><p>{</p><p> return (n == 1 || n == 2) ? 1 : Fib(n - 1) + Fib(n - 2);</p><p>}</p><p>銆�銆�榪欐浠ｇ爜搴旇綆楁槸鐭皬綺炬倣錛堟墽琛屼唬鐮佸彧鏈変竴琛岋級錛岀洿瑙傛竻鏅幫紝鑰屼笖闈炲父絎﹀悎璁稿紼嬪簭鍛樼殑浠ｇ爜緹庡錛岃澶氫漢鍦ㄩ潰璇曟椂鍐欏嚭榪欐牱鐨勪唬鐮佸彲鑳藉績閲岃繕浼氭殫鐖姐�備絾鏄鏋滅敤榪欐浠ｇ爜璇曡瘯璁＄畻Fib(100)鎴戞兂灝卞啀涔熺埥涓嶈搗鏉ヤ簡錛屼及璁′笅鏄熸湡鐢氳嚦涓嬩釜鏈堝墠緇撴灉寰堥毦綆楀緱鍑烘潵銆?/p><p>銆�銆�鐪嬫潵濂界湅鐨勪唬鐮佹湭蹇呬腑鐢紝濡傛灉紼嬪簭鍦ㄦ晥鐜囦笉鑳芥帴鍙楅偅緹庤紲為┈鐨勫氨閮芥槸嫻簯浜嗐�傚鏋滅畝鍗曞垎鏋愪竴涓嬬▼搴忕殑鎵ц嫻侊紝灝變細鍙戠幇闂鍦ㄥ摢錛屼互璁＄畻Fibonacci(5)涓轟緥錛?/p><p>銆�銆�浠庝笂鍥懼彲浠ョ湅鍑猴紝鍦ㄨ綆桭ib(5)鐨勮繃紼嬩腑錛孎ib(1)璁＄畻浜嗕袱嬈°�丗ib(2)璁＄畻浜?嬈★紝Fib(3)璁＄畻浜嗕袱嬈★紝鏈潵鍙渶瑕?嬈¤綆楀氨鍙互瀹屾垚鐨勪換鍔″嵈璁＄畻浜?嬈°�傝繖涓棶棰橀殢鐫�瑙勬ā鐨勫鍔犱細鎰堝彂鍑告樉錛屼互鑷充簬Fib(100)宸茬粡鏃犳硶鍐嶅彲鎺ュ彈鐨勬椂闂村唴綆楀嚭銆傝櫧鐒跺彲浠ラ�氳繃灝鵑�掑綊浼樺寲灝嗗弻閫掑綊鍙樹負鍗曢�掑綊錛屼絾鏄晥鏋滀篃騫朵笉鐞嗘兂銆?/p><p>銆�銆�榪欐槸涓�涓潪甯稿吀鍨嬬殑蹇借鈥滆綆楀鐢ㄢ�濈殑渚嬪瓙銆傝綆楀鐢ㄧ殑鐩爣鍦ㄤ簬淇濊瘉璁＄畻榪囩▼涓悓涓�璁＄畻瀛愯繃紼嬪彧榪涜涓�嬈★紝閫氳繃淇濆瓨瀛愯繃紼嬭綆楃粨鏋滃茍澶嶇敤鏉ユ彁楂樿綆楁晥鐜囥�傚叾瀹炵被浼間笂闈㈢殑浠ｇ爜鍑虹幇鍦ㄥ緢澶氭暀縐戜功涓紝濡傛灉鏄負浜嗗睍紺烘枑娉㈤偅濂戞暟鍒楃殑鏁板鐗規�у綋鐒舵棤鍙帤闈烇紝浣嗘槸浣滀負璁＄畻鏈虹▼搴忓氨寰堟湁闂浜嗐�傚洜涓烘暟瀛﹀拰璁＄畻縐戝鏄湁鍖哄埆鐨勶紝鏁板瑕佹眰涓ヨ皚鍜岀畝媧佺殑琛ㄨ揪錛岃�岃綆楃瀛﹀垯闇�瑕佸敖閲忓揩鐨勫緱鍑虹粨鏋滐紝濂界殑鏁板鍏紡鏈繀鏄ソ鐨勮綆楀叕寮忋�傝繖涔熻鏄庣▼搴忚璁′笉鏄畝鍗曠殑灝嗘暟瀛﹁璦�緲昏瘧涓鴻綆楁満璇█灝卞彲浠ヤ簡錛岀▼搴忓憳搴旇鑳藉皢鏁板璇█棣栧厛緲昏瘧鎴愯綆楃瀛﹁璦�錛堢畻娉曪紵錛夛紝鐒跺悗鍐嶇炕璇戞垚鏈哄櫒璇█銆傚洜姝ょ▼搴忓憳鐨勫伐浣滅粷涓嶆槸鏈烘鐨勶紝鑰屾槸瑕佹湁涓�瀹氱殑鍒涢�犳�э紝鎵�浠ュ繀瑕佺殑綆楁硶鐭ヨ瘑瀵圭▼搴忓憳鑷沖叧閲嶈錛屽洜涓虹畻娉曟暀浼氱▼搴忓憳濡備綍鐢ㄦ渶鏈夋晥鐜囩殑鏂瑰紡鍘葷紪鍐欑▼搴忋�?/p><p>銆�銆�璦�褰掓浼狅紝鏍規嵁浠ヤ笂鍒嗘瀽錛屽彲浠ュ啓鍑轟竴涓洿楂樻晥鐨勬枑娉㈤偅濂戞暟鍒楄綆楃▼搴忥細</p><p>public static ulong Fib(ulong n)</p><p>{</p><p> if (n == 1 || n == 2)</p><p> {</p><p> return 1;</p><p> }</p><p> ulong m1 = 1, m2 = 1;</p><p> for (ulong i = 3; i <= n; i++)</p><p> {</p><p> m2 = m1 + m2;</p><p> m1 = m2 - m1;</p><p> }</p><p> return m2;</p><p>}</p><p>銆�銆�榪欐浠ｇ爜鍙兘鐪嬭搗鏉ヤ笉濡備笂涓�孌甸偅涔堜紭緹庯紝浣嗘槸鍏舵晥鐜囧嵈鏄涓�孌典唬鐮佷笉鍙瘮鎷熺殑銆備緥濡傝綆桭ib(40)錛屽湪鎴戠殑鏈哄櫒涓婏紝絎竴孌典唬鐮佺敤鏃?.5縐掞紝鑰岀浜屾浠ｇ爜灝忎簬0.001縐掋�傝繖涓樊璺濋殢鐫�瑙勬ā澧炲ぇ浼氭洿鏄庢樉錛屼緥濡侳ib(100)錛岀涓�孌典唬鐮佸彲鑳介渶瑕佸嚑澶╃敋鑷沖嚑鍛紝鑰岀浜屾浠ｇ爜鑰楁椂浠嶇劧灝忎簬0.001縐掋�傚ぉ澹や箣鍒紒</p><p>銆�銆�濡傛灉浠庤綆楀鏉傛�х殑瑙掑害鍒嗘瀽錛岀涓�孌典唬鐮佺殑澶嶆潅搴︿負O(1.6^n)錛屽鏁板鏁忔劅鐨勬湅鍙嬪簲璇ヨ兘浣撲細鍒拌繖涓嚱鏁板彲鎬曠殑澧為暱閫熷害錛岃繖鐢氳嚦涓嶆槸涓�涓欏瑰紡綰у埆鐨勫鏉傚害錛岃�岀浜屾浠ｇ爜浠呬負O(n)銆傜湅鍒板姝ょ畝鍗曚竴涓緥瀛愬嚭鐜板姝ゅ樊鍒紝榪樿兘璇寸▼搴忓憳瀛︿範綆楁硶娌℃湁鐢ㄥ悧銆?/p><p>銆�銆�涓婇潰浠ｇ爜瀵逛簬鈥滆綆楀鐢ㄢ�濈殑鎬濇兂浣撶幇涓嶆槸寰堟槑鏄撅紝鍥犱負鎴戜滑浠呬粎闇�瑕佷竴涓粨鏋滐紝涓棿緇撴灉閮借涓㈠純浜嗭紝濡傛灉鏄綆?<=i<=n鐨勬墍鏈塅ib(i)錛岄偅涔堣綆楀鐢ㄧ殑鎬濇兂灝變細浣撶幇鐨勬瘮杈冩槑鏄俱�?/p><p>銆�銆�鐭╅樀涔樻硶涓嶴trassen綆楁硶</p><p>銆�銆�涓嬮潰璇翠竴涓皢璁＄畻澶嶇敤鍙戞尌鍒版瀬鑷寸殑渚嬪瓙錛岃瀹炶瘽鐩村埌鐜板湪姣忔鐪嬪埌Strassen綆楁硶鎴戦兘瑙夊緱闇囨捈錛屼笉鐭trassen褰撳勾鏄暱浜嗕綍絳夊ぉ鎵嶇殑鑴戝瓙鎵嶅彂鐜拌繖涔堟紓浜殑涓�涓畻娉曘�?/p><p>銆�銆�鐭╅樀璁＄畻鍦ㄨ澶氶鍩熷鏈哄櫒瀛︿範銆佸浘褰㈠浘鍍忓鐞嗐�佹ā寮忚瘑鍒腑鍧囧崰鏈夐噸瑕佸湴浣嶃�傝�岃綆椾袱涓猲*n鐭╅樀涔樼Н鐨勮繍綆楁槸鐭╅樀璁＄畻涓父瑙佺殑璁＄畻銆傜敱鐭╅樀鐞嗚鍙煡錛屾櫘閫氭柟娉曡綆椾袱涓猲闃舵柟闃電殑涔樼Н闇�瑕佽繘琛宯^3嬈′箻娉曡綆楋紝鍏惰綆楀鏉傚害鑷劧鏄疧(n^3)銆備絾鏄痙鍥芥暟瀛﹀Volker Strassen閫氳繃鎷嗗垎鐭╅樀騫跺鐢ㄨ綆楃粨鏋滐紝鍙戠幇浜嗕竴縐嶅鏉傚害涓篛(n^2.81)鐨勭畻娉曪紝榪欎釜綆楁硶綆�鍗曡鏉ュ涓嬨�?/p><p>銆�銆�鍋囪n涓?鐨勫箓錛堜笉涓?鐨勫箓涔熻兘璁＄畻錛岃繖閲屾槸涓轟簡鏂逛究璇存槑錛夛紝A鍜孊鏄袱涓猲闃舵柟闃碉紝鍒橝鍜孊鍒嗗埆鍙互鍒嗚В鎴?涓猲/2闃舵柟闃碉細</p><p> </p><p>銆�銆�鍒欙細</p><p> </p><p>銆�銆�鍙儨榪欐牱緇忚繃8嬈/2闃舵柟闃電浉涔橈紝澶嶆潅搴﹁繕鏄疧(n^3)錛屾病鏈夐檷浣庡鏉傚害銆傚ぉ鎵嶇殑Volker Strassen鍙戠幇浜嗕竴縐嶉�氳繃璁＄畻7嬈/2闃舵柟闃墊潵寰楀嚭n闃舵柟闃典箻縐殑鏂規硶銆傚叿浣撴潵璇達紝璁撅細</p><p> </p><p>銆�銆�娉ㄦ剰鍦ㄨ綆桺1-P7榪囩▼涓紝铏界劧鍙寵竟鍏辨湁20涓瓙鐭╅樀涔樼Н錛屼絾鏄幓閲嶅鍚庡彧鏈塧e錛宐g錛宎f錛宐h錛宑e錛宒g錛宑f錛宒h錛屽彧鏈?涓紒鍥犳閫氳繃璁＄畻澶嶇敤鐨勬�濇兂鍙互閫氳繃7嬈″瓙鐭╅樀涔樼Н緇撴灉璁＄畻鍑篜1-P7錛岀劧鍚庯細</p><p> </p><p>銆�銆�榪欐牱灝辯粍鍚堝嚭浜咥B錛岃繖涓柟娉曠殑澶嶆潅搴︿負O(n^2.81)錛岃繖涓畻娉曞疄鍦ㄦ槸澶紓浜簡銆傚ぉ鎵嶏紒緇濆鐨勫ぉ鎵嶅晩錛佸浜庤繖縐嶄漢闄や簡鏃犻檺宕囨暚鎴戠湡鏄病鏈夊叾瀹冩兂娉曚簡錛岃兘灝嗚綆楀鐢ㄥ彂鎸ュ埌濡傛澧冨湴錛屼笉鐭ヤ笘闂磋兘鏈夊嚑浜恒�?/p><p>銆�銆�璁＄畻澶嶇敤瀵硅蔣浠跺紑鍙戠殑鍚ず</p><p>銆�銆�涔熻鏈夌殑鏈嬪弸浼氳錛屸�滄垜鍙堜笉寮�鍙戞暟鍊艱綆楀瀷紼嬪簭錛屼篃涓嶄細鎺ヨЕ濡傛澶嶆潅鐨勭畻娉曪紝璁＄畻澶嶇敤涓庢垜浣曞共錛熲�濄�傚疄闄呬笂鍗充嬌寮�鍙戦潪鏁板�煎瀷紼嬪簭錛岃綆楀鐢ㄧ殑鎬濇兂涔熸槸澶ф湁鐢ㄩ�旂殑銆備緥濡傛垜鏇劇粡鍦ㄤ竴涓湡瀹炵殑PHP寮�鍙戠殑琛屼笟緋葷粺涓榪囩被浼艱繖鏍風殑浠ｇ爜錛?/p><p>foreach($items as $k => $v){</p><p> //...</p><p> $money = $v->money + getTax();</p><p> //...</p><p>}</p><p>銆�銆�褰撴椂鎴戦棶寮�鍙戣繖涓▼搴忕殑浜鴻繖閲実etTax鐨勮繑鍥炲�煎拰姣忎釜item鏈夊叧緋誨悧錛屼粬璇寸◣璐規槸涓�濂楀鏉傜殑綆楁硶綆楀嚭鏉ョ殑錛屼絾鏄叾鍊煎浐瀹氱殑銆傞偅榪欓噷鍙氨澶氮璐逛簡錛屾瘡嬈″驚鐜兘璁＄畻涓�嬈★紝濡傛灉鏀逛負濡備笅錛?/p><p>$tax = getTax();</p><p>foreach($items as $k => $v){</p><p> //...</p><p> $money = $v->money + $tax;</p><p> //...</p><p>}</p><p>銆�銆�鍒欏彲浠ヨ妭鐪佷笉灝戣綆楄祫婧愩�傚湪鍚庢潵鐨勬矡閫氫腑鍙戠幇榪欎釜闂鍘熸潵鏄噸鏋勭殑閬楃暀闂錛屼互鍓嶇郴緇熶腑鐨勭◣鐜囪綆楁槸鍐欏湪紼嬪簭閲岀殑錛屽悗鏉ュ彂鐜拌繖涓綆楄秺鏉ヨ秺澶氾紝灝變嬌鐢ㄢ�淓xtract Method鈥濋噸鏋勬ā寮忔彁鍙栨垚浜唃etTax鍑芥暟錛屼絾鏄繖鏍風殑鍚庢灉灝辨槸鍒板閮芥槸getTax璋冪敤錛屾湁鐨勭▼搴忔鐢氳嚦璋冪敤涓冨叓嬈★紝浣嗘槸濡傛灉搴旂敤璁＄畻澶嶇敤鐨勬�濇兂錛屽垯搴旇鍦ㄨ剼鏈紑濮嬪彧璁＄畻涓�嬈＄◣璐瑰茍淇濆瓨錛屽悗闈㈠叏閮戒嬌鐢ㄨ繖涓彉閲忚�屼笉鏄瘡嬈¤皟鐢╣etTax銆?/p><p>銆�銆�鎬諱箣錛屽彧瑕佹煇涓綆楃粨鏋滀笌鎵ц涓婁笅鏂囨棤鍏籌紝騫朵笖鍦ㄤ竴涓墽琛屾祦涓秴榪囦竴嬈¤浣跨敤錛屽垯搴旇浣跨敤璁＄畻澶嶇敤銆?/p><p>銆�銆�榪欎釜渚嬪瓙榪樼畻鏄庢樉鐨勶紝鏈夋椂鍙兘涓嶄細榪欎箞鏄庢樉錛屼緥濡傛垜浠煡閬揓avaScript涓粠娣卞眰鍑芥暟涓紩鐢ㄥ叏灞�瀵硅薄鐨勪唬浠鋒槸寰堥珮鐨勶紝鍥犱負闇�瑕侀亶鍘嗕綔鐢ㄥ煙閾撅紙褰撶劧鏄殣寮忕殑錛夛紝鍥犳鍦↗S涓鏋滄繁灞傚嚱鏁頒唬鐮侀綣佷嬌鐢ㄥ叏灞�瀵硅薄錛屽垯瑕佷粯鍑哄緢楂樼殑浠ｄ環銆傚鏋滅▼搴忓憳涓嶆噦寰楀璞″強浣滅敤鍩熼摼鐩稿叧鐭ヨ瘑錛屽垯涓嶄細鍙戠幇榪欑娼滃湪鐨勬晥鐜囬棶棰橈紝鑰屾紜殑鍋氭硶鏄嬌鐢ㄤ竴涓眬閮ㄥ彉閲忎繚瀛樺鍏ㄥ眬瀵硅薄鐨勫紩鐢ㄨ�屼笉鏄瘡嬈￠兘鐩存帴浣跨敤鍏ㄥ眬鍙橀噺銆?/p><p>銆�銆�寰堝鎴愮啛鐨勪駭鍝佷篃澶勫浣撶幇鐫�璁＄畻澶嶇敤鐨勬�濇兂錛屽鍦≒HP涓紝涓嬮潰浠ｇ爜鍙互寰楀埌涓�涓暟緇勭殑鍏冪礌涓暟錛?/p><p>echo count($arr);</p><p>銆�銆�濡傛灉鎴戜滑鏉ュ疄鐜幫紝鏈�鑷劧鐨勬兂娉曞氨鏄亶鍘嗘暟緇勩�備絾鏄疨HP鐨勫紑鍙戣�呮槑鏄炬洿鑱槑錛屼粬浠湪寤虹珛鏁扮粍鏃跺悓鏃跺緩绔嬩竴涓笌涔嬪叧鑱旂殑鍐呴儴鐨勬暟閲忚鏁板彉閲忥紙瀵筆HP紼嬪簭鍛橀�忔槑錛夛紝闅忕潃鏁扮粍鍏冪礌鐨勫鍑忥紝榪欎釜鍙橀噺涔熺浉搴斿鍑忥紝姣忔璋冪敤count鍑芥暟鐩存帴榪斿洖榪欎釜鍙橀噺鍗沖彲錛岃繖灝卞皢count鐨勫鏉傚害浠嶰(n)闄嶄負O(1)錛岃繖涔熸槸璁＄畻澶嶇敤鐨勪竴涓吀鍨嬪簲鐢ㄣ�?/p><p>銆�銆�鍙﹀錛屽叾瀹炶綆楀鐢ㄥ拰緙撳瓨鐨勬蹇墊槸鐩擱�氱殑錛屽緢澶氱紦瀛樼郴緇熷氨浣跨敤浜嗚綆楀鐢ㄧ殑鎬濇兂銆?/p><p><br/></p></div>
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