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鍦ㄥ叿浣撹璁轟箣鍓嶏紝鏈枃鍏堝帢娓匲UID錛圲niversally Unique IDentifier錛変笌GUID錛圙lobally Unique IDentifier錛夌殑鍏崇郴銆?/p>

鍦ㄥ垎甯冨紡銆佺綉緇溿佸崟鏈虹幆澧冧笅錛屼負浜嗚兘澶熶嬌鐢ㄥ叿鏈夋煇縐嶅艦寮忕殑ID鍞竴鏍囪瘑緋葷粺涓殑浠諱竴鍏冪礌錛岃繖鏍風殑ID鍙互涓嶄緷璧栦腑蹇冭璇佽嚜鍔ㄧ敓鎴愶紝浜庢槸UUID灝辮癁鐢熶簡銆?/p>

UUID鏍囧噯鐨勫巻鍙叉部闈╁拰鍏蜂綋瀹炵幇鍦?a title="RFC4122" target="_blank">RFC 4122銆?a title="ITU-T rec. x.667" target="_blank">ITU-T Rec. X.667鍜?a title="ISO/IEC 9834-8:2008" target="_blank">ISO/IEC 9834-8:2008涓潎鏈夎緇嗘弿榪般侷TU鍜孖SO閲囩敤鐨勬爣鍑嗗拰RFC 4122閮芥槸鍦║UID鐨勬棭鏈熺増鏈熀紜涓婂畬鎴愶紝鍚勭増鏈箣闂村叿鏈変竴鑷存у拰鍏煎鎬с?/p>

鍥犱負涓嶈兘淇濊瘉UUID鐨勫敮涓鎬э紝ITU鍜孖SO閽堝UUID鐨勪嬌鐢ㄩ兘鏈?a id="eac3" title="鍏嶈矗澹版槑" target="_blank">鍏嶈矗澹版槑銆?/p>

GUID涓鑸槸鎸嘙icrosoft瀵逛簬UUID鏍囧噯鐨勫疄鐜幫紝UUID鐨勫疄鐜板垯澶氳浜庡叾浠栫郴緇燂紙*NIX銆丮AC OS絳夛級涓傚湪浜嗚В浜嗚繖涓鍖哄埆鍚庯紝鏈枃灝嗙粺涓浣跨敤UUID鏉ユ寚浠e搴旂殑鍘熺悊銆佺畻娉曞強瀹炵幇銆?/p>

鏂囦腑鍏充簬UUID鐨勮璁哄叏閮ㄥ熀浜嶳FC 4122鍜孖TU-T Rec. X.667浠ュ強OSF銆両ETF銆両TU錛峊銆両SO銆丗IPS鐨勫悇縐嶆爣鍑嗘枃妗c傝孶UID鐨勭粏鑺傦紙濡傜粨鏋勩佽〃紺恒佺畻娉曘佸疄鐜扮瓑錛夊潎浠TU-T Rec. X667涓哄敮涓钃濇湰錛屾枃涓?#8220;鏈爣鍑?#8221;鍗蟲寚浠h钃濇湰銆?/p>

o 浠嬬粛

UUID鏄暱搴︿負16-byte錛?28-bit錛夌殑ID錛屼竴鑸互褰㈠f81d4fae-7dec-11d0-a765-00a0c91e6bf6鐨勫瓧絎︿覆浣滀負URN錛圲niform Resource Name錛岀粺涓璧勬簮鍚嶇О錛夈?/p>

o 鍔ㄦ満

鏃犻』涓績璁よ瘉錛岃嚜鍔ㄧ敓鎴愶紝鏀寔涓鍙版満鍣ㄦ瘡縐掔敓鎴?0M嬈★紙100綰崇綰э紝鍏墮殣鍚師鍥犳槸鎸囪兘澶熷尯鍒嗙殑鏈灝忔椂闂村崟浣嶄負100ns錛屽皢鏃墮棿浣滀負鍥犲瓙鏃訛紝榪炵畫鐢熸垚涓や釜UUID鐨勬椂闂磋嚦灝戣闂撮殧100ns錛夈傛柟渚垮瓨鍙栥佸垎閰嶃佹帓搴忋佹煡鎵俱?/p>

o 緇撴瀯


   76543210765432107654321076543210
   + – - – = – - – = – - – = – - – +
15 |            TimeLow            | 12
11 |    TimeMid    |   Version..   |  8
7  |Vari.. |Clock..|     Node      |  4
3  |             Node              |  0
   + – - – = – - – = – - – = – - – +
15 – 12: TimeLow 鏃墮棿鍊肩殑浣庝綅
11 – 10: TimeMid 鏃墮棿鍊肩殑涓綅
09 – 08: VersionAndTimeHigh 4浣嶇増鏈彿鍜屾椂闂村肩殑楂樹綅
07: VariantAndClockSeqHigh 2浣嶅彉浣擄紙ITU-T錛夊拰鏃墮挓搴忓垪楂樹綅
06: ClockSeqLow 鏃墮挓搴忓垪浣庝綅
05 – 00: Node 緇撶偣
hexOctet = hexDigit hexDigit
hexDigit =
“0″ / “1″ / “2″ / “3″ / “4″ / “5″ / “6″ / “7″ / “8″ / “9″ /
“a” / “b” / “c” / “d” / “e” / “f” /
“A” / “B” / “C” / “D” / “E” / “F”
UUID =
TimeLow
“-” TimeMid
“-” VersionAndTimeHigh
“-” VariantAndClockSeqHigh ClockSeqLow
“-” Node

UUID鐢變笂榪?涓煙鏋勬垚錛屾瘡涓煙緙栫爜涓鴻嫢騫插瓧鑺傦紝騫朵互16榪涘埗鏁拌〃紺鴻繖128浣嶇殑UUID錛岀浉閭誨煙浠ュ噺鍙?#8220;-”鍒嗛殧 錛圴ariantAndClockSeqHigh鍜孋lockSeqLow瀵瑰簲鐨勪袱涓瓧鑺備緥澶栵紝濡備笂鎵紺猴級銆傝緇撴瀯涓寘鍚増鏈紙Version錛夈佸彉浣? 錛圴ariant錛夈佹椂闂達紙Time錛夈佹椂閽熷簭鍒楋紙Clock Sequence錛夈佽妭鐐癸紙Note錛変俊鎭紙浠ユ棤絎﹀彿鏁村瀷鍊艱〃紺猴級銆?/p>

o 鍚堟硶鎬?/strong>

闄ゅ垽鏂璿ariant浣嶈緗槸鍚︽紜佸熀浜庢椂闂寸敓鎴愮殑UUID鏃墮棿鍊兼槸鍚︿負鏈粡鍒嗛厤鐨勫皢鏉ユ椂闂村錛屽疄闄呭簲鐢ㄤ腑娌℃湁鍏朵粬鏈哄埗鍙互鍒ゅ畾UUID鏄惁鍚堟硶銆?/p>

o 鍙樹綋

Variant浣嶆槸UUID絎?瀛楄妭錛圴ariantAndClockSeqHigh錛夌殑鏈楂?浣嶏紝

7 6 5  Description
0 – –  NCS鍚戝悗鍏煎
1 0 –  鏈爣鍑?br> 1 1 0  Microsoft鍚戝悗鍏煎
1 1 1  ITU-T Rec. X.667淇濈暀

o 鐗堟湰

UUID鐨勭敓鎴愭湁鏃墮棿銆佸悕縐般侀殢鏈烘暟涓夌絳栫暐錛屼互絎?瀛楄妭錛圴ersionAndTimeHigh錛夌殑鏈楂?浣嶈〃紺恒?/p>

鐩墠UUID瀹氫箟鏈?涓増鏈細

7 6 5 4  Ver  Description
0 0 0 1  1    鍩轟簬鏃墮棿鐨勭増鏈紙鏈爣鍑嗭級
0 0 0 0  2    浣跨敤宓屽叆寮廝OSIX錛圖CE瀹夊叏鐗堟湰錛?br> 0 0 1 1  3    浣跨敤MD5鍝堝笇鐨勫熀浜庡悕縐扮殑鐗堟湰錛堟湰鏍囧噯錛?br> 0 1 0 0  4    鍩轟簬闅忔満鏁扮殑鐗堟湰錛堟湰鏍囧噯錛?br> 0 1 0 1  5    浣跨敤SHA-1鐨勫熀浜庡悕縐扮殑鐗堟湰錛堟湰鏍囧噯錛?/p>

o 鏃墮棿

鏃墮棿鏄竴涓?0浣嶇殑鏁村瀷鍊鹼紙闄?浣嶇増鏈彿澶栫殑鍓?瀛楄妭錛夛紝瀵瑰簲UTC錛堟牸鏋楀凹娌繪椂闂?582騫?0鏈?5鏃ュ崍澶滃錛夌殑100ns鏃墮棿闂撮殧璁℃暟銆?/p>

瀵逛簬ver 4鍜?錛岃鍊煎垎鍒搴斾竴涓殢鏈烘暟鍜屼竴涓叏灞鍞竴鐨勫悕縐般?/p>

o 鏃墮挓搴忓垪

瀵瑰熀浜庢椂闂寸殑UUID鐗堟湰錛屾椂闂村簭鍒楃敤浜庨伩鍏嶅洜鏃墮棿鍚戝悗璁劇疆鎴栬妭鐐瑰兼敼鍙樺彲鑳介犳垚鐨刄UID閲嶅錛屽鍩轟簬鍚嶇О鎴栭殢鏈烘暟鐨勭増鏈悓鏍鋒湁鐢細鐩殑閮芥槸涓轟簡闃叉UUID閲嶅銆?/p>

濡傛灉鍓嶄竴鏃墮挓搴忓垪宸茬煡錛岄氳繃鑷瀹炵幇鏃墮挓搴忓垪鍊肩殑鏀瑰彉錛涘惁鍒欙紝閫氳繃瀵嗙爜瀛︼紙浼級闅忔満鏁拌緗柊鐨勬椂閽熷簭鍒楀箋?/p>

o 鑺傜偣

瀵瑰熀浜庢椂闂寸殑UUID鐗堟湰錛岃妭鐐圭敱48浣嶇殑鍗曟挱MAC鍦板潃鏋勬垚銆傚浜庢病鏈塎AC鍦板潃鐨勭郴緇燂紝鑺傜偣鍊間負涓涓瘑鐮佸錛堜吉錛夐殢鏈烘暟錛堜負闃叉涓嶮AC鍦板潃鍙戠敓紕版挒錛岄渶璁劇疆澶氭挱浣嶏級銆?/p>


o 鍩轟簬鏃墮棿鐨刄UID鐢熸垚綆楁硶

o 紜畾UTC鏃墮棿錛?0浣?Time錛夊拰鏃墮棿搴忓垪鍊鹼紙14浣?ClockSequence錛夛紱

o 璁劇疆TimeLow錛堝搴擳ime鐨?1-0浣嶏級錛?/p>

o 璁劇疆TimeMid錛堝搴擳ime鐨?7-32浣嶏級錛?/p>

o 璁劇疆VersionAndTimeHigh錛?浣嶇増鏈彿鍙奣ime鐨?9-48浣嶏級錛?/p>

o 璁劇疆VariantAndClockSeqHigh錛堝彉浣撲綅鍙婂搴擟lockSequence鐨?3-8浣嶏級錛?/p>

o 璁劇疆ClockSeqLow錛堝搴擟lockSequence鐨?-0浣嶏級錛?/p>

o 璁劇疆Node錛堝搴?8浣峂AC鍦板潃錛夈?/p>

o 鍩轟簬鍚嶇О鐨刄UID鐢熸垚綆楁硶

o 閽堝鐩稿簲鐨勫懡鍚嶇┖闂達紙濡侱NS銆乁RL銆丱ID絳夛級鍒嗛厤涓涓猆UID浣滀負鎵鏈塙UID鐨勫懡鍚嶇┖闂存爣璇嗭紱

o 灝嗗悕縐拌漿鎹負瀛楄妭鏁板垪錛?/p>

o 浣跨敤MD5鎴朣HA-1綆楁硶瀵逛笌鍚嶇О鍏寵仈鐨勫懡鍚嶇┖闂存爣璇嗚繘琛岃綆楋紝浜х敓16瀛楄妭鍝堝笇緇撴灉錛?/p>

o 璁劇疆TimeLow錛堝搴斿搱甯屽肩殑3-0瀛楄妭錛夛紱

o 璁劇疆TimeMid錛堝搴斿搱甯屽肩殑5-4瀛楄妭錛夛紱

o 璁劇疆VersionAndTimeHigh錛堝搴斿搱甯屽肩殑7-6瀛楄妭錛夛紝浠ョ浉搴旂増鏈彿閲嶅啓瀵瑰簲浣嶏紙絎?瀛楄妭鐨勯珮4浣嶏級錛?/p>

o 璁劇疆VariantAndClockSeqHigh錛堝搴斿搱甯屽肩殑絎?瀛楄妭錛夛紝閲嶅啓鍙樹綋瀵瑰簲浣嶏紙絎?瀛楄妭鐨勯珮2浣嶏紝鏈爣鍑嗗搴斿間負10錛夛紱

o 璁劇疆ClockSeqLow錛堝搴斿搱甯屽肩殑絎?瀛楄妭錛夛紱

o 璁劇疆Node錛堝搴斿搱甯屽肩殑15-10瀛楄妭錛夈?/p>

鐢? 浜嶮D5紕版挒闂錛孧D5鍙敤浜庡悜鍚庡吋瀹圭殑UUID鐢熸垚錛屼笉鍐嶈鎺ㄨ崘浣跨敤銆傜敱浜嶴HA-1鍝堝笇緇撴灉涓?60浣嶏紙20瀛楄妭錛夛紝鏈畻娉曚腑錛岄渶瑕佸皢FIPS PUB 180-2涓殑SHA-1綆楁硶鐨勫搱甯屽煎瓧鑺傞『搴忓弽杞紙瀛楄妭鍐呴『搴忎笉鍙橈級錛孶UID浣跨敤鍏?5-0瀛楄妭錛?9-16瀛楄妭琚涪寮冦?/p>

o 鍩轟簬闅忔満鏁扮殑UUID鐢熸垚綆楁硶

o 璁劇疆VariantAndClockSeqHigh鐨勫彉浣撲綅鍊間負10錛?/p>

o 璁劇疆VersionAndTimeHigh鐨?浣嶇増鏈彿錛?/p>

o 璁劇疆鍓╀綑浣嶄負闅忔満鍊箋?/p>

鏈枃涓璁虹殑瀵嗙爜瀛﹂殢鏈烘暟錛屼富瑕佹牴鎹郴緇熷彲浠ユ彁渚涚殑淇℃伅錛堝唴瀛樸佺‖鐩樸佸彞鏌勩佺▼搴忚繍琛岀殑綰跨▼銆佽繘紼嬨佸彞鏌勩佸爢鏍堢瓑錛夛紝鍒╃敤SHA-1絳夊搱甯岀畻娉曞緱鍒般?/p>

鍏朵粬鍏充簬瀵嗙爜瀛﹂殢鏈烘暟鐨勬弿榪幫紝鎴戞浘鍦?a id="dtto" title="鍏鋒湁瀵嗙爜瀛︽剰涔夌殑PRNG錛圕SPRNG錛? target="_blank">榪欑瘒鏂囩珷涓畝鍗曟彁鍒般?/p>


鍏蜂綋綆楁硶瀹炵幇鍙互鍙傝冩枃妗e拰寮婧愪唬鐮併?


Fox 2009-12-06 15:07 鍙戣〃璇勮
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緇堣Fibonacci鏁?/title><link>http://www.shnenglu.com/Fox/archive/2008/11/06/66071.html</link><dc:creator>Fox</dc:creator><author>Fox</author><pubDate>Wed, 05 Nov 2008 16:34:00 GMT</pubDate><guid>http://www.shnenglu.com/Fox/archive/2008/11/06/66071.html</guid><wfw:comment>http://www.shnenglu.com/Fox/comments/66071.html</wfw:comment><comments>http://www.shnenglu.com/Fox/archive/2008/11/06/66071.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.shnenglu.com/Fox/comments/commentRss/66071.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/Fox/services/trackbacks/66071.html</trackback:ping><description><![CDATA[<p>鐜板湪姣忓ぉ鐨勫伐浣滀富瑕佹槸涓轟簡婊¤凍欏圭洰闇姹傚拰榪涘害鑰屼笉鍋滅殑鎬濊冦佹暡閿洏銆傛湁鏃跺欎篃紜疄闇瑕佹娊鐐規椂闂存潵鎬濊冩濊冮偅浜涚湅涓婂幓鐢ㄤ笉鍒扮殑涓浜涗笢瑗匡紝鍙堟兂璧蜂簡<strong>Fibonacci鏁?/strong>銆?/p> <p>涔嬪墠鏇劇粡涓夋鍐欒繃<strong>Fibonacci鏁?/strong>錛?007騫?鏈堢殑<a title="鎴戠殑Fibonacci鏁板垪" target="_blank">鎴戠殑Fibonacci鏁板垪</a>錛?007騫?2鏈堢殑<a title="涔熻璇寸駭鏁版眰鍜?1+2+3…N)鍜屽叾浠? target="_blank">涔熻璇寸駭鏁版眰鍜?1+2+3鈥)鍜屽叾浠?/a>錛?008騫?鏈堢殑<a >鍔ㄦ佽鍒掔畻娉?/a>錛屼絾緇欏嚭鐨勯兘涓嶆槸闈炲父浼樼殑綆楁硶銆?/p> <p>涓婃鍥炲幓鎶婂悓瀛﹀熺殑銆婄紪紼嬩箣緹庛嬪伔榪囨潵榪樻病鎬庝箞鐪嬶紝鏅氫笂緲諱簡涓涓嬶紝鐪嬪埌鏈夎<strong>Fibonacci鏁?/strong>錛屾兂璧鋒潵<a title="Donald E.Knuth" target="_blank" rel="tag">Knuth</a>鐨凾he Art of Computer Programming Vol.1涔熻榪囷紝瑙夊緱鏈夊繀瑕佸<strong>Fibonacci鏁?/strong>鍋氫釜浜嗘柇銆?/p> <p>璇氬<a title="Donald E.Knuth" target="_blank" rel="tag">Knuth</a>鍦═he Art of Computer Programming Vol.1鎵榪幫紝<a title="Fibonacci" target="_blank" rel="tag">Fibonacci</a>鏄腑涓栫邯浠ユ潵嬈ф床鏈浼熷ぇ鐨勬暟瀛﹀錛屼粬鍏充簬al-Khwarizmi鐨勭爺絀跺偓鐢熶簡綆楁硶錛坅lgorithm錛変竴璇嶃?/p> <p><a target="_blank">闃呰鍏ㄦ枃</a></p> <p><strong>鐪嬪埌榪欎簺錛屾垜鍙堟縺鍔ㄤ簡錛屾暟瀛︿箣緹庯紝涓嶆鏄編鍦ㄨ繖浜涘湴鏂瑰悧錛熸垜浠笉鏄鍋氭暟瀛﹀錛屼絾榪欏茍涓嶅Θ紕嶆垜浠珯鍦ㄩ棬鍙e悜閲屽紶鏈涒︹?/strong></p><img src ="http://www.shnenglu.com/Fox/aggbug/66071.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.shnenglu.com/Fox/" target="_blank">Fox</a> 2008-11-06 00:34 <a href="http://www.shnenglu.com/Fox/archive/2008/11/06/66071.html#Feedback" target="_blank" style="text-decoration:none;">鍙戣〃璇勮</a></div>]]></description></item><item><title>鍔ㄦ佽鍒掔畻娉?/title><link>http://www.shnenglu.com/Fox/archive/2008/05/07/Dynamic_programming.html</link><dc:creator>Fox</dc:creator><author>Fox</author><pubDate>Wed, 07 May 2008 12:43:00 GMT</pubDate><guid>http://www.shnenglu.com/Fox/archive/2008/05/07/Dynamic_programming.html</guid><wfw:comment>http://www.shnenglu.com/Fox/comments/49153.html</wfw:comment><comments>http://www.shnenglu.com/Fox/archive/2008/05/07/Dynamic_programming.html#Feedback</comments><slash:comments>6</slash:comments><wfw:commentRss>http://www.shnenglu.com/Fox/comments/commentRss/49153.html</wfw:commentRss><trackback:ping>http://www.shnenglu.com/Fox/services/trackbacks/49153.html</trackback:ping><description><![CDATA[<p>浠ュ墠鍦ㄥ涔犻潪鏁板肩畻娉曠殑鏃跺欙紝鏇劇粡浜嗚В榪?a target="_blank">鍔ㄦ佽鍒掔畻娉曪紙Dynamic programming錛?/a>錛屼互涓嬫槸瀵?a target="_blank">Wikipedia</a>涓?a target="_blank">鍔ㄦ佽鍒?/a>鐨勭炕璇戯紝鍥句篃鏄?a target="_blank">Wikipedia</a>涓婄殑錛屼粨淇冭鏂囷紝涓嶅埌涔嬪錛岃鏂瑰鎸囨銆?/p> <p>榪欑瘒鏂囩珷鐨勬湳璇疄鍦ㄦ槸澶浜嗭紝鎵浠ユ垜鍦ㄦ枃涓姞鍏ヤ簡灝戦噺娉ㄩ噴錛屼竴寰嬩互<em><strong>綺楁枩浣?/strong></em>娉ㄦ槑銆?/p> <p>鏈枃鐨勪笉瓚充箣澶勫皢<strong>闅忔椂淇</strong>錛孧IT鐨勩?a target="_blank">Introduction to Algorithms</a>銆嬬15绔犳槸涓撻棬璁插姩鎬佽鍒掔殑銆?/p> <p>_____________________________________________________________</p> <p align="center"><strong><a target="_blank">鍔ㄦ佽鍒?/a></strong></p> <p>鍦ㄦ暟瀛︿笌璁$畻鏈虹瀛﹂鍩燂紝<strong>鍔ㄦ佽鍒?/strong>鐢ㄤ簬瑙e喅閭d簺鍙垎瑙d負<a target="_blank">閲嶅瀛愰棶棰?/a>錛坥verlapping subproblems錛?em><strong>鎯蟲兂閫掑綊姹傞樁涔樺惂</strong></em>錛夊茍鍏鋒湁<a target="_blank">鏈浼樺瓙緇撴瀯</a>錛坥ptimal substructure錛?strong><em>鎯蟲兂鏈鐭礬寰勭畻娉?/em></strong>錛夛紙濡備笅鎵榪幫級鐨勯棶棰橈紝鍔ㄦ佽鍒掓瘮閫氬父綆楁硶鑺辮垂鏇村皯鏃墮棿銆? <p>涓婁笘綰?0騫翠唬錛?a target="_blank">Richard Bellman</a>鏈鏃╀嬌鐢ㄥ姩鎬佽鍒掕繖涓姒傚康琛ㄨ堪閫氳繃閬嶅巻瀵繪壘鏈浼樺喅絳栬В闂鐨勬眰瑙h繃紼嬨?953騫達紝Richard Bellman灝嗗姩鎬佽鍒?a target="_blank">璧嬩簣鐜頒唬鎰忎箟</a>錛岃棰嗗煙琚獻EEE綰沖叆緋葷粺鍒嗘瀽鍜屽伐紼嬩腑銆備負綰康Bellman鐨勮礎鐚紝鍔ㄦ佽鍒掔殑鏍稿績鏂圭▼琚懡鍚嶄負<a target="_blank">璐濆皵鏇兼柟紼?/a>錛岃鏂圭▼浠?a target="_blank">閫掑綊</a>褰㈠紡閲嶇敵浜嗕竴涓紭鍖栭棶棰樸? <p>鍦ㄢ滃姩鎬佽鍒掆濓紙dynamic programming錛変竴璇嶄腑錛宲rogramming涓庘滆綆楁満緙栫▼鈥濓紙computer programming錛変腑鐨刾rogramming騫舵棤鍏寵仈錛岃屾槸鏉ヨ嚜鈥?a target="_blank">鏁板瑙勫垝</a>鈥濓紙mathematical programming錛夛紝涔熺О浼樺寲銆傚洜姝わ紝瑙勫垝鏄寚瀵圭敓鎴愭椿鍔ㄧ殑浼樺寲絳栫暐銆備婦涓緥瀛愶紝緙栧埗涓鍦哄睍瑙堢殑鏃ョ▼鍙О涓鴻鍒掋?鍦ㄦ鎰忎箟涓婏紝瑙勫垝鎰忓懗鐫鎵懼埌涓涓彲琛岀殑媧誨姩璁″垝銆? <ul> <li> <div align="left"><strong>姒傝堪</strong></div></li></ul> <p><img style="margin: 10px" src="http://upload.wikimedia.org/wikipedia/en/4/42/Shortest_path_optimal_substructure.png" align="left"> <p><strong></strong>  <p><strong>鍥?</strong> 浣跨敤鏈浼樺瓙緇撴瀯瀵繪壘鏈鐭礬寰勶細鐩寸嚎琛ㄧず杈癸紝娉㈢姸綰胯〃紺轟袱欏剁偣闂寸殑鏈鐭礬寰勶紙璺緞涓叾浠栬妭鐐規湭鏄劇ず錛夛紱綺楃嚎琛ㄧず浠庤搗鐐瑰埌緇堢偣鐨勬渶鐭礬寰勩? <p><strong><em>涓嶉毦鐪嬪嚭錛宻tart鍒癵oal鐨勬渶鐭礬寰勭敱start鐨勭浉閭昏妭鐐瑰埌goal鐨勬渶鐭礬寰勫強start鍒板叾鐩擱偦鑺傜偣鐨勬垚鏈喅瀹氥?/em></strong> <p><strong><em></em></strong>  <p>  <p>鏈浼樺瓙緇撴瀯鍗沖彲鐢ㄦ潵瀵繪壘鏁翠釜闂鏈浼樿В鐨勫瓙闂鐨勬渶浼樿В銆備婦渚嬫潵璇達紝瀵繪壘<a target="_blank">鍥?/a>涓婃煇欏剁偣鍒扮粓鐐圭殑<a target="_blank">鏈鐭礬寰?/a>錛屽彲鍏堣綆楄欏剁偣鎵鏈夌浉閭婚《鐐硅嚦緇堢偣鐨勬渶鐭礬寰勶紝鐒跺悗浠ユ鏉ラ夋嫨鏈浣蟲暣浣撹礬寰勶紝濡?strong>鍥?</strong>鎵紺恒? <p>涓鑸岃█錛屾渶浼樺瓙緇撴瀯閫氳繃濡備笅涓変釜姝ラ瑙e喅闂錛? <p>a) 灝嗛棶棰樺垎瑙f垚杈冨皬鐨勫瓙闂錛? <p>b) 閫氳繃閫掑綊浣跨敤榪欎笁涓楠ゆ眰鍑哄瓙闂鐨勬渶浼樿В錛? <p>c) 浣跨敤榪欎簺鏈浼樿В鏋勯犲垵濮嬮棶棰樼殑鏈浼樿В銆? <p>瀛愰棶棰樼殑姹傝В鏄氳繃涓嶆柇鍒掑垎涓烘洿灝忕殑瀛愰棶棰樺疄鐜扮殑錛岀洿鑷蟲垜浠彲浠ュ湪甯告暟鏃墮棿鍐呮眰瑙c? <p><img style="margin: 10px" src="http://upload.wikimedia.org/wikipedia/commons/thumb/0/06/Fibonacci_dynamic_programming.svg/108px-Fibonacci_dynamic_programming.svg.png" align="left"> <p><strong></strong>  <p><strong></strong>  <p><strong>鍥?</strong> Fibonacci搴忓垪鐨勫瓙闂紺烘剰鍥撅細浣跨敤<a target="_blank">鏈夊悜鏃犵幆鍥?/a>錛圖AG, directed acyclic graph錛夎岄潪<a target="_blank">鏍?/a>琛ㄧず閲嶅瀛愰棶棰樼殑鍒嗚В銆? <p><strong><em>涓轟粈涔堟槸DAG鑰屼笉鏄爲鍛紵絳旀灝辨槸錛屽鏋滄槸鏍戠殑璇濓紝浼氭湁寰堝閲嶅璁$畻錛屼笅闈㈡湁鐩稿叧鐨勮В閲娿?/em></strong> <p>  <p>  <p>涓涓棶棰樺彲鍒掑垎涓洪噸澶嶅瓙闂鏄寚閫氳繃鐩稿悓鐨勫瓙闂鍙互瑙e喅涓嶅悓鐨勮緝澶ч棶棰樸備緥濡傦紝鍦‵ibonacci搴忓垪涓紝F3 = F1 + F2鍜孎4 = F2 + F3閮藉寘鍚綆桭2銆傜敱浜庤綆桭5闇瑕佽綆桭3鍜孎4錛屼竴涓瘮杈冪鐨勮綆桭5鐨勬柟娉曞彲鑳戒細閲嶅璁$畻F2涓ゆ鐢氳嚦涓ゆ浠ヤ笂銆傝繖涓鐐瑰鎵鏈夐噸澶嶅瓙闂閮介傜敤錛氭剼锠㈢殑鍋氭硶鍙兘浼氫負閲嶅璁$畻宸茬粡瑙e喅鐨勬渶浼樺瓙闂鐨勮В鑰屾氮璐規椂闂淬? <p>涓洪伩鍏嶉噸澶嶈綆楋紝鍙皢宸茬粡寰楀埌鐨勫瓙闂鐨勮В淇濆瓨璧鋒潵錛屽綋鎴戜滑瑕佽В鍐崇浉鍚岀殑瀛愰棶棰樻椂錛岄噸鐢ㄥ嵆鍙傝鏂規硶鍗蟲墍璋撶殑<a target="_blank">緙撳瓨</a>錛坢emoization錛岃屼笉鏄瓨鍌╩emorization錛岃櫧鐒惰繖涓瘝浜﹂傚悎錛?strong><em>濮戜笖榪欎箞鍙惂錛岃繖涓崟璇嶅お闅劇炕璇戜簡錛岀畝鐩村氨鏄彲鎰忎細涓嶅彲璦浼狅紝鍏舵剰涔夋槸娌¤綆楄繃鍒欒綆楋紝璁$畻榪囧垯淇濆瓨</em></strong>錛夈傚綋鎴戜滑紜俊灝嗕笉浼氬啀闇瑕佹煇涓瑙f椂錛屽彲浠ュ皢鍏舵姏寮冿紝浠ヨ妭鐪佺┖闂淬傚湪鏌愪簺鎯呭喌涓嬶紝鎴戜滑鐢氳嚦鍙互鎻愬墠璁$畻鍑洪偅浜涘皢鏉ヤ細鐢ㄥ埌鐨勫瓙闂鐨勮В銆? <p>鎬繪嫭鑰岃█錛屽姩鎬佽鍒掑埄鐢細 <p>1) <a target="_blank">閲嶅瀛愰棶棰?/a> <p>2) <a target="_blank">鏈浼樺瓙緇撴瀯</a> <p>3) <a target="_blank">緙撳瓨</a> <p>鍔ㄦ佽鍒掗氬父閲囩敤浠ヤ笅涓ょ鏂瑰紡涓殑涓縐嶄袱涓姙娉曪細 <p><a target="_blank">鑷《鍚戜笅</a>錛氬皢闂鍒掑垎涓鴻嫢騫插瓙闂錛屾眰瑙h繖浜涘瓙闂騫朵繚瀛樼粨鏋滀互鍏嶉噸澶嶈綆椼傝鏂規硶灝嗛掑綊鍜岀紦瀛樼粨鍚堝湪涓璧楓? <p><a target="_blank">鑷笅鑰屼笂</a>錛氬厛琛屾眰瑙f墍鏈夊彲鑳界敤鍒扮殑瀛愰棶棰橈紝鐒跺悗鐢ㄥ叾鏋勯犳洿澶ч棶棰樼殑瑙c傝鏂規硶鍦ㄨ妭鐪佸爢鏍堢┖闂村拰鍑忓皯鍑芥暟璋冪敤鏁伴噺涓婄暐鏈変紭鍔匡紝浣嗘湁鏃舵兂鎵懼嚭緇欏畾闂鐨勬墍鏈夊瓙闂騫朵笉閭d箞鐩磋銆? <p>涓轟簡鎻愰珮<a target="_blank">鎸夊悕浼犻?/a>錛坈all-by-name錛岃繖涓鏈哄埗涓?a target="_blank">鎸夐渶浼犻?/a>call-by-need鐩稿叧錛?strong><em>澶嶄範涓涓嬪弬鏁頒紶閫掔殑鍚勭瑙勫垯鍚э紝綆鍗曡涓涓嬶紝鎸夊悕浼犻掑厑璁告敼鍙樺疄鍙傚?/em></strong>錛夌殑鏁堢巼錛屼竴浜涚紪紼嬭璦灝嗗嚱鏁扮殑榪斿洖鍊尖滆嚜鍔ㄢ濈紦瀛樺湪鍑芥暟鐨勭壒瀹氬弬鏁伴泦鍚堜腑銆備竴浜涜璦灝嗚繖涓鐗規у敖鍙兘綆鍖栵紙濡?a target="_blank">Scheme</a>銆?a target="_blank">Common Lisp</a>鍜?a target="_blank">Perl</a>錛夛紝涔熸湁涓浜涜璦闇瑕佽繘琛岀壒孌婃墿灞曪紙濡侰++錛?strong><em>C++涓嬌鐢ㄧ殑鏄寜鍊間紶閫掑拰鎸夊紩鐢ㄤ紶閫掞紝鍥犳C++涓湰鏃犺嚜鍔ㄧ紦瀛樻満鍒訛紝闇鑷瀹炵幇錛屽叿浣撳疄鐜扮殑涓涓緥瀛愭槸<a target="_blank">Automated Memoization in C++</a></em></strong>錛夈傛棤璁哄浣曪紝鍙湁<a target="_blank">鎸囩О閫忔槑</a>錛坮eferentially transparent錛?strong><em>鎸囩О閫忔槑鏄寚鍦ㄧ▼搴忎腑浣跨敤琛ㄨ揪寮忋佸嚱鏁版湰韜垨浠ュ叾鍊兼浛鎹㈠紼嬪簭緇撴灉娌℃湁浠諱綍褰卞搷</em></strong>錛夊嚱鏁版墠鍏鋒湁榪欎竴鐗規с? <ul> <li><strong>渚嬪瓙</strong> </li></ul> <p><strong>1. Fibonacci搴忓垪</strong> <p>瀵繪壘<a target="_blank">Fibonacci搴忓垪</a>涓n涓暟錛屽熀浜庡叾鏁板瀹氫箟鐨勭洿鎺ュ疄鐜幫細 <p>   function fib(n)<br>       if n = 0 <br>           return 0<br>       else if n = 1<br>           return 1<br>       return fib(n-1) + fib(n-2) <p>濡傛灉鎴戜滑璋冪敤fib(5)錛屽皢浜х敓涓媯靛浜庡悓涓鍊奸噸澶嶈綆楀嬈$殑璋冪敤鏍戯細 <ol> <li>fib(5) <li>fib(4) + fib(3) <li>(fib(3) + fib(2)) + (fib(2) + fib(1)) <li>((fib(2) + fib(1)) + (fib(1) + fib(0))) + ((fib(1) + fib(0)) + fib(1)) <li>(((fib(1) + fib(0)) + fib(1)) + (fib(1) + fib(0))) + ((fib(1) + fib(0)) + fib(1)) </li></ol> <p>鐗瑰埆鏄紝fib(2)璁$畻浜?嬈°傚湪鏇村ぇ瑙勬ā鐨勪緥瀛愪腑錛岃繕鏈夋洿澶歠ib鐨勫艱閲嶅璁$畻錛屽皢娑堣楁寚鏁扮駭鏃墮棿銆? <p>鐜板湪錛屽亣璁炬垜浠湁涓涓畝鍗曠殑<a target="_blank">鏄犲皠</a>錛坢ap錛夊璞?em>m</em>錛屼負姣忎竴涓綆楄繃鐨刦ib鍙婂叾榪斿洖鍊煎緩绔嬫槧灝勶紝淇敼涓婇潰鐨勫嚱鏁癴ib錛屼嬌鐢ㄥ茍涓嶆柇鏇存柊<em>m</em>銆傛柊鐨勫嚱鏁板皢鍙渶<em>O</em>(<em>n</em>)鐨勬椂闂達紝鑰岄潪鎸囨暟鏃墮棿錛? <p>   var m := map(0 鈫?1, 1 鈫?1)<br>   function fib(n)<br>       if map m does not contain key n<br>           m[n] := fib(n-1) + fib(n-2)<br>       return m[n] <p>榪欎竴淇濆瓨宸茶綆楀嚭鐨勬暟鍊肩殑鎶鏈嵆琚О涓?a target="_blank">緙撳瓨</a>錛岃繖鍎夸嬌鐢ㄧ殑鏄?strong>鑷《鍚戜笅</strong>鐨勬柟娉曪細鍏堝皢闂鍒掑垎涓鴻嫢騫插瓙闂錛岀劧鍚庤綆楀拰瀛樺偍鍊箋? <p>鍦?strong>鑷笅鑰屼笂</strong>鐨勬柟娉曚腑錛屾垜浠厛璁$畻杈冨皬鐨刦ib錛岀劧鍚庡熀浜庡叾璁$畻鏇村ぇ鐨刦ib銆傝繖縐嶆柟娉曚篃鍙姳璐圭嚎鎬э紙<em>O</em>(<em>n</em>)錛夋椂闂達紝鍥犱負瀹冨寘鍚竴涓?em>n</em>-1嬈$殑寰幆銆傜劧鑰岋紝榪欎竴鏂規硶鍙渶瑕佸父鏁幫紙<em>O</em>(1)錛夌殑絀洪棿錛岀浉鍙嶏紝<strong>鑷《鍚戜笅</strong>鐨勬柟娉曞垯闇瑕丱(<em>n</em>)鐨勭┖闂存潵鍌ㄥ瓨鏄犲皠鍏崇郴銆? <p>   function fib(n)<br>       var previousFib := 0, currentFib := 1<br>       if n = 0 <br>           return 0<br>       else if n = 1<br>           return 1<br>       repeat n-1 times<br>           var newFib := previousFib + currentFib<br>           previousFib := currentFib<br>           currentFib  := newFib<br>       return currentFib <p>鍦ㄨ繖涓や釜渚嬪瓙錛屾垜浠兘鍙綆梖ib(2)涓嬈★紝鐒跺悗鐢ㄥ畠鏉ヨ綆梖ib(3)鍜宖ib(4)錛岃屼笉鏄瘡嬈¢兘閲嶆柊璁$畻銆? <p><strong>2. 涓縐嶅鉤琛$殑0-1鐭╅樀</strong> <p>鑰冭檻<em>n</em>*<em>n</em>鐭╅樀鐨勮祴鍊奸棶棰橈細鍙兘璧?鍜?錛?em>n</em>涓哄伓鏁幫紝浣挎瘡涓琛屽拰鍒楀潎鍚?em>n</em>/2涓?鍙?em>n</em>/2涓?銆備緥濡傦紝褰?em>n</em>=4鏃訛紝涓ょ鍙兘鐨勬柟妗堟槸錛? <p>+ - - - - +             + - - - - +<br>| 0 1 0 1 |             | 0 0 1 1 |<br>| 1 0 1 0 |             | 0 0 1 1 |<br>| 0 1 0 1 |             | 1 1 0 0 |<br>| 1 0 1 0 |             | 1 1 0 0 |<br>+ - - - - +             + - - - - + <p>闂細瀵逛簬緇欏畾<em>n</em>錛屽叡鏈夊灝戠涓嶅悓鐨勮祴鍊兼柟妗堛? <p>鑷沖皯鏈変笁縐嶅彲鑳界殑綆楁硶鏉ヨВ鍐寵繖涓闂錛?a target="_blank">絀蜂婦娉?/a>錛坆rute force錛夈?a target="_blank">鍥炴函娉?/a>錛坆acktracking錛夊強鍔ㄦ佽鍒掞紙dynamic programming錛夈傜┓涓炬硶鍒椾婦鎵鏈夎祴鍊兼柟妗堬紝騫墮愪竴鎵懼嚭婊¤凍騫寵 鏉′歡鐨勬柟妗堛傜敱浜庡叡鏈塁(<em>n</em>, <em>n</em>/2)^<em>n</em>縐嶆柟妗堬紙<strong><em>鍦ㄤ竴琛屼腑錛屽惈n/2涓?鍙妌/2涓?鐨勭粍鍚堟暟涓篊(n,n/2)錛岀浉褰撲簬浠巒涓綅緗腑閫夊彇n/2涓綅緗疆0錛屽墿涓嬬殑鑷劧鏄?</em></strong>錛夛紝褰?em>n</em>=6鏃訛紝絀蜂婦娉曞氨宸茬粡鍑犱箮涓嶅彲琛屼簡銆傚洖婧硶鍏堝皢鐭╅樀涓儴鍒嗗厓绱犵疆涓?鎴?錛岀劧鍚庢鏌ユ瘡涓琛屽拰鍒椾腑鏈璧嬪肩殑鍏冪礌騫惰祴鍊鹼紝浣垮叾婊¤凍姣忎竴琛屽拰鍒椾腑0鍜?鐨勬暟閲忓潎涓?em>n</em>/2銆傚洖婧硶姣旂┓涓炬硶鏇村姞宸у涓浜涳紝浣嗕粛闇閬嶅巻鎵鏈夎В鎵嶈兘紜畾瑙g殑鏁扮洰錛屽彲浠ョ湅鍒幫紝褰?em>n</em>=8鏃訛紝璇ラ瑙g殑鏁扮洰宸茬粡楂樿揪116963796250銆傚姩鎬佽鍒掑垯鏃犻渶閬嶅巻鎵鏈夎В渚垮彲紜畾瑙g殑鏁扮洰錛?strong><em>鎰忔濇槸鍒掑垎瀛愰棶棰樺悗錛屽彲鏈夋晥閬垮厤鑻ュ共瀛愰棶棰樼殑閲嶅璁$畻</em></strong>錛夈? <p>閫氳繃鍔ㄦ佽鍒掓眰瑙h闂鍑轟箮鎰忔枡鐨勭畝鍗曘傝冭檻姣忎竴琛屾伆鍚?em>n</em>/2涓?鍜?em>n</em>/2涓?鐨?em>k</em>*<em>n</em>(1<=<em>k</em><=<em>n</em>)鐨勫瓙鐭╅樀錛屽嚱鏁癴鏍規嵁姣忎竴琛岀殑鍙兘鐨勮祴鍊兼槧灝勪負涓涓悜閲忥紝姣忎釜鍚戦噺鐢?em>n</em>涓暣鏁板鏋勬垚銆傚悜閲忔瘡涓鍒楀搴旂殑涓涓暣鏁板涓殑涓や釜鏁存暟鍒嗗埆琛ㄧず璇ュ垪涓婅琛屼互涓嬪凡緇忔斁緗殑0鍜?鐨勬暟閲忋傝闂鍗寵漿鍖栦負瀵繪壘f((<em>n</em>/2,<em>n</em>/2),(<em>n</em>/2,<em>n</em>/2),...,(<em>n</em>/2,<em>n</em>/2))錛堝叿鏈?em>n</em>涓弬鏁版垨鑰呰鏄竴涓惈<em>n</em>涓厓绱犵殑鍚戦噺錛夌殑鍊箋傚叾瀛愰棶棰樼殑鏋勯犺繃紼嬪涓嬶細 <p>1) 鏈涓婇潰涓琛岋紙<strong><em>絎琸琛?/em></strong>錛夊叿鏈塁(<em>n</em>, <em>n</em>/2)縐嶈祴鍊鹼紱 <p>2) 鏍規嵁鏈涓婇潰涓琛屼腑姣忎竴鍒楃殑璧嬪兼儏鍐碉紙涓?鎴?錛夛紝灝嗗叾瀵瑰簲鏁存暟瀵逛腑鐩稿簲鐨勫厓绱犲煎噺1錛? <p>3) 濡傛灉浠諱竴鏁存暟瀵逛腑鐨勪換涓鍏冪礌涓鴻礋錛屽垯璇ヨ祴鍊奸潪娉曪紝涓嶈兘鎴愪負姝g‘瑙o紱 <p>4) 鍚﹀垯錛屽畬鎴愬<em>k</em>*<em>n</em>鐨勫瓙鐭╅樀涓渶涓婇潰涓琛岀殑璧嬪鹼紝鍙?em>k</em>=<em>k</em>-1錛岃綆楀墿浣欑殑(<em>k</em>-1)*<em>n</em>鐨勫瓙鐭╅樀鐨勮祴鍊鹼紱 <p>5) 鍩烘湰鎯呭喌鏄竴涓?*<em>n</em>鐨勭粏灝忕殑瀛愰棶棰橈紝姝ゆ椂錛岃瀛愰棶棰樼殑瑙g殑鏁伴噺涓?鎴?錛屽彇鍐充簬鍏跺悜閲忔槸鍚︽槸<em>n</em>/2涓?0, 1)鍜?em>n</em>/2涓?1, 0)鐨勬帓鍒椼? <p>渚嬪錛屽湪涓婇潰緇欏嚭鐨勪袱縐嶆柟妗堜腑錛屽悜閲忓簭鍒椾負錛? <p>((2, 2) (2, 2) (2, 2) (2, 2))       ((2, 2) (2, 2) (2, 2) (2, 2))     k = 4<br>  0      1      0      1              0       0       1      1 <p><font color="#800000">((1, 2) (2, 1) (1, 2) (2, 1))       ((1, 2) (1, 2) (2, 1) (2, 1))     k = 3</font><br>  1      0      1      0              0      0      1      1 <p>((1, 1) (1, 1) (1, 1) (1, 1))       ((0, 2) (0, 2) (2, 0) (2, 0))     k = 2<br>  0      1      0      1              1      1      0      0 <p>((0, 1) (1, 0) (0, 1) (1, 0))       ((0, 1) (0, 1) (1, 0) (1, 0))     k = 1<br>  1      0      1      0              1      1      0      0 <p>((0, 0) (0, 0) (0, 0) (0, 0))       ((0, 0) (0, 0), (0, 0) (0, 0)) <p><strong><font color="#800000"><em>鍔ㄦ佽鍒掑湪姝ょ殑鎰忎箟鍦ㄤ簬閬垮厤浜嗙浉鍚宖鐨勯噸澶嶈綆楋紝鏇磋繘涓姝ョ殑錛屼笂闈㈢潃鑹茬殑涓や釜f錛岃櫧鐒跺搴斿悜閲忎笉鍚岋紝浣唂鐨勫兼槸鐩稿悓鐨勶紝鎯蟲兂涓轟粈涔堝惂</em>:D<em>銆?/em></font></strong> <p>璇ラ棶棰樿В鐨勬暟閲忥紙搴忓垪a058527鍦∣EIS錛夋槸1, 2, 90, 297200, 116963796250, 6736218287430460752, ... <p>涓嬮潰鐨勫閮ㄩ摼鎺ヤ腑鍖呭惈鍥炴函娉曠殑Perl婧愪唬鐮佸疄鐜幫紝浠ュ強鍔ㄦ佽鍒掓硶鐨凪APLE鍜孋璇█鐨勫疄鐜般? <p><strong>3. 媯嬬洏</strong> <p>鑰冭檻<em>n</em>*<em>n</em>鐨勬鐩樺強鎴愭湰鍑芥暟C(<em>i</em>,<em>j</em>)錛岃鍑芥暟榪斿洖鏂規牸(<em>i</em>,<em>j</em>)鐩稿叧鐨勬垚鏈備互5*5鐨勬鐩樹負渚嬶細 <p>5 | 6 7 4 7 8<br>4 | 7 6 1 1 4<br>3 | 3 5 7 8 2<br>2 | 2 6 7 0 2<br>1 | 7 3 5 6 1<br>- + - - - - -<br>  | 1 2 3 4 5 <p>鍙互鐪嬪埌錛欳(1,3)=5 <p>浠庢鐩樼殑浠諱竴鏂規牸鐨勭涓闃訛紙鍗寵錛夊紑濮嬶紝瀵繪壘鍒拌揪鏈鍚庝竴闃剁殑鏈鐭礬寰勶紙浣挎墍鏈夌粡榪囩殑鏂規牸鐨勬垚鏈箣鍜屾渶灝忥級錛屽亣瀹氬彧鍏佽鍚戝乏瀵硅銆佸彸瀵硅鎴栧瀭鐩寸Щ鍔ㄤ竴鏍箋? <p>5 |<br>4 |<br>3 |<br>2 |   x x x<br>1 |     o<br>- + - - - - -<br>  | 1 2 3 4 5 <p>璇ラ棶棰樺睍紺轟簡鏈浼樺瓙緇撴瀯銆傚嵆鏁翠釜闂鐨勫叏灞瑙d緷璧栦簬瀛愰棶棰樼殑瑙c傚畾涔夊嚱鏁皅(<em>i</em>,<em>j</em>)錛屼護錛歲(<em>i</em>,<em>j</em>)琛ㄧず鍒拌揪鏂規牸(<em>i</em>,<em>j</em>)鐨勬渶浣庢垚鏈? <p>濡傛灉鎴戜滑鍙互姹傚嚭絎?em>n</em>闃舵墍鏈夋柟鏍肩殑q(<em>i</em>,<em>j</em>)鍊鹼紝鍙栧叾鏈灝忓煎茍閫嗗悜璇ヨ礬寰勫嵆鍙緱鍒版渶鐭礬寰勩? <p>璁皅(<em>i</em>,<em>j</em>)涓烘柟鏍?<em>i</em>,<em>j</em>)鑷沖叾涓嬩笁涓柟鏍鹼紙<strong><em>(i-1,j-1)銆?i-1,j)銆?i-1,j+1)</em></strong>錛夋渶浣庢垚鏈笌c(<em>i</em>,<em>j</em>)涔嬪拰錛屼緥濡傦細 <p>5 |<br>4 |     <em>A</em><br>3 |   <em>B C D<br></em>2 |<br>1 |<br>- + - - - - -<br>  | 1 2 3 4 5 <p>q(<em>A</em>) = min(q(<em>B</em>),q(<em>C</em>),q(<em>D</em>)) + c(<em>A</em>) <p>瀹氫箟q(<em>i</em>,<em>j</em>)鐨勪竴鑸艦寮忥細 <p>            |-  inf.                                                  <em>j</em><1 or <em>j</em>>n<br>q(<em>i</em>,<em>j</em>) = -+-  c(<em>i</em>,<em>j</em>)                                                i=1<br>            |-  min(q(<em>i</em>-1,<em>j</em>-1),q(<em>i</em>-1,<em>j</em>),q(<em>i</em>-1,<em>j</em>+1))+c(<em>i</em>,<em>j</em>)   otherwise. <p>鏂圭▼鐨勭涓琛屾槸涓轟簡淇濊瘉閫掑綊鍙互閫鍑猴紙澶勭悊杈圭晫鏃跺彧闇璋冪敤涓嬈¢掑綊鍑芥暟錛夈傜浜岃鏄涓闃剁殑鍙栧鹼紝浣滀負璁$畻鐨勮搗鐐廣傜涓夎鐨勯掑綊鏄畻娉曠殑閲嶈緇勬垚閮ㄥ垎錛屼笌渚嬪瓙<em>A</em>銆?em>B</em>銆?em>C</em>銆?em>D</em>綾諱技銆備粠璇ュ畾涔夋垜浠彲浠ョ洿鎺ョ粰鍑鴻綆梣(<em>i</em>,<em>j</em>)鐨勭畝鍗曠殑閫掑綊浠g爜銆傚湪涓嬮潰鐨勪吉浠g爜涓紝<em>n</em>琛ㄧず媯嬬洏鐨勭淮鏁幫紝C(<em>i</em>,<em>j</em>)鏄垚鏈嚱鏁幫紝min()榪斿洖涓緇勬暟鐨勬渶灝忓鹼細 <p>function minCost(i, j)<br>    if j < 1 or j > n<br>        return infinity<br>    else if i = 1<br>        return c(i,j)<br>    else<br>        return min(minCost(i-1,j-1),minCost(i-1,j),minCost(i-1,j+1))+c(i,j) <p>闇瑕佹寚鍑虹殑鏄紝minCost鍙綆楄礬寰勬垚鏈紝騫朵笉鏄渶緇堢殑瀹為檯璺緞錛屼簩鑰呯浉鍘諱笉榪溿備笌Fibonacci鏁扮浉浼鹼紝鐢變簬鑺辮垂澶ч噺鏃墮棿閲嶅璁$畻鐩稿悓鐨勬渶鐭礬寰勶紝榪欎竴鏂瑰紡鎱㈢殑鎭愭栥備笉榪囷紝濡傛灉閲囩敤鑷笅鑰屼笂娉曪紝浣跨敤浜岀淮鏁扮粍q[i,j]浠f浛鍑芥暟minCost錛屽皢浣胯綆楄繃紼嬪揩寰楀銆傛垜浠負浠涔堣榪欐牱鍋氬憿錛熼夋嫨淇濆瓨鍊兼樉鐒舵瘮浣跨敤鍑芥暟閲嶅璁$畻鐩稿悓璺緞瑕佺畝鍗曠殑澶氥? <p>鎴戜滑榪橀渶瑕佺煡閬撳疄闄呰礬寰勩傝礬寰勯棶棰橈紝鎴戜滑鍙互閫氳繃鍙︿竴涓墠浠繪暟緇刾[i,j]瑙e喅銆傝繖涓暟緇勭敤浜庢弿榪拌礬寰勶紝浠g爜濡備笅錛? <p>function computeShortestPathArrays()<br>     for x from 1 to n<br>         q[1, x] := c(1, x)<br>     for y from 1 to n<br>         q[y, 0]     := infinity<br>         q[y, n + 1] := infinity<br>     for y from 2 to n<br>         for x from 1 to n<br>             m := min(q[y-1, x-1], q[y-1, x], q[y-1, x+1])<br>             q[y, x] := m + c(y, x)<br>             if m = q[y-1, x-1]<br>                 p[y, x] := -1<br>             else if m = q[y-1, x]<br>                 p[y, x] :=  0<br>             else<br>                 p[y, x] :=  1 <p>鍓╀笅鐨勬眰鏈灝忓煎拰杈撳嚭灝辨瘮杈冪畝鍗曚簡錛? <p>function computeShortestPath()<br>     computeShortestPathArrays()<br>     minIndex := 1<br>     min := q[n, 1] <br>     for i from 2 to n <br>         if q[n, i] < min<br>             minIndex := i<br>             min := q[n, i]<br>     printPath(n, minIndex) <p>function printPath(y, x)<br>     print(x)<br>     print("<-")<br>     if y = 2<br>         print(x + p[y, x])<br>     else<br>         printPath(y-1, x + p[y, x]) <p><strong>4. 搴忓垪姣斿 </strong> <p><a target="_blank">搴忓垪姣斿</a>鏄姩鎬佽鍒掔殑涓涓噸瑕佸簲鐢ㄣ傚簭鍒楁瘮瀵歸棶棰橀氬父鏄嬌鐢ㄧ紪杈戞搷浣滐紙鏇挎崲銆佹彃鍏ャ佸垹闄や竴涓绱犵瓑錛夎繘琛屽簭鍒楄漿鎹€傛瘡嬈℃搷浣滃搴斾笉鍚屾垚鏈紝鐩爣鏄壘鍒扮紪杈戝簭鍒楃殑鏈浣庢垚鏈? <p>鍙互寰堣嚜鐒跺湴鎯沖埌浣跨敤閫掑綊瑙e喅榪欎釜闂錛屽簭鍒?em>A</em>鍒?em>B</em>鐨勬渶浼樼紪杈戦氳繃浠ヤ笅鎺柦涔嬩竴瀹炵幇錛? <p>鎻掑叆<em>B</em>鐨勭涓涓瓧絎︼紝瀵?em>A</em>鍜?em>B</em>鐨勫墿浣欏簭鍒楄繘琛屾渶浼樻瘮瀵癸紱 <p>鍒犲幓<em>A</em>鐨勭涓涓瓧絎︼紝瀵?em>A</em>鍜?em>B</em>榪涜鏈浼樻瘮瀵癸紱 <p>鐢?em>B</em>鐨勭涓涓瓧絎︽浛鎹?em>A</em>鐨勭涓涓瓧絎︼紝瀵?em>A</em>鐨勫墿浣欏簭鍒楀拰<em>B</em>榪涜鏈浼樻瘮瀵廣? <p>灞閮ㄦ瘮瀵瑰彲鍦ㄧ煩闃典腑鍒楄〃琛ㄧず錛屽崟鍏?<em>i</em>,<em>j</em>)琛ㄧずA[1..<em>i</em>]鍒癰[1..<em>j</em>]鏈浼樻瘮瀵圭殑鎴愭湰銆傚崟鍏?<em>i</em>,<em>j</em>)鐨勬垚鏈綆楀彲閫氳繃绱姞鐩擱偦鍗曞厓鐨勬搷浣滄垚鏈茍閫夋嫨鏈浼樿В瀹炵幇銆傝嚦浜庡簭鍒楁瘮瀵圭殑涓嶅悓瀹炵幇綆楁硶錛屽弬瑙?a target="_blank">Smith-Waterman</a>鍜?a target="_blank">Needleman-Wunsch</a>銆? <p><strong><em>瀵瑰簭鍒楁瘮瀵圭殑璇濋騫朵笉鐔熸倝錛屾洿澶氱殑璇濅篃鏃犱粠璋堣搗錛屾湁鐔熸倝鐨勬湅鍙嬪掓槸鍙互浠嬬粛涓涓嬨?/em></strong> <ul> <li><strong>搴旂敤鍔ㄦ佽鍒掔殑綆楁硶</strong> </li></ul> <p>1) 璁稿<a target="_blank">瀛楃涓?/a>鎿嶄綔綆楁硶濡?a target="_blank">鏈闀垮叕鍏卞瓙鍒?/a>銆?a target="_blank">鏈闀塊掑瀛愬垪</a>銆?a target="_blank">鏈闀垮叕鍏卞瓧涓?/a>錛?</p> <p>2) 灝嗗姩鎬佽鍒掔敤浜?a target="_blank">鍥?/a>鐨勬爲鍒嗚В錛屽彲浠ユ湁鏁堣В鍐蟲湁鐣?a target="_blank">鏍戝鍥?/a>鐨?a target="_blank">鐢熸垚鏍?/a>絳夎澶氫笌鍥劇浉鍏崇殑綆楁硶闂錛? <p>3) 鍐沖畾鏄惁鍙婂浣曞彲浠ラ氳繃鏌愪竴鐗瑰畾<a target="_blank">涓婁笅鏂囨棤鍏蟲枃娉?/a>浜х敓緇欏畾瀛楃涓茬殑<a target="_blank">Cocke-Younger-Kasami</a> (CYK)綆楁硶錛? <p>4) <a target="_blank">璁$畻鏈哄浗闄呰薄媯?/a>涓?a target="_blank">杞崲琛?/a>鍜?a target="_blank">椹蟲枼琛?/a>鐨勪嬌鐢紱 <p>5) <a target="_blank">Viterbi綆楁硶</a>錛堢敤浜?a target="_blank">闅愬紡椹皵鍙か妯″瀷</a>錛夛紱 <p>6) <a target="_blank">Earley綆楁硶</a>錛堜竴綾?a target="_blank">鍥捐〃鍒嗘瀽鍣?/a>錛夛紱 <p>7) <a target="_blank">Needleman-Wunsch</a>鍙婂叾浠?a target="_blank">鐢熺墿淇℃伅瀛?/a>涓嬌鐢ㄧ殑綆楁硶錛屽寘鎷?a target="_blank">搴忓垪姣斿</a>銆?a target="_blank">緇撴瀯姣斿</a>銆?a target="_blank">RNA緇撴瀯</a>棰勬祴錛? <p>8) <a target="_blank">Levenshtein璺濈</a>錛堢紪杈戣窛紱伙級錛? <p>9) <a target="_blank">寮楁礇浼婂痙鏈鐭礬寰?/a>綆楁硶錛? <p>10) <a target="_blank">榪為攣鐭╅樀涔樻硶</a>嬈″簭浼樺寲錛? <p>11) <a target="_blank">瀛愰泦姹傚拰</a>銆?a target="_blank">鑳屽寘闂</a>鍜?a target="_blank">鍒嗘不闂</a>鐨勪吉澶氶」寮忔椂闂寸畻娉曪紱 <p>12) 璁$畻涓や釜鏃墮棿搴忓垪鍏ㄥ眬璺濈鐨?a target="_blank">鍔ㄦ佹椂闂磋鏁?/a>綆楁硶錛? <p>13) 鍏崇郴鍨嬫暟鎹簱鐨勬煡璇紭鍖栫殑<a target="_blank">Selinger</a>錛堝張鍚?a target="_blank">System R</a>錛夌畻娉曪紱 <p>14) 璇勪環B鏍鋒潯鏇茬嚎鐨?a target="_blank">De Boor綆楁硶</a>錛? <p>15) 鐢ㄤ簬瑙e喅鏉跨悆榪愬姩涓柇闂鐨?a target="_blank">Duckworth-Lewis</a>鏂規硶錛? <p>16) 浠峰艱凱浠f硶姹傝В<a target="_blank">椹皵鍙か鍐崇瓥榪囩▼</a>錛? <p>17) 涓浜涘浘褰㈠浘鍍忚竟緙樹互涓嬬殑閫夋嫨鏂規硶錛屽鈥滅閾佲濋夋嫨宸ュ叿鍦?a target="_blank">Photoshop</a>錛? <p>18) <a target="_blank">闂撮殧璋冨害</a>錛? <p>19) <a target="_blank">鑷姩鎹㈣</a>錛? <p>20) <a target="_blank">宸″洖鏃呰鍟嗛棶棰?/a>錛?strong><em>鍙堢О閭樊闂鎴栬揣鎷呴儙闂</em></strong>錛夛紱 <p>21) <a target="_blank">鍒嗘鏈灝忎簩涔樻硶</a>錛? <p>22) <a target="_blank">闊充箰淇℃伅媯绱?/a>璺熻釜銆? <p><strong><em>瀵逛簬榪欎簺綆楁硶搴旂敤錛屽ぇ澶氭湭鏇炬帴瑙︼紝鐢氳嚦鏈緲昏瘧鐨勯兘鏈夐棶棰橈紝閴翠簬鏈枃涓昏鍦ㄤ簬浠嬬粛鍔ㄦ佽鍒掞紝鎵浠ヤ粨淇冧箣涓紝鏈強鏌ヨ瘉銆?/em></strong> <ul> <li><strong>鐩稿叧</strong> </li></ul> <p>1) <a target="_blank">璐濆皵鏇兼柟紼?/a> <p>2) <a target="_blank">椹皵鍙か鍐崇瓥榪囩▼</a> <p>3) <a target="_blank">璐績綆楁硶</a> </p> <ul> <li><strong>鍙傝?/strong> </li></ul> <li>Adda, Jerome, and Cooper, Russell, 2003. <em><a >Dynamic Economics.</a></em> MIT Press. An accessible introduction to dynamic programming in economics. The link contains sample programs. <li>Richard Bellman, 1957, <em>Dynamic Programming</em>, Princeton University Press. Dover paperback edition (2003), <a >ISBN 0486428095</a>. <li>Bertsekas, D. P., 2000. <em>Dynamic Programming and Optimal Control, Vols. 1 & 2</em>, 2nd ed. Athena Scientific. <a >ISBN 1-886529-09-4</a>. <li><a >Thomas H. Cormen</a>, <a >Charles E. Leiserson</a>, <a >Ronald L. Rivest</a>, and <a >Clifford Stein</a>, 2001. <em><a >Introduction to Algorithms</a></em>, 2nd ed. MIT Press & McGraw-Hill. <a >ISBN 0-262-03293-7</a>. Especially pp. 323鈥?9. <li>Giegerich, R., Meyer, C., and Steffen, P., 2004, "<a >A Discipline of Dynamic Programming over Sequence Data,</a>" <em>Science of Computer Programming 51</em>: 215-263. <li><a >Nancy Stokey</a>, and <a >Robert E. Lucas</a>, with <a >Edward Prescott</a>, 1989. <em>Recursive Methods in Economic Dynamics</em>. Harvard Univ. Press. <li>S. P. Meyn, 2007. <a >Control Techniques for Complex Networks</a>, Cambridge University Press, 2007. <ul> <li><strong>澶栭儴閾炬帴</strong> </li></ul> <ul> <li><a >Dyna</a>, a declarative programming language for dynamic programming algorithms <li>Wagner, David B., 1995, "<a >Dynamic Programming.</a>" An introductory article on dynamic programming in <a >Mathematica</a>. <li><a >Ohio State University: CIS 680: class notes on dynamic programming</a>, by Eitan M. Gurari <li><a >A Tutorial on Dynamic programming</a> <li><a >MIT course on algorithms</a> - Includes a video lecture on DP along with lecture notes -- See lecture 15. <li><a >More DP Notes</a> <li>King, Ian, 2002 (1987), "<a >A Simple Introduction to Dynamic Programming in Macroeconomic Models.</a>" An introduction to dynamic programming as an important tool in economic theory. <li><a >Dynamic Programming: from novice to advanced</a> A TopCoder.com article by Dumitru on Dynamic Programming <li><a >Algebraic Dynamic Programming</a> - a formalized framework for dynamic programming, including an <a >entry-level course</a> to DP, University of Bielefeld <li>Dreyfus, Stuart, "<a >Richard Bellman on the birth of Dynamic Programming.</a>" <li><a >Dynamic programming tutorial</a> <li><a >An Introduction to Dynamic Programming</a> </li></ul> <p>_____________________________________________________________</p> <p>鍏充簬鍔ㄦ佽鍒掞紝榪欏彧鏄竴綃囪瘧鏂囷紝鍚庨潰灝嗘牴鎹疄闄呴棶棰樺叿浣撳啓鐐瑰姩鎬佽鍒掔殑搴旂敤銆?/p></li><img src 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