浠ヤ笅鏄垜浠庣綉涓婃敹闆嗙殑鍏充簬緇勫悎鍗氬紙鐨勮祫鏂欐眹鎬伙細(xì)
鏈変竴縐嶅緢鏈夋剰鎬濈殑娓告垙錛屽氨鏄湁鐗╀綋鑻ュ共鍫嗭紝鍙互鏄伀鏌存鎴栨槸鍥存瀛愮瓑絳夊潎鍙備袱涓?br>浜鴻疆?huà)箒浠庡爢涓彇鐗╀綋鑻ヲq詫紝瑙勫畾鏈鍚庡彇鍏夌墿浣撹呭彇鑳溿傝繖鏄垜鍥芥皯闂村緢鍙よ佺殑涓涓父鎴?br>錛屽埆鐪嬭繖娓告垙鏋佸叾綆鍗曪紝鍗磋暣鍚潃娣卞埢鐨勬暟瀛﹀師鐞嗐備笅闈㈡垜浠潵鍒嗘瀽涓涓嬭濡備綍鎵嶈兘澶?br>鍙栬儨銆?/p>
錛堜竴錛?strong>宸翠粈鍗氬錛圔ash Game錛夛細(xì)鍙湁涓鍫唍涓墿鍝侊紝涓や釜浜鴻疆?huà)箒浠帢q欏爢鐗╁搧涓彇鐗╋紝瑙?br>瀹氭瘡嬈¤嚦灝戝彇涓涓紝鏈澶氬彇m涓傛渶鍚庡彇鍏夎呭緱鑳溿?/span>
鏄劇劧錛屽鏋渘=m+1錛岄偅涔堢敱浜庝竴嬈℃渶澶氬彧鑳藉彇m涓紝鎵浠ワ紝鏃犺鍏堝彇鑰呮嬁璧板灝戜釜錛?br>鍚庡彇鑰呴兘鑳藉涓嬈℃嬁璧板墿浣欑殑鐗╁搧錛屽悗鑰呭彇鑳溿傚洜姝ゆ垜浠彂鐜頒簡(jiǎn)濡備綍鍙栬儨鐨勬硶鍒欙細(xì)濡傛灉 鍙互鐪嬪嚭,a0=b0=0,ak鏄湭鍦ㄥ墠闈㈠嚭鐜拌繃鐨勬渶灝忚嚜鐒舵暟,鑰?bk= ak + k錛屽寮傚眬鍔挎湁 1銆備換浣曡嚜鐒舵暟閮藉寘鍚湪涓涓笖浠呮湁涓涓寮傚眬鍔夸腑銆?br> 鐢變簬ak鏄湭鍦ㄥ墠闈㈠嚭鐜拌繃鐨勬渶灝忚嚜鐒舵暟錛屾墍浠ユ湁ak > ak-1 錛岃?bk= ak + k > ak 鍋囪闈㈠鐨勫眬鍔挎槸錛坅,b錛夛紝鑻?b = a錛屽垯鍚屾椂浠庝袱鍫嗕腑鍙栬蛋 a 涓墿浣擄紝灝卞彉?shù)皋Z簡(jiǎn) 浠庡涓婃ц川鍙煡錛屼袱涓漢濡傛灉閮介噰鐢ㄦ紜搷浣滐紝閭ｄ箞闈㈠闈炲寮傚眬鍔匡紝鍏堟嬁鑰呭繀鑳?br>錛涘弽涔嬶紝鍒欏悗鎷胯呭彇鑳溿?/p> 閭ｄ箞浠葷粰涓涓眬鍔匡紙a錛宐錛夛紝鎬庢牱鍒ゆ柇瀹冩槸涓嶆槸濂囧紓灞鍔垮憿錛熸垜浠湁濡備笅鍏紡錛?/p> ak =[k錛?+√5錛?2]錛宐k= ak + k 錛坘=0錛?錛?錛?#8230;,n 鏂規(guī)嫭鍙瘋〃紺哄彇鏁村嚱鏁? 錛堜笁錛?span style="font-family: 'Courier New'; color: rgb(255, 0, 0); ">灝煎鍗氬錛圢imm Game錛夛細(xì)
n=錛坢+1錛塺+s錛岋紙r涓轟換鎰忚嚜鐒舵暟錛宻≤m),閭ｄ箞鍏堝彇鑰呰鎷胯蛋s涓墿鍝侊紝濡傛灉鍚庡彇鑰呮嬁璧?br>k錛?#8804;m)涓紝閭ｄ箞鍏堝彇鑰呭啀鎷胯蛋m+1-k涓紝緇撴灉鍓╀笅錛坢+1錛夛紙r-1錛変釜錛屼互鍚庝繚鎸佽繖鏍風(fēng)殑
鍙栨硶錛岄偅涔堝厛鍙栬呰偗瀹氳幏鑳溿傛諱箣錛岃淇濇寔緇欏鎵嬬暀涓嬶紙m+1錛夌殑鍊嶆暟錛屽氨鑳芥渶鍚庤幏鑳溿?br> 榪欎釜娓告垙榪樺彲浠ユ湁涓縐嶅彉鐩哥殑鐜╂硶錛氫袱涓漢杞祦鎶ユ暟錛屾瘡嬈¤嚦灝戞姤涓涓紝鏈澶氭姤鍗?br>涓紝璋佽兘鎶ュ埌100鑰呰儨銆?br>錛堜簩錛?strong>濞佷綈澶崥濂曪紙Wythoff Game錛夛細(xì)鏈変袱鍫嗗悇鑻ュ共涓墿鍝侊紝涓や釜浜鴻疆?huà)箒浠庢煇涓鍫嗘垨鍚?br>鏃朵粠涓ゅ爢涓彇鍚屾牱澶氱殑鐗╁搧錛岃瀹氭瘡嬈¤嚦灝戝彇涓涓紝澶氳呬笉闄愶紝鏈鍚庡彇鍏夎呭緱鑳溿?br>
榪欑鎯呭喌涓嬫槸棰囦負(fù)澶嶆潅鐨勩傛垜浠敤錛坅k錛宐k錛夛紙ak ≤ bk ,k=0錛?錛?錛?#8230;,n)琛ㄧず
涓ゅ爢鐗╁搧鐨勬暟閲忓茍縐板叾涓?strong>灞鍔?/strong>錛屽鏋滅敳闈㈠錛?錛?錛夛紝閭ｄ箞鐢插凡緇忚緭浜?jiǎn)锛寴q欑灞鍔挎垜浠?br>縐頒負(fù)濂囧紓灞鍔?/strong>銆傚墠鍑犱釜濂囧紓灞鍔挎槸錛氾紙0錛?錛夈侊紙1錛?錛夈侊紙3錛?錛夈侊紙4錛?錛夈侊紙6錛?br>10錛夈侊紙8錛?3錛夈侊紙9錛?5錛夈侊紙11錛?8錛夈侊紙12錛?0錛夈?/p>
濡備笅涓夋潯鎬ц川錛?/p>
-1 + k-1 = bk-1 > ak-1 銆傛墍浠ユц川1銆傛垚绔嬨?br> 2銆備換鎰忔搷浣滈兘鍙皢濂囧紓灞鍔垮彉?shù)负闈炲寮傚眬鍔褲?br> 浜嬪疄涓婏紝鑻ュ彧鏀瑰彉濂囧紓灞鍔匡紙ak錛宐k錛夌殑鏌愪竴涓垎閲忥紝閭ｄ箞鍙︿竴涓垎閲忎笉鍙兘鍦ㄥ叾
浠栧寮傚眬鍔夸腑錛屾墍浠ュ繀鐒舵槸闈炲寮傚眬鍔褲傚鏋滀嬌錛坅k錛宐k錛夌殑涓や釜鍒嗛噺鍚屾椂鍑忓皯錛屽垯鐢?br>浜庡叾宸笉鍙橈紝涓斾笉鍙兘鏄叾浠栧寮傚眬鍔跨殑宸紝鍥犳涔熸槸闈炲寮傚眬鍔褲?br> 3銆傞噰鐢ㄩ傚綋鐨勬柟娉曪紝鍙互灝嗛潪濂囧紓灞鍔垮彉?shù)负濂囧紓灞鍔褲?/p>
濂囧紓灞鍔匡紙0錛?錛夛紱濡傛灉a = ak 錛宐 > bk錛岄偅涔堬紝鍙栬蛋b – bk涓墿浣擄紝鍗沖彉?shù)负濂囧紓灞
鍔匡紱濡傛灉 a = ak 錛?nbsp; b < bk ,鍒欏悓鏃朵粠涓ゅ爢涓嬁璧?ak – ab – ak涓墿浣?鍙樹(shù)負(fù)濂囧紓灞
鍔匡紙 ab – ak , ab – ak+ b – ak錛夛紱濡傛灉a > ak 錛宐= ak + k,鍒欎粠絎竴鍫嗕腑鎷胯蛋澶氫綑
鐨勬暟閲廰 – ak 鍗沖彲錛涘鏋渁 < ak 錛宐= ak + k,鍒嗕袱縐嶆儏鍐碉紝絎竴縐嶏紝a=aj 錛坖 < k錛?br>,浠庣浜屽爢閲岄潰鎷胯蛋 b – bj 鍗沖彲錛涚浜岀錛宎=bj 錛坖 < k錛?浠庣浜屽爢閲岄潰鎷胯蛋 b – a
j 鍗沖彲銆?/p>
濂囧鐨勬槸鍏朵腑鍑虹幇浜?jiǎn)榛勯噾鍒嗗壊鏁板Q?+√5錛?2 = 1銆?18…,鍥犳,鐢盿k錛宐k緇勬垚鐨勭煩褰㈣繎
浼間負(fù)榛勯噾鐭╁艦錛岀敱浜?/錛?+√5錛?錛?#8730;5-1錛?2錛屽彲浠ュ厛姹傚嚭j=[a錛?#8730;5-1錛?2]錛岃嫢a=[
j錛?+√5錛?2]錛岄偅涔坅 = aj錛宐j = aj + j錛岃嫢涓嶇瓑浜庯紝閭ｄ箞a = aj+1錛宐j+1 = aj+1
+ j + 1錛岃嫢閮戒笉鏄紝閭ｄ箞灝變笉鏄寮傚眬鍔褲傜劧鍚庡啀鎸夌収涓婅堪娉曞垯榪涜錛屼竴瀹氫細(xì)閬囧埌濂囧紓
灞鍔褲?/p>
鐗╁搧錛岃瀹氭瘡嬈¤嚦灝戝彇涓涓紝澶氳呬笉闄愶紝鏈鍚庡彇鍏夎呭緱鑳溿?/span>
榪欑鎯呭喌鏈鏈夋剰鎬濓紝瀹冧笌浜岃繘鍒舵湁瀵嗗垏鍏崇郴錛屾垜浠敤錛坅錛宐錛宑錛夎〃紺烘煇縐嶅眬鍔匡紝棣?br>鍏堬紙0錛?錛?錛夋樉鐒舵槸濂囧紓灞鍔匡紝鏃犺璋侀潰瀵瑰寮傚眬鍔匡紝閮藉繀鐒跺け璐ャ傜浜岀濂囧紓灞鍔挎槸
錛?錛宯錛宯錛夛紝鍙涓庡鎵嬫嬁璧頒竴鏍峰鐨勭墿鍝侊紝鏈鍚庨兘灝嗗鑷達(dá)紙0錛?錛?錛夈備粩緇嗗垎鏋愪竴
涓嬶紝錛?錛?錛?錛変篃鏄寮傚眬鍔匡紝鏃犺瀵規(guī)墜濡備綍鎷匡紝鎺ヤ笅鏉ラ兘鍙互鍙樹(shù)負(fù)錛?錛宯錛宯錛夌殑鎯?br>褰€?/p>
璁＄畻鏈虹畻娉曢噷闈㈡湁涓縐嶅彨鍋氭寜浣嶆ā2鍔狅紝涔熷彨鍋氬紓鎴栫殑榪愮畻錛屾垜浠敤絎﹀彿錛?錛夎〃紺?br>榪欑榪愮畻銆傝繖縐嶈繍綆楀拰涓鑸姞娉曚笉鍚岀殑涓鐐規(guī)槸1+1=0銆傚厛鐪嬶紙1錛?錛?錛夌殑鎸変綅妯?鍔犵殑緇?br>鏋滐細(xì)
1 =浜岃繘鍒?1
2 =浜岃繘鍒?0
3 =浜岃繘鍒?1 錛?錛?br>鈥斺斺斺斺斺斺?br>0 =浜岃繘鍒?0 錛堟敞鎰忎笉榪涗綅錛?/p>
瀵逛簬濂囧紓灞鍔匡紙0錛宯錛宯錛変篃涓鏍鳳紝緇撴灉涔熸槸0銆?/p>
浠諱綍濂囧紓灞鍔匡紙a錛宐錛宑錛夐兘鏈塧錛?錛塨錛?錛塩 =0銆?/p>
濡傛灉鎴戜滑闈㈠鐨勬槸涓涓潪濂囧紓灞鍔匡紙a錛宐錛宑錛夛紝瑕佸浣曞彉?shù)负濂囧紓灞鍔垮憿錛熷亣璁?a < b
< c,鎴戜滑鍙灝?c 鍙樹(shù)負(fù) a錛?錛塨,鍗沖彲,鍥犱負(fù)鏈夊涓嬬殑榪愮畻緇撴灉: a錛?錛塨錛?錛?a錛?錛?br>b)=(a錛?錛塧)錛?錛?b錛?錛塨)=0錛?錛?=0銆傝灝哻 鍙樹(shù)負(fù)a錛?錛塨錛?span style="font-family: 'Courier New'; color: rgb(0, 128, 0); ">鍙浠?c涓噺鍘?c-錛?br>a錛?錛塨錛夊嵆鍙?br>
渚?銆傦紙14錛?1錛?9錛夛紝14錛?錛?1=27錛?9-27=12錛屾墍浠ヤ粠39涓嬁璧?2涓墿浣撳嵆鍙揪
鍒板寮傚眬鍔匡紙14錛?1錛?7錛夈?/p>
渚?銆傦紙55錛?1錛?21錛夛紝55錛?錛?1=102錛?21-102=19錛屾墍浠ヤ粠121涓嬁璧?9涓墿鍝?br>灝卞艦鎴愪簡(jiǎn)濂囧紓灞鍔匡紙55錛?1錛?02錛夈?/p>
渚?銆傦紙29錛?5錛?8錛夛紝29錛?錛?5=48錛?8-48=10錛屼粠58涓嬁璧?0涓紝鍙樹(shù)負(fù)錛?9錛?
5錛?8錛夈?/p>
渚?銆傛垜浠潵瀹為檯榪涜涓鐩樻瘮璧涚湅鐪嬶細(xì)
鐢?(7,8,9)->(1,8,9)濂囧紓灞鍔?br> 涔?(1,8,9)->(1,8,4)
鐢?(1,8,4)->(1,5,4)濂囧紓灞鍔?br> 涔?(1,5,4)->(1,4,4)
鐢?(1,4,4)->(0,4,4)濂囧紓灞鍔?br> 涔?(0,4,4)->(0,4,2)
鐢?(0.4,2)->(0,2,2)濂囧紓灞鍔?br> 涔?(0,2,2)->(0,2,1)
鐢?(0,2,1)->(0,1,1)濂囧紓灞鍔?br> 涔?(0,1,1)->(0,1,0)
鐢?(0,1,0)->(0,0,0)濂囧紓灞鍔?br> 鐢茶儨銆?/p>
棰樼洰1錛氫粖鏈夎嫢騫插爢鐏煷錛屼袱浜轟緷嬈′粠涓嬁鍙栵紝瑙勫畾姣忔鍙兘浠庝竴鍫嗕腑鍙栬嫢騫叉牴錛?nbsp;
鍙皢涓鍫嗗叏鍙栬蛋錛屼絾涓嶅彲涓嶅彇錛屾渶鍚庡彇瀹岃呬負(fù)鑳滐紝姹傚繀鑳滅殑鏂規(guī)硶銆?nbsp;
棰樼洰2錛氫粖鏈夎嫢騫插爢鐏煷錛屼袱浜轟緷嬈′粠涓嬁鍙栵紝瑙勫畾姣忔鍙兘浠庝竴鍫嗕腑鍙栬嫢騫叉牴錛?nbsp;
鍙皢涓鍫嗗叏鍙栬蛋錛屼絾涓嶅彲涓嶅彇錛屾渶鍚庡彇瀹岃呬負(fù)璐燂紝姹傚繀鑳滅殑鏂規(guī)硶銆?br>鍢垮樋錛岃繖涓父鎴忔垜鏃╁氨瑙佽瘑榪囦簡(jiǎn)銆傚皬鏃跺欑敤鐝犵畻鐜╄繖涓父鎴忥細(xì)絎竴妗ｆ嫧涓涓紝絎簩妗ｆ嫧涓や釜錛屼緷嬈＄洿鍒扮浜旀。鎷ㄤ簲涓傜劧鍚庝袱涓漢灝辮疆?huà)箒鍐嶆妸妫嬪瓙鎷ㄤ笅鏉ュQ岃皝瑕佹槸鏈鍚庝竴涓嫧璋佸氨璧€傛湁涓嬈℃殤鍋囩湅瑙佷袱涓皬瀛╁瓙鍦ㄧ帺榪欎釜娓告垙錛屾垜灝卞湪鎯蟲(chóng)湁娌℃湁涓涓畾璁哄憿銆備笅闈㈠氨鏉ヨ瘯鐫璇佹槑涓涓嬪惂
鍏堣В鍐崇涓涓棶棰樺惂銆?br>瀹氫箟錛氳嫢鎵鏈夌伀鏌存暟寮傛垨涓?錛屽垯璇ョ姸鎬佽縐頒負(fù)鍒╀粬鎬侊紝鐢ㄥ瓧姣峊琛ㄧず錛涘惁鍒欙紝
涓哄埄宸辨侊紝鐢⊿琛ㄧず銆?br>[瀹氱悊1]錛氬浜庝換浣曚竴涓猄鎬侊紝鎬昏兘浠庝竴鍫嗙伀鏌翠腑鍙栧嚭鑻ュ共涓嬌涔嬫垚涓篢鎬併?br>璇佹槑錛?br> 鑻ユ湁n鍫嗙伀鏌達(dá)紝姣忓爢鐏煷鏈堿(i)鏍圭伀鏌存暟錛岄偅涔堟棦鐒剁幇鍦ㄥ浜嶴鎬侊紝
c = A(1) xor A(2) xor … xor A(n) > 0;
鎶奵琛ㄧず鎴愪簩榪涘埗錛岃瀹冪殑浜岃繘鍒舵暟鐨勬渶楂樹(shù)綅涓虹p浣嶏紝鍒欏繀鐒跺瓨鍦ㄤ竴涓狝(t),瀹冧簩榪涘埗鐨勭p浣嶄篃鏄?銆傦紙鍚﹀垯錛岃嫢鎵鏈夌殑A(i)鐨勭p浣嶉兘鏄?錛岃繖涓巆鐨勭p浣嶅氨涔熶負(fù)0鐭涚浘錛夈?br> 閭ｄ箞鎴戜滑鎶妜 = A(t) xor c,鍒欏緱鍒皒 < A(t).榪欐槸鍥犱負(fù)鏃㈢劧A(t)鐨勭p浣嶄笌c鐨勭p浣嶅悓涓?,閭ｄ箞x鐨勭p浣嶅彉?shù)?,鑰岄珮?shù)簬p鐨勪綅騫舵病鏈夋敼鍙樸傛墍浠 < A(t).鑰?br> A(1) xor A(2) xor … xor x xor … xor A(n)
= A(1) xor A(2) xor … xor A(t) xor c xor … xor A(n)
= A(1) xor A(2) xor… xor A(n) xor A(1) xor A(2) xor … xor A(n)
= 0
榪欏氨鏄浠嶢(t)鍫嗕腑鍙栧嚭 A(t) – x 鏍圭伀鏌村悗鐘舵佸氨浼?xì)浠嶴鎬佸彉?shù)负T鎬併傝瘉姣?br>[瀹氱悊2]錛歍鎬侊紝鍙栦換浣曚竴鍫嗙殑鑻ュ共鏍癸紝閮藉皢鎴愪負(fù)S鎬併?br>璇佹槑錛氱敤鍙嶈瘉娉曡瘯璇曘?br> 鑻?br> c = A(1) xor A(2) xor … xor A(i) xor … xor A(n) = 0錛?br> c’ = A(1) xor A(2) xor … xor A(i’) xor c xor … xor A(n) = 0;
鍒欐湁
c xor c’ = A(1) xor A(2) xor … xor A(i) xor … xor A(n) xor A(1) xor A(2) xor … xor A(i’) xor c xor … xor A(n) = A(i) xor A(i’) =0
榪涜屾帹鍑篈(i) = A(i’)錛岃繖涓庡凡鐭ョ煕鐩俱傛墍浠ュ懡棰樺緱璇併?br>[瀹氱悊 3]錛歋鎬侊紝鍙鏂規(guī)硶姝ｇ‘錛屽繀璧€?nbsp;
鏈緇堣儨鍒╁嵆鐢盨鎬佽漿鍙樹(shù)負(fù)T鎬侊紝浠諱綍涓涓猄鎬侊紝鍙鎶婂畠鍙樹(shù)負(fù)T鎬侊紝錛堢敱瀹氱悊1錛屽彲浠ユ妸瀹冨彉鎴怲鎬併傦級(jí)瀵規(guī)柟鍙兘鎶奣鎬佽漿鍙樹(shù)負(fù)S鎬?瀹氱悊2)銆傝繖鏍鳳紝鎵鏈塖鎬佸悜T鎬佺殑杞彉閮藉彲浠ユ湁宸辨柟鎺у埗錛屽鏂瑰彧鑳借鍔ㄥ湴瀹炵幇鐢盩鎬佽漿鍙樹(shù)負(fù)S鎬併傛晠S鎬佸繀璧€?br>[瀹氱悊4]錛歍鎬侊紝鍙瀵規(guī)柟娉曟紜紝蹇呰觸銆?nbsp;
鐢卞畾鐞?鏄撳緱銆?nbsp;
鎺ョ潃鏉ヨВ鍐崇浜屼釜闂銆?br>瀹氫箟錛氳嫢涓鍫嗕腑浠呮湁1鏍圭伀鏌達(dá)紝鍒欒縐頒負(fù)瀛ゅ崟鍫嗐傝嫢澶т簬1鏍癸紝鍒欑О涓哄厖瑁曞爢銆?br>瀹氫箟錛歍鎬佷腑錛岃嫢鍏呰鍫嗙殑鍫嗘暟澶т簬絳変簬2錛屽垯縐頒負(fù)瀹屽叏鍒╀粬鎬侊紝鐢═2琛ㄧず錛涜嫢鍏呰鍫嗙殑鍫嗘暟絳変簬0錛屽垯縐頒負(fù)閮ㄥ垎鍒╀粬鎬侊紝鐢═0琛ㄧず銆?br>
瀛ゅ崟鍫嗙殑鏍規(guī)暟寮傛垨鍙細(xì)褰卞搷浜岃繘鍒剁殑鏈鍚庝竴浣嶏紝浣嗗厖瑁曞爢浼?xì)濯?jiǎng)鍝嶉珮?shù)綅锛堥潪鏈鍚庝竴浣嶏級(jí)銆備竴涓厖瑁曞爢錛岄珮?shù)綅蹇呮湁涓浣嶄笉涓?錛屽垯鎵鏈夋牴鏁板紓鎴栦笉涓?銆傛晠涓嶄細(xì)鏄疶鎬併?br>[瀹氱悊5]錛歋0鎬侊紝鍗充粎鏈夊鏁頒釜瀛ゅ崟鍫嗭紝蹇呰觸銆俆0鎬佸繀鑳溿?nbsp;
璇佹槑錛?br>S0鎬侊紝鍏跺疄灝辨槸姣忔鍙兘鍙栦竴鏍廣傛瘡嬈＄濂囨暟鏍歸兘鐢卞繁鍙栵紝絎伓鏁版牴閮界敱瀵?nbsp;
鏂瑰彇錛屾墍浠ユ渶鍚庝竴鏍瑰繀宸卞彇銆傝觸銆傚悓鐞? T0鎬佸繀鑳?
[瀹氱悊6]錛歋1鎬侊紝鍙鏂規(guī)硶姝ｇ‘錛屽繀鑳溿?nbsp;
璇佹槑錛?br>鑻ユ鏃跺鍗曞爢鍫嗘暟涓哄鏁幫紝鎶婂厖瑁曞爢鍙栧畬錛涘惁鍒欙紝鍙栨垚涓鏍廣傝繖鏍鳳紝灝卞彉鎴愬鏁頒釜瀛ゅ崟鍫嗭紝鐢卞鏂瑰彇銆傜敱瀹氱悊5錛屽鏂瑰繀杈撱傚繁蹇呰儨銆?nbsp; #
[瀹氱悊7]錛歋2鎬佷笉鍙漿涓嬈″彉?shù)负T0鎬併?nbsp;
璇佹槑錛?br>鍏呰鍫嗘暟涓嶅彲鑳戒竴嬈＄敱2鍙樹(shù)負(fù)0銆傚緱璇併?nbsp; #
[瀹氱悊8]錛歋2鎬佸彲涓嬈¤漿鍙樹(shù)負(fù)T2鎬併?nbsp;
璇佹槑錛?br>鐢卞畾鐞?錛孲鎬佸彲杞彉?shù)负T鎬侊紝鎬佸彲涓嬈¤漿鍙樹(shù)負(fù)T鎬侊紝鍙堢敱瀹氱悊6錛孲2鎬佷笉鍙漿涓嬈″彉?shù)负T0鎬侊紝鎵浠ヨ漿鍙樼殑T鎬佷負(fù)T2鎬併?nbsp; #
[瀹氱悊9]錛歍2鎬侊紝鍙兘杞彉?shù)负S2鎬佹垨S1鎬併?nbsp;
璇佹槑錛?br>鐢卞畾鐞?錛孴鎬佸繀鐒跺彉?shù)负S鎬併傜敱浜庡厖瑁曞爢鏁頒笉鍙兘涓嬈＄敱2鍙樹(shù)負(fù)0錛屾墍浠ユ鏃剁殑S鎬佷笉鍙兘涓篠0鎬併傚懡棰樺緱璇併?nbsp;
[瀹氱悊10]錛歋2鎬侊紝鍙鏂規(guī)硶姝ｇ‘錛屽繀鑳?
璇佹槑錛?br>鏂規(guī)硶濡備笅錛?nbsp;
1錛?nbsp; S2鎬侊紝灝辨妸瀹冨彉?shù)负T2鎬併傦紙鐢卞畾鐞?錛?nbsp;
2錛?nbsp; 瀵規(guī)柟鍙兘T2杞彉鎴怱2鎬佹垨S1鎬侊紙瀹氱悊9錛?br> 鑻ヨ漿鍙樹(shù)負(fù)S2, 杞悜1錛?nbsp;
鑻ヨ漿鍙樹(shù)負(fù)S1, 榪欏繁蹇呰儨銆傦紙瀹氱悊5錛?nbsp;
[瀹氱悊11]錛歍2鎬佸繀杈撱?nbsp;
璇佹槑錛氬悓10銆?nbsp;
緇間笂鎵榪幫紝蹇呰緭鎬佹湁錛?nbsp; T2,S0
蹇呰儨鎬侊細(xì) S2,S1,T0.
涓ら姣旇緝錛?nbsp;
絎竴棰樼殑鍏ㄨ繃紼嬪叾瀹炲涓嬶細(xì)
S2->T2->S2->T2-> …… ->T2->S1->T0->S0->T0->……->S0->T0(鍏?)
絎簩棰樼殑鍏ㄨ繃紼嬪叾瀹炲涓嬶細(xì)
S2->T2->S2->T2-> …… ->T2->S1->S0->T0->S0->……->S0->T0(鍏?)
涓嬪垝綰胯〃紺鴻儨鍒╀竴鏂圭殑鍙栨硶銆?nbsp; 鏄惁鍙戠幇浜?jiǎn)浠栦滑鐨勬儕錆h鐩鎬技涔嬪銆?nbsp;
鎴戜滑涓嶉毦鍙戠幇(瑙佸姞榛戦儴鍒?錛孲1鎬佸彲浠ヨ漿鍙樹(shù)負(fù)S0鎬侊紙絎簩棰樺仛娉曪級(jí)錛屼篃鍙互杞彉?shù)?nbsp;
T0錛堢涓棰樺仛娉曪級(jí)銆傚摢涓鏂規(guī)帶鍒朵簡(jiǎn)S1鎬侊紝浠栧嵆鍙互鏈夊姙娉曚嬌鑷繁寰楀埌鏈鍚庝竴鏍癸紙杞彉?shù)?nbsp;
T0錛?涔熷彲浠ヤ嬌瀵規(guī)柟寰楀埌鏈鍚庝竴鏍癸紙杞彉?shù)负S0錛夈?nbsp;
鎵浠ワ紝鎶㈠ずS1鏄埗鑳滅殑鍏抽敭錛?nbsp;
涓烘錛屽緇堟妸T2鎬佽緇欏鏂癸紝灝嗕嬌瀵規(guī)柟澶勪簬琚姩鐘舵侊紝浠栨棭鏅氬皢鎶婄姸鎬佸彉?shù)负S1.
http://acm.hdu.edu.cn/showproblem.php?pid=1907
http://acm.hdu.edu.cn/showproblem.php?pid=2509
鐪嬪畬涓婇潰鐨勭粨璁猴紝灝辮兘欏哄埄瑙ｅ喅涓婇潰2閬撲簡(jiǎn)
灝忓瓙鏈榪戣糠閫斾簬鍗氬紙涔嬩腑銆傘傘傛劅瑙﹂娣便?br>涓轟簡(jiǎn)璁╁ぇ瀹惰兘澶熷湪瀛︿範(fàn)鍗氬紙鐨勬椂鍊欏皯璧板集璺紝鏈閲嶈鐨勪篃鏄負(fù)浜?jiǎn)鍔犳忿p嚜宸辯殑褰卞搷錛屾俯鏁呰岀煡鏂幫紝鐗瑰彂姝よ創(chuàng)涓庡ぇ瀹跺叡鍕夈?br>瀛﹀崥寮堝厛浠庢蹇靛紑濮嬶細(xì)
鐗瑰埆鎺ㄨ崘LCY鑰佸笀鐨勮浠訛細(xì)鍗氬紙鍏ラ棬銆?br>涓嬭澆鍦板潃錛?a id="url_5" target="_blank" style="color: rgb(41, 112, 166); text-decoration: none; ">http://acm.hdu.edu.cn/forum/read.php?tid=6875
榪欎釜璇句歡涓漢璁や負(fù)浠庡崥寮堢殑鍩烘湰鎬濇兂錛屼竴鐩村埌瑙ｅ崥寮堢殑涓績(jī)綆楁硶鍋氫簡(jiǎn)寰堝ソ鐨勮癄閲娿備絾鏄壒鍒娉ㄦ剰鐨勬槸銆傝浠跺悗闈竴閮ㄥ垎鑻辮鍐欑殑璁蹭箟鏄噸涓箣閲嶃傚皬瀛愯嫳璇緢寮憋紝鍦ㄨ繖鍥版壈寰堜箙銆傜幇鍦ㄤ負(fù)澶у澶ф浠嬬粛涓涓嬨?br>涓昏鏄悗緇х偣鍜孲G鍊肩殑闂:
SG鍊鹼細(xì)涓涓偣鐨凷G鍊煎氨鏄竴涓笉絳変簬瀹冪殑鍚庣戶鐐圭殑SG鐨勪笖澶т簬絳変簬闆剁殑鏈灝忔暣鏁般?br>鍚庣戶鐐癸細(xì)涔熷氨鏄寜鐓ч鐩姹傜殑璧版硶錛堟瘮濡傚彇鐭沖瓙鍙互鍙栫殑鏁伴噺錛屾柟娉曪級(jí)鑳藉璧頒竴姝ヨ揪鍒扮殑閭ｄ釜鐐廣?br>鍏蜂綋鐨勬湁鍏砈G鍊兼槸鎬庝箞榪愮敤鐨勫笇鏈涘ぇ瀹惰嚜宸卞鎯蟲(chóng)兂銆?br>璇句歡鍚庨潰鏈変竴涓?536鐨勪唬鐮併傚彲浠ユ斁鍦ㄥ悗闈㈠仛鍋?br>鐪嬪埌榪欓噷鎺ㄨ崘澶у鍋氬嚑閬撻錛?846錛堟渶綆鍗曠殑鍗氬紙姘撮錛?br>1847錛堟眰SG鍊鹼級(jí)
鏈変簡(jiǎn)涓婇潰鐨勭煡璇嗘帴涓嬫潵鎴戜滑鏉ョ湅鐪嬬粍鍚堝崥寮堬紙n鍫嗙煶瀛愶級(jí)
鎺ㄨ崘澶у鐪嬩釜璧勬枡錛?br>鍗氬紙-鍙栫煶瀛愭父鎴?鎺ㄨ崘絳夌駭浜旀槦綰?
http://acm.hdu.edu.cn/forum/read.php?fid=20&tid=5748
http://hi.baidu.com/netnode/blog/item/30932c2edc7384514fc226ea.html
榪欓噷鎻愬嚭浜?jiǎn)涓涓寮傜姸鎬佺殑闂銆傜湅浜?jiǎn)杩櫧媷鏂囩珷浣犱細(xì)鍙戠幇寮傛垨杩惤帡鍦ㄥ崥寮堜腑鋴社敤鐨勫澶勩傚綋鐒惰繖閲屾寚鍑虹殑鍙槸緇勫悎鍗氬紙涓竴縐嶇壒孌婃儏鍐點(diǎn)?br>鐜嬮亾榪樻槸瀵筍G鍊肩殑姹傝В錛屼絾鏄煡閬撹繖涔堜竴縐嶆濊礬鏃犵枒瀵規(guī)濈淮鐨勫箍搴﹀拰娣卞害鎵╁睍鏄緢鏈夊府鍔╃殑銆?br>ZZ鍗氬紙
http://acm.hdu.edu.cn/forum/read.php?fid=9&tid=10617
榪欓噷浠嬬粛浜?jiǎn)缁勫拰鍗氬紙鐨勪袱绉嶅ぇ鐨劸c誨瀷錛屼竴縐嶆槸鏈鍚庡彇鐨勬槸N鐘舵佷竴縐嶆槸鏈鍚庡彇鐨勬槸P鐘舵侊紝涓や釜鐘舵佺殑瑙ｉ鏂規(guī)硶鑳界湅鎳傚緢鏈夊府鍔┿傚綋鐒?dòng)灱岃兘澶熸妸鎺ㄥD繃紼嬬悊瑙ｏ紝鍚冮忔棤鐤戞槸澶х墰綰х殑鍋氭硶~灝忓瓙涔熶僵鏈嶇殑绱
1536棰樻帹鑽愬仛鍋氳繖棰橈紝榪欓鍓嶉潰鎻愰啋澶у鏄竴涓眰SG鍊肩殑棰樼洰錛岄鐩墠闈㈡槸瀵瑰紓鎴栬繍綆楄繍鐢ㄥ湪緇勫悎鍗氬紙闂?shù)腑鐨勫緢濂界殑瑙ｉ噴銆傚綋鐒墮鐩湰韜槸鏈夋墍涓嶅悓鐨勩傚洜涓哄湪榪欓噷闈㈠鍙栨硶鏈夋墍瑕佹眰銆傞偅涔堣繖鏍峰氨鍥炲綊鍒頒簡(jiǎn)瑙ｅ喅鍗氬紙闂鐨勭帇閬撶畻娉曗斺旀眰SG鍊間笂銆?br> 鏈夊叧榪愮敤姹係G鍊肩殑鍗氬紙棰樼洰鏈夛細(xì) 1850錛堜篃鍙熀浜庡寮傜姸鎬佸紓鎴栵級(jí)
1848錛堜腑鍜岀殑澶ф枑娉㈤偅濂戞暟鍒楃殑鍏稿瀷姹係G鍊奸錛?br>1517錛堜釜浜鴻涓烘湁鐐圭尌鐞愮殑棰樼洰銆傘傘傘傚湪姝ら?shù)笂鍥版壈寰堜箙銆傚綋鐒舵悶鍑烘潵寰堝紑蹇?jī)銆傚皬瀛愭槸鐢ㄦ瘮杈冭鐭╃殑姹係G鍊肩殑鏂規(guī)硶姹傚嚭鏉ョ殑錛屼絾鏄鍧涙湁浜哄鍏舵帹鍑烘潵浜?jiǎn)瑙勫緥锛寴q欓噷浣╂湇涓涓嬶紝澶у鍙互瀛︿範(fàn)涓涓嬶級(jí)
1079錛堟洿鐚ョ悙鐨勯鐩紝瀵規(guī)柊鎵嬭姹傝緝楂橈紝鍥犱負(fù)鎸変紶緇熸柟娉曢渶瑕佹瘮杈冪粏鑷寸殑妯℃嫙鍔犲杈硅鐘舵佺殑鑰冭檻錛屽悓鏍鋒湁浜烘帹鍑烘潵浜?jiǎn)鍏紡锛?jí)
褰撲綘鍏ㄩ儴鐪嬪畬浠ヤ笂鐨勪笢瑗褲傚仛瀹屼互涓婄殑棰樼洰鐨勮瘽銆傘傘傚皬瀛愭伃鍠滀綘~浣犲崥寮堝叆闂ㄤ簡(jiǎn)~~~~
榪欓噷灝忓瓙鍛婅瘔澶у銆傚崥寮堝緢寮哄ぇ銆傚涔?fàn)瑕佽愬績(jī)~璋㈣阿
Current System Time : 2008-12-11 19:16:03
ACM璇句綔涓氾細(xì)
1001 Brave Game
1002 Good Luck in CET-4 Everybody!
1003 Fibonacci again and again
1004 Rabbit and Grass
1005 Being a Good Boy in Spring Festival
1006 Public Sale
1007 鎮(zhèn)煎康512姹跺窛澶у湴闇囬亣闅懼悓鑳?yōu)鈥斺旈夋嫈蹇楁効鑰?nbsp;
1008 kiki’s game
1009 Calendar Game
1010 A Multiplication Game
1011 Digital Deletions
1012 S-Nim
http://acm.hdu.edu.cn/forum/read.php?tid=11339&fpage=0&toread=&page=1
Copy code
//鍗氬紙-鍩轟簬姹係G鍊?br>//Accepted 1536 578MS 416K 904 B
#include”iostream”
using namespace std;
int f[101],sg[10001],k;
int mex(int b)
{
int a[101]={0},i;
for(i=0;i<k;i++)
{
if(b-f<0)//b-f鍚庣戶鐐?br> break;
if(sg[b-f]==-1)
{
sg[b-f]=mex(b-f);
}
a[sg[b-f]]=1;
}
for(i=0;i<k;i++)
if(!a)
{
return i;
}
}
int main()
{
int i,t,n,s,bead,j;
while(cin >> k,k)
{
for(i=0;i<k;i++)
{
cin >> f;
}
memset(sg,-1,sizeof(sg));
for(i=0;i<k;i++)
for(j=i+1;j<k;j++)
if(f>f[j])
{
f+=f[j];
f[j]=f-f[j];
f-=f[j];
}
sg[0]=0;
cin >> t;
while(t–)
{
cin >> n;
s=0;
while(n–)
{
cin >> bead;//璇ュ爢鐨勬垚鍛樹(shù)釜鏁?br> if(sg[bead]==-1)
sg[bead]=mex(bead);
s=s^sg[bead];
}
if(s==0)
cout << “L”;
else
cout << “W”;
}
cout << endl;
}
return 0;
}
Copy code
//鍗氬紙-鍩轟簬姹係G鍊?br>//Accepted 1517 234MS 0K 837 B
#include”iostream”
using namespace std;
int main()
{
__int64 a[7000]={1},min,n;
int p[10],sg[7000],i,j,k;
for(i=2;i<10;p=0,i++);
for(i=1;i<7000;i++)
{
for(j=2,min=-1;j<10;j++)
if(min==-1||a[p[j]]*j<a[p[min]]*min)
min=j;
a=a[p[min]]*min;
min=a[p[min]]*min;
if(a>=5000000000)
break;
for(j=2;j<10;j++)
if(a[p[j]]*j==min)
p[j]++;
}//浠庡皬鍒板ぇ姹傚嚭鎵鏈変箻縐?br> while(scanf(“%I64d”,&n)!=EOF)
{
for(i=0;i<7000;i++)
{
sg=0;
if(a>=n)
break;
}
for(j=i-1;a[j]*9>=n&&j>=0;j–)
sg[j]=1;
while(j>=0)
{
for(k=j+1;k<i&&a[j]*9>=a[k];k++)
if(a[k]%a[j]==0&&sg[k]==0)
{
sg[j]=1;
break;
}
j–;
}
puts(sg[0]?”Stan wins.”:”Ollie wins.”);
}
return 0;
}
榪欓噷鎰熻阿sh菐宕藉悓瀛︾殑涓孌典唬鐮佽灝忓瓙瀛︿細(xì)浜?jiǎn)puts鐨勫鐢?/em>
#include”iostream”
using namespace std;
int main()
{
int temp,t,n,s,x,i;
cin >> t;
while(t–)
{
cin >> n;
for(i=s=temp=0;i<n;i++)
{
cin >> x;
if(x>1) temp=1;
s^=x;
}
if((s&&temp)||(!s&&!temp))
cout << “John” << endl;
else
cout << “Brother” << endl;
}
return 0;
}
]]>
棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=2147
棰樼洰鎻忚堪:
Time Limit: 5000/1000 MS (Java/Others) Memory Limit: 40000/1000 K (Java/Others)
Total Submission(s): 1806 Accepted Submission(s): 1055
Problem Description
Recently kiki has nothing to do. While she is bored, an idea appears in his mind, she just playes the checkerboard game.The size of the chesserboard is n*m.First of all, a coin is placed in the top right corner(1,m). Each time one people can move the coin into the left, the underneath or the left-underneath blank space.The person who can't make a move will lose the game. kiki plays it with ZZ.The game always starts with kiki. If both play perfectly, who will win the game?
Input
Input contains multiple test cases. Each line contains two integer n, m (0<n,m<=2000). The input is terminated when n=0 and m=0.
Output
If kiki wins the game printf "Wonderful!", else "What a pity!".
Sample Input
5 3
5 4
6 6
0 0
Sample Output
What a pity!
Wonderful!
Wonderful!
棰樼洰鍒嗘瀽:
鍒嗘瀽濡備笅:
P鐐癸細(xì)灝辨槸P涓煶瀛愮殑鏃跺欙紝瀵規(guī)柟鎷垮彲浠ヨ耽(鑷繁杈撶殑)
N鐐癸細(xì)灝辨槸N涓煶瀛愮殑鏃跺欙紝鑷繁鎷垮彲浠ヨ耽
鐜板湪鍏充簬P,N鐨勬眰瑙ｆ湁涓変釜瑙勫垯
錛?錛夛細(xì)鏈緇堟侀兘鏄疨
錛?錛夛細(xì)鎸夌収娓告垙瑙勫垯錛屽埌杈懼綋鍓嶆佺殑鍓嶆侀兘鏄疦鐨勮瘽錛屽綋鍓嶆佹槸P
錛?錛夛細(xì)鎸夌収娓告垙瑙勫垯錛屽埌杈懼綋鍓嶆佺殑鍓嶆佽嚦灝戞湁涓涓狿鐨勮瘽錛屽綋鍓嶆佹槸N
棰樻剰錛?/p>
鍦ㄤ竴涓猰*n鐨勬鐩樺唴錛屼粠(1,m)鐐瑰嚭鍙戯紝姣忔鍙互榪涜鐨勭Щ鍔ㄦ槸錛氬乏縐諱竴錛屼笅縐諱竴錛屽乏涓嬬Щ涓銆傜劧鍚巏iki姣忔鍏堣蛋錛屽垽鏂璳iki鏃跺欎細(xì)璧紙瀵規(guī)柟鏃犺礬鍙蛋鐨勬椂鍊欙級(jí)銆?/p>
鎴戜滑鍙互鎶奝N鐘舵佺殑鐐規(guī)弿緇樺嚭鏉ワ細(xì)錛?/p>
榪欎簺鐐圭殑鎻忕粯鏈変竴涓▼搴忥細(xì)錛?/p>
銆?/p>
#include<iostream>
using namespace std;
bool map[2001][2001];//1 P 0 N;
int main(){
int i,j,k;
map[1][1]=1;
for(i=2;i<=2000;i++)
{
if(map[i-1][1])
map[i][1]=0;
else map[i][1]=1;
for(j=2;j<i;j++){
if(!map[i][j-1]&&!map[i-1][j-1]&&!map[i-1][j])
map[i][j]=1;
else map[i][j]=0;
}
if(map[1][i-1])
map[1][i]=0;
else map[1][i]=1;
for(j=2;j<i;j++){
if(!map[j-1][i]&&!map[j-1][i-1]&&!map[j][i-1])
map[j][i]=1;
else map[j][i]=0;
}
if(!map[i][i-1]&&!map[i-1][i-1]&&!map[i-1][i])
map[i][i]=1;
else map[i][i]=0;
}
int M,N;
for(i=1;i<=10;i++){
for(j=1;j<=10;j++)
printf("%c ",map[i][j]?'P':'N');
printf("\n");
}
while(scanf("%d%d",&M,&N)&&M&&N){
if(map[M][N]) printf("What a pity!\n");
else printf("Wonderful!\n");
}
return 0;
}
銆?/p>
鍏蜂綋浠ｇ爜濡備笅:
using namespace std;
int main ()
{
int n,m;
while ( cin >> n >> m , n + m )
{
puts ( n%2 && m % 2 ? "What a pity!" : "Wonderful!");
}
return 0;
}
]]>
棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=2149
棰樼洰鎻忚堪:
Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 719 Accepted Submission(s): 419
Problem Description
铏界劧涓嶆兂錛屼絾鏄幇瀹炴誨綊鏄幇瀹烇紝Lele濮嬬粓娌℃湁閫冭繃閫瀛︾殑鍛借繍錛屽洜涓轟粬娌℃湁鎷垮埌濂栧閲戙傜幇鍦ㄧ瓑寰呬粬鐨勶紝灝辨槸鍍廎armJohn涓鏍風(fēng)殑鍐滅敯鐢熸動(dòng)銆?br>
瑕佺鐢板緱鏈夌敯鎵嶈錛孡ele鍚琛椾笂姝ｅ湪涓捐涓鍦哄埆寮鐢熼潰鐨勬媿鍗栦細(xì)錛屾媿鍗栫殑鐗╁搧姝ｅソ灝辨槸涓鍧?0浜╃殑鐢板湴銆備簬鏄紝Lele甯︿笂浠栫殑鍏ㄩ儴縐搫錛屽啿寰鎷嶅崠浼?xì)銆?br>
鍚庢潵鍙戠幇錛屾暣涓媿鍗栦細(xì)鍙湁Lele鍜屼粬鐨勬瀵瑰ごYueyue銆?br>
閫氳繃鎵撳惉錛孡ele鐭ラ亾榪欏満鎷嶅崠鐨勮鍒欐槸榪欐牱鐨勶細(xì)鍒氬紑濮嬪簳浠蜂負(fù)0錛屼袱涓漢杞祦寮濮嬪姞浠鳳紝涓嶈繃姣忔鍔犱環(huán)鐨勫箙搴﹁鍦?锝濶涔嬮棿錛屽綋浠鋒牸澶т簬鎴栫瓑浜庣敯鍦扮殑鎴愭湰浠?nbsp;M 鏃訛紝涓誨姙鏂瑰氨鎶婅繖鍧楃敯鍦板崠緇欒繖嬈″彨浠風(fēng)殑浜恒?br>
Lele鍜孻ueyue铏界劧鑰冭瘯涓嶈錛屼絾鏄鎷嶅崠鍗村崄鍒嗙簿閫氾紝鑰屼笖浠栦滑涓や釜浜洪兘鍗佸垎鎯沖緱鍒拌繖鍧楃敯鍦般傛墍浠ヤ粬浠瘡嬈￠兘鏄夊鑷繁鏈鏈夊埄鐨勬柟寮忚繘琛屽姞浠楓?br>
鐢變簬Lele瀛楀吀搴忔瘮Yueyue闈犲墠錛屾墍浠ユ瘡嬈￠兘鏄敱Lele鍏堝紑濮嬪姞浠鳳紝璇烽棶錛岀涓嬈″姞浠風(fēng)殑鏃跺欙紝
Lele瑕佸嚭澶氬皯鎵嶈兘淇濊瘉鑷繁涔板緱鍒拌繖鍧楀湴鍛紵
Input
鏈鐩寘鍚緇勬祴璇曪紝璇峰鐞嗗埌鏂囦歡緇撴潫(EOF)銆傛瘡緇勬祴璇曞崰涓琛屻?br>姣忕粍嫻嬭瘯鍖呭惈涓や釜鏁存暟M鍜孨(鍚箟瑙侀鐩弿榪幫紝0<N錛孧<1100)
Output
瀵逛簬姣忕粍鏁版嵁錛屽湪涓琛岄噷鎸夐掑鐨勯『搴忚緭鍑篖ele絎竴嬈″彲浠ュ姞鐨勪環(huán)銆備袱涓暟鎹箣闂寸敤絀烘牸闅斿紑銆?br>濡傛灉Lele鍦ㄧ涓嬈℃棤璁哄浣曞嚭浠烽兘鏃犳硶涔板埌榪欏潡鍦熷湴錛屽氨杈撳嚭"none"銆?br>
Sample Input
4 2
3 2
3 5
Sample Output
1
none
3 4 5
棰樼洰鍒嗘瀽:
浠ｇ爜濡備笅:
#include <iostream>
int main ()
{
int n,m;
while ( scanf ( "%d%d", &m, &n ) != EOF )
{
if ( m % ( n + 1 ) == 0 )
{
puts ( "none" );
}
else
{
if ( n >= m )
{
for ( int i = m; i <= n; ++ i )
{
printf ( i == m ? "%d" : " %d",i );
}
putchar ( '\n' );
}
else
{
printf ( "%d\n", m % ( n + 1 ) );
}
}
}
return 0;
}
]]>
棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=2188
棰樼洰鎻忚堪:
Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1337 Accepted Submission(s): 716
Problem Description
瀵逛簬鍥涘窛鍚岃優(yōu)閬彈鐨勭伨闅撅紝鍏ㄥ浗浜烘皯綰風(fēng)悍浼稿嚭鎻村姪涔嬫墜錛屽嚑涔庢瘡涓渷甯?jìng)閮綃z懼嚭浜?jiǎn)澶ч噺鐨勬晳鎻翠汉鍛樺Q岃繖鍏朵腑鍖呮嫭鎶㈤櫓鏁戠伨鐨勬璀﹂儴闃燂紝娌葷枟鍜岄槻鐤殑鍖繪姢浜哄憳錛屼互鍙?qiáng)杩涜蹇?jī)鐞嗙枏瀵肩殑蹇?jī)鐞嗗涓撳銆傛牴鎹姹傦紝鎴戞牎涔熸湁涓涓璧寸伨鍖烘晳鐏劇殑鍚嶉錛岀敱浜庡箍澶у笀鐢熸姤鍚嶈笂璺冿紝瀛︽牎涓嶅緱涓嶈繘琛岄夋嫈鏉ュ喅瀹氭渶鍚庣殑浜洪夈傜粡榪囧杞殑鑰冩牳錛屽艦鍔塊愭笎鏄庢湕錛屾渶鍚庣殑鍚嶉灝嗗湪“鏋楅槦”鍜?#8220;寰愰槦”涔嬮棿浜х敓銆備絾鏄緢宸у悎錛?涓漢鐨勭畝鍘嗗嚑涔庝竴妯′竴鏍鳳紝榪欒涓繪寔閫夋嫈鐨?600寰堟槸涓洪毦銆傛棤濂堬紝浠栧喅瀹氶氳繃鎹愭鏉ュ喅瀹氫袱浜鴻皝鑳藉叆閫夈?br>閫夋嫈瑙勫垯濡備笅錛?br>1銆佹渶鍒濈殑鎹愭綆辨槸絀虹殑錛?br>2銆佷袱浜鴻疆?huà)箒鎹悑凭锛屾瘡娆℃崘娆鹃蹇厵逯M負(fù)姝ｆ暣鏁幫紝騫朵笖姣忎漢姣忔鎹愭鏈澶氫笉瓚呰繃m鍏?1<=m<=10)銆?br>3銆佹渶鍏堜嬌寰楁繪崘嬈鵑杈懼埌鎴栬呰秴榪噉鍏冿紙0<n<10000錛夌殑涓鏂逛負(fù)鑳滆咃紝鍒欏叾鍙互浜茶蕩鐏懼尯鏈嶅姟銆?br>鎴戜滑鐭ラ亾錛屼袱浜洪兘寰堟兂鍏ラ夊織鎰胯呭悕鍗曪紝騫朵笖閮芥槸闈炲父鑱槑鐨勪漢錛屽亣璁炬灄闃熷厛鎹愶紝璇蜂綘鍒ゆ柇璋佽兘鍏ラ夋渶鍚庣殑鍚嶅崟錛?br>
Input
杈撳叆鏁版嵁棣栧厛鍖呭惈涓涓鏁存暟C錛岃〃紺哄寘鍚獵緇勬祴璇曠敤渚嬶紝鐒跺悗鏄疌琛屾暟鎹紝姣忚鍖呭惈涓や釜姝ｆ暣鏁皀錛宮錛宯鍜宮鐨勫惈涔夊弬瑙佷笂闈㈡彁鍒扮殑瑙勫垯銆?br>
Output
瀵逛簬姣忕粍嫻嬭瘯鏁版嵁錛屽鏋滄灄闃熻兘鍏ラ夛紝璇瘋緭鍑哄瓧絎︿覆"Grass"錛?nbsp;濡傛灉寰愰槦鑳藉叆閫夛紝璇瘋緭鍑哄瓧絎︿覆"Rabbit"錛屾瘡涓疄渚嬬殑杈撳嚭鍗犱竴琛屻?br>
Sample Input
2
8 10
11 10
Sample Output
Grass
Rabbit
棰樼洰鍒嗘瀽:
浠ｇ爜濡備笅:
#include <iostream>
int main ()
{
int T;
scanf ( "%d",&T );
{
while ( T -- )
{
int n,m;
scanf ( "%d%d", &n, &m );
puts ( n % ( 1 + m ) != 0 ? "Grass" : "Rabbit" );
}
}
return 0;
}
]]>
棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=1847
棰樼洰鎻忚堪:
澶у鑻辮鍥涚駭鑰冭瘯灝辮鏉ヤ復(fù)浜?jiǎn)锛屼綘鏄笉鏄湪绱у紶鐨勫涔?fàn)錛熶篃璁哥揣寮犲緱榪炵煭瀛︽湡鐨凙CM閮芥病宸ュか緇冧範(fàn)浜?jiǎn)锛屽弽姝ｆ垜鐭ラ亾鐨凨iki鍜孋ici閮芥槸濡傛銆傚綋鐒?dòng)灱屼綔湄?fù)鍦ㄨ冨満嫻告鼎浜?jiǎn)鍗佸嚑铦茬殑褰撲唬澶у鐢熷Q孠iki鍜孋ici鏇存噦寰楄冨墠鐨勬斁鏉撅紝鎵璋?#8220;寮犲紱鏈夐亾”灝辨槸榪欎釜鎰忔濄傝繖涓嶏紝Kiki鍜孋ici鍦ㄦ瘡澶╂櫄涓婁紤鎭箣鍓嶉兘瑕佺帺涓浼?xì)鍎挎墤鍏嬬墝浠ユ斁鏉炯湠缁忋?br>“鍗囩駭”錛?#8220;鍙屾墸”錛?#8220;綰簲”錛熻繕鏄?#8220;鏂楀湴涓?#8221;錛?br>褰撶劧閮戒笉鏄紒閭ｅ淇楀晩~
浣滀負(fù)璁＄畻鏈哄闄㈢殑瀛︾敓錛孠iki鍜孋ici鎵撶墝鐨勬椂鍊欏彲娌″繕璁頒笓涓氾紝濂逛滑鎵撶墝鐨勮鍒欐槸榪欐牱鐨勶細(xì)
1銆?nbsp; 鎬誨叡n寮犵墝;
2銆?nbsp; 鍙屾柟杞祦鎶撶墝錛?br>3銆?nbsp; 姣忎漢姣忔鎶撶墝鐨勪釜鏁板彧鑳芥槸2鐨勫箓嬈★紙鍗籌細(xì)1錛?/span>2錛?/span>4錛?/span>8錛?/span>16…錛?br>4銆?nbsp; 鎶撳畬鐗岋紝鑳滆礋緇撴灉涔熷嚭鏉ヤ簡(jiǎn)錛氭渶鍚庢姄瀹岀墝鐨勪漢涓鴻儨鑰咃紱
鍋囪Kiki鍜孋ici閮芥槸瓚沖鑱槑錛堝叾瀹炰笉鐢ㄥ亣璁撅紝鍝湁涓嶈仾鏄庣殑瀛︾敓~錛夛紝騫朵笖姣忔閮芥槸Kiki鍏堟姄鐗岋紝璇烽棶璋佽兘璧㈠憿錛?br>褰撶劧錛屾墦鐗屾棤璁鴻皝璧㈤兘闂?shù)笉澶уQ岄噸瑕佺殑鏄┈涓婂埌鏉ョ殑CET-4鑳芥湁濂界殑鐘舵併?br>
Good luck in CET-4 everybody!
Input
杈撳叆鏁版嵁鍖呭惈澶氫釜嫻嬭瘯鐢ㄤ緥錛屾瘡涓祴璇曠敤渚嬪崰涓琛岋紝鍖呭惈涓涓暣鏁皀錛?/span>1<=n<=1000錛夈?br>
Output
濡傛灉Kiki鑳借耽鐨勮瘽錛岃杈撳嚭“Kiki”錛屽惁鍒欒杈撳嚭“Cici”錛屾瘡涓疄渚嬬殑杈撳嚭鍗犱竴琛屻?br>
Sample Input
1
3
Sample Output
Kiki
Cici
棰樼洰鍒嗘瀽:
棣栧厛鎴戜滑鍙互鎯沖埌鍦ㄩ潰瀵?鐨勬椂鍊欐槸蹇呰觸灞錛岃皝闈㈠3鏃舵棤璁烘嬁澶氬皯閮戒細(xì)璐?! <---榪欐槸鍏抽敭
閭ｄ箞灝辮灝介噺閫犳垚榪欐牱鐨勫眬鍔跨粰瀵規(guī)柟錛屽洜涓轟換浣曚笉鏄?鐨勫嶆暟鐨勬暟鍔?鎴?閮藉彲浠ュ彉鎴?鐨勫嶆暟錛?br>鍚岀悊鍑忓幓1鎴?涔熷彲浠ュ彉鎴?鐨勫嶆暟錛屼篃灝辨槸璇村亣璁劇洰鍓嶇殑涓暟涓嶆槸3鐨勫嶆暟錛岄偅鎴戣偗瀹氳兘鎶婂畠
鎷挎垚3鐨勫嶆暟錛屾瘮濡傜幇鍦ㄦ槸11涓紝閭ｆ垜鎷胯蛋2涓氨鍙樻垚9錛岃繖鏍峰氨閫犳垚瀵規(guī)柟涓?鐨勫嶆暟灞鍔匡紝閭?br>涔堝鏂規(guī)嬁m涓垜閮藉彲浠ラ氳繃鎷?鎴栬?浣挎誨叡涓杞嬁鐨勬暟鐩垚涓?鐨勫嶆暟錛岃繖鏍峰氨浼?xì)鏈変袱绉嶆儏鍐?
1.鍒氬ソ鎷垮畬.
2.鍓╀笅鐨勮繕鏈?鐨勫嶆暟涓紝閭ｇ戶緇?
鎵浠ヨ繖鏍鋒嬁涓嬪幓蹇呰儨
浠ｇ爜濡備笅:
#include <iostream>
using namespace std;
int main ()
{
int N;
while ( cin >> N )
{
puts ( N % 3 != 0 ? "Kiki" : "Cici" );
}
return 0;
}
]]>
棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=1849
棰樼洰鎻忚堪:
澶у鏃跺厜鏄氮婕殑錛屽コ鐢熸槸嫻極鐨勶紝鍦ｈ癁鏇存槸嫻極鐨勶紝浣嗘槸Rabbit鍜孏rass榪欎袱涓ぇ瀛﹀コ鐢熷湪浠婂勾鐨勫湥璇炶妭鍗磋〃鐜板緱涓鐐歸兘涓嶆氮婕細(xì)涓嶅幓閫涘晢鍦猴紝涓嶅幓閫涘叕鍥紝涓嶅幓鍜孉C鐢風(fēng)害浼?xì)锛屼袱涓汉绔熺劧鐚湪瀵濋涓媼?#8230;…
璇存槸涓嬫錛屽叾瀹炲彧鏄竴涓畝鍗曠殑灝忔父鎴忚屽凡錛屾父鎴忕殑瑙勫垯鏄繖鏍風(fēng)殑錛?br>1銆?nbsp; 媯嬬洏鍖呭惈1*n涓柟鏍鹼紝鏂規(guī)牸浠庡乏鍒板彸鍒嗗埆緙栧彿涓?錛?/span>1錛?/span>2錛?#8230;錛宯-1錛?br>2銆?nbsp; m涓瀛愭斁鍦ㄦ鐩樼殑鏂規(guī)牸涓婏紝鏂規(guī)牸鍙互涓虹┖錛屼篃鍙互鏀懼浜庝竴涓殑媯嬪瓙錛?br>3銆?nbsp; 鍙屾柟杞祦璧版錛?br>4銆?nbsp; 姣忎竴姝ュ彲浠ラ夋嫨浠繪剰涓涓瀛愬悜宸︾Щ鍔ㄥ埌浠繪剰鐨勪綅緗紙鍙互澶氫釜媯嬪瓙浣嶄簬鍚屼竴涓柟鏍鹼級(jí)錛屽綋鐒?dòng)灱屼恢M綍媯嬪瓙涓嶈兘瓚呭嚭媯嬬洏杈圭晫錛?br>5銆?nbsp; 濡傛灉鎵鏈夌殑媯嬪瓙閮戒綅浜庢渶宸﹁竟錛堝嵆緙栧彿涓?鐨勪綅緗級(jí)錛屽垯娓告垙緇撴潫錛屽茍涓旇瀹氭渶鍚庤蛋媯嬬殑涓鏂逛負(fù)鑳滆呫?br>
瀵逛簬鏈錛屼綘涓嶉渶瑕佽冭檻n鐨勫ぇ灝忥紙鎴戜滑鍙互鍋囪鍦ㄥ垵濮嬬姸鎬侊紝媯嬪瓙鎬繪槸浣嶄簬媯嬬洏鐨勯傚綋浣嶇疆錛夈備笅闈㈢殑紺烘剰鍥懼嵆涓轟竴涓?*15鐨勬鐩橈紝鍏辨湁6涓瀛愶紝鍏朵腑錛岀紪鍙?鐨勪綅緗湁涓や釜媯嬪瓙銆?br>
澶у鐭ラ亾錛岃櫧鐒跺伓灝?dāng)涓嶅娴极锛屼絾鏄疪abbit鍜孏rass閮芥槸鍐伴洩鑱槑鐨勫コ鐢燂紝濡傛灉姣忔閮芥槸Rabbit鍏堣蛋媯嬶紝璇瘋緭鍑烘渶鍚庣殑緇撴灉銆?br>
Input
杈撳叆鏁版嵁鍖呭惈澶氱粍嫻嬭瘯鐢ㄤ緥錛屾瘡涓祴璇曠敤渚嬪崰浜岃錛岄鍏堜竴琛屽寘鍚竴涓暣鏁癿錛?/span>0<=m<=1000錛夛紝琛ㄧず鏈祴璇曠敤渚嬬殑媯嬪瓙鏁扮洰錛岀揣璺熺潃鐨勪竴琛屽寘鍚玬涓暣鏁癒i(i=1…m; 0<=Ki<=1000)錛屽垎鍒〃紺簃涓瀛愬垵濮嬬殑浣嶇疆錛宮=0鍒欑粨鏉熻緭鍏ャ?br>
Output
濡傛灉Rabbit鑳借耽鐨勮瘽錛岃杈撳嚭“Rabbit Win!”錛屽惁鍒欒杈撳嚭“Grass Win!”錛屾瘡涓疄渚嬬殑杈撳嚭鍗犱竴琛屻?br>
Sample Input
2
3 5
3
3 5 6
0
Sample Output
Rabbit Win!
Grass Win!
棰樼洰鍒嗘瀽 :
鏍囧噯 鐨?nim 鍗氬紙 闂, 涓嶈鎯沖鏉備簡(jiǎn) . 鍥犱負(fù)鍙兘寰宸︾Щ, 鎵浠ュ彲浠ュ皢 鍒濆鐨勬瘡涓瀛愮殑浣嶇疆鐪嬫垚涓涓爢, 姣斿璇? 1涓瀛愬湪 n-1鏍? 閭ｄ箞灝變唬琛ㄨ繖涓爢鏈?n-1涓暟
宸︾Щ1鏍?灝辨槸鍙栬蛋涓涓? 鎵浠ユ湁 m 媯嬪瓙灝變唬琛ㄦ湁m涓爢, 鍏ㄩ儴鍒?灝辨槸鍙栧畬浜?........... 鏇村叿浣撶殑 nim 鍗氬紙浠嬬粛璇風(fēng)偣鍑?nbsp; << 鍗氬紙鍏ラ棬 >>
浠ｇ爜濡備笅:
#include <iostream>
int heap[1001];
int main ()
{
int T;
while ( scanf ( "%d",&T ), T )
{
int res = 0 , nCount = 0;
for ( int i = 0; i != T; ++ i )
{
scanf ( "%d",heap + i );
res ^= heap[i];
}
puts ( res == 0 ? "Grass Win!" : "Rabbit Win!" );
}
return 0;
}
]]>
棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=1846
棰樼洰鎻忚堪:
鍗佸勾鍓嶈澶у鐨勬椂鍊欙紝涓浗姣忓勾閮借浠庡浗澶栧紩榪涗竴浜涚數(shù)褰卞ぇ鐗囷紝鍏朵腑鏈変竴閮ㄧ數(shù)褰卞氨鍙婂媷鏁㈣呯殑娓告垙銆嬶紙鑻辨枃鍚嶇О錛歓athura錛夛紝涓鐩村埌鐜板湪錛屾垜渚濈劧瀵逛簬鐢?shù)濯?jiǎng)涓殑閮ㄥ垎鐢?shù)鑴戠壱?guī)妧鍗拌薄娣卞埢銆?br>浠婂ぉ錛屽ぇ瀹墮夋嫨涓婃満鑰冭瘯錛屽氨鏄竴縐嶅媷鏁紙brave錛夌殑閫夋嫨錛涜繖涓煭瀛︽湡錛屾垜浠鐨勬槸鍗氬紙錛坓ame錛変笓棰橈紱鎵浠ワ紝澶у鐜板湪鐜╃殑涔熸槸“鍕囨暍鑰呯殑娓告垙”錛岃繖涔熸槸鎴戝懡鍚嶈繖涓鐩殑鍘熷洜銆?br>褰撶劧錛岄櫎浜?#8220;鍕囨暍”錛屾垜榪樺笇鏈涚湅鍒?#8220;璇氫俊”錛屾棤璁鴻冭瘯鎴愮嘩濡備綍錛屽笇鏈涚湅鍒扮殑閮芥槸涓涓湡瀹炵殑緇撴灉錛屾垜涔熺浉淇″ぇ瀹朵竴瀹氳兘鍋氬埌鐨?/span>~
鍚勪綅鍕囨暍鑰呰鐜╃殑絎竴涓父鎴忔槸浠涔堝憿錛熷緢綆鍗曪紝瀹冩槸榪欐牱瀹氫箟鐨勶細(xì)
1銆?nbsp; 鏈父鎴忔槸涓涓簩浜烘父鎴?
2銆?nbsp; 鏈変竴鍫嗙煶瀛愪竴鍏辨湁n涓紱
3銆?nbsp; 涓や漢杞祦榪涜;
4銆?nbsp; 姣忚蛋涓姝ュ彲浠ュ彇璧?…m涓煶瀛愶紱
5銆?nbsp; 鏈鍏堝彇鍏夌煶瀛愮殑涓鏂逛負(fù)鑳滐紱
濡傛灉娓告垙鐨勫弻鏂逛嬌鐢ㄧ殑閮芥槸鏈浼樼瓥鐣ワ紝璇瘋緭鍑哄摢涓漢鑳借耽銆?br>
Input
杈撳叆鏁版嵁棣栧厛鍖呭惈涓涓鏁存暟C(C<=100)錛岃〃紺烘湁C緇勬祴璇曟暟鎹?br>姣忕粍嫻嬭瘯鏁版嵁鍗犱竴琛岋紝鍖呭惈涓や釜鏁存暟n鍜宮錛?/span>1<=n,m<=1000錛夛紝n鍜宮鐨勫惈涔夎棰樼洰鎻忚堪銆?br>
Output
濡傛灉鍏堣蛋鐨勪漢鑳借耽錛岃杈撳嚭“first”錛屽惁鍒欒杈撳嚭“second”錛屾瘡涓疄渚嬬殑杈撳嚭鍗犱竴琛屻?br>
Sample Input
2
23 2
4 3
Sample Output
first
second
棰樼洰鍒嗘瀽:
宸翠粈鍗氬紙錛屼竴涓漢鎷?锝瀖涓紝閭ｈ皝闈㈠m+1鐨勫眬鍔跨殑鐨勬椂鍊欏垯蹇呰觸錛屽緢鏄庢樉錛屽厛鎷跨殑灝辨槸瑕侀犺繖涓眬鍔?濡傛灉n鏄?m+1)*r+s(k涓轟換鎰忥紝s<m+1),閭ｄ箞寰堟槑鏄懼厛鎷跨殑鎷挎帀s鍚庯紝鐒跺悗鏃犺涓嬩竴涓嬁澶氬皯浣犻兘鍙互淇濊瘉浣犳嬁瀹屽悗閮芥槸鎷夸簡(jiǎn)m+1涓紝榪欐牱鍚庢嬁鐨勫繀瀹氶潰瀵瑰繀璐ュ眬鍔匡紝姣斿23 2錛?3=錛?×7錛?2錛涢偅鎴戠涓嬈℃嬁鎺?錛岀劧鍚庢棤璁烘瘡嬈＄浜屼釜鎷垮嚑鎴戦兘鍙互浣垮緱榪欒疆鎬誨叡鎷?錛岀劧鍚庝粬蹇呭畾浼?xì)闈㈠?榪欎釜灞鍔匡紝鐒跺悗鎴戝氨蹇呰儨錛岄偅浠涔堟椂鍊欏繀璐ュ憿錛屽緢鏄庢樉濡傛灉鎴戦潰瀵圭殑鏄紙m+1錛夌殑鍊嶆暟鐨勫眬鍔垮氨蹇呰觸銆?br>puts ( n % ( 1 + m ) != 0 ? "first" : "second" );
緇撴灉绔熺劧琚繖棰樼粰闃翠簡(jiǎn)....while(scanf("%d",&c)!=EOF) --> 緇撴灉WA, YM
鐒跺悗鏀規(guī)垚 scanf("%d",&c) 灞呯劧 AC 浜? ...................鎮(zhèn)插墽锝烇綖锝?/p>
浠ｇ爜濡備笅 :
#include <iostream>
int main ()
{
int T;
scanf ( "%d",&T );
{
while ( T -- )
{
int n,m;
scanf ( "%d%d", &n, &m );
puts ( n % ( 1 + m ) != 0 ? "first" : "second" );
}
}
return 0;
}
]]>
棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=1850
棰樼洰鎻忚堪:
涓騫村湪澶?nbsp;鐖舵瘝鏃跺埢鐗墊寕
鏄ヨ妭鍥炲 浣犺兘鍋氬嚑澶╁ソ瀛╁瓙鍚?br>瀵掑亣閲屽皾璇曞仛鍋氫笅闈㈢殑浜嬫儏鍚?br>
闄濡堥涗竴嬈¤彍鍦?br>鎮(zhèn)勬?zhèn)劸l欑埜鐖鎬拱涓皬紺肩墿
涓誨姩鍦?nbsp;寮虹儓鍦?nbsp;瑕佹眰媧椾竴嬈＄
鏌愪竴澶╂棭璧?nbsp;緇欑埜濡堢敤蹇?jī)鍦板仛鍥炴棭椁?br>
濡傛灉鎰挎剰 浣犺繕鍙互鍜岀埜濡堣
鍜變滑鐜╀釜灝忔父鎴忓惂 ACM璇句笂瀛︾殑鍛綖
涓嬮潰鏄竴涓簩浜哄皬娓告垙錛氭瀛愪笂鏈塎鍫嗘墤鍏嬬墝錛涙瘡鍫嗙墝鐨勬暟閲忓垎鍒負(fù)Ni(i=1…M)錛涗袱浜鴻疆?huà)箒杩涜锛涙瘡璧颁竴姝ュ彲浠ヤ換鎰忛夋嫨涓鍫嗗茍鍙栬蛋鍏朵腑鐨勪換鎰忓紶鐗岋紱妗屽瓙涓婄殑鎵戝厠鍏ㄩ儴鍙栧厜錛屽垯娓告垙緇撴潫錛涙渶鍚庝竴嬈″彇鐗岀殑浜轟負(fù)鑳滆呫?br>鐜板湪鎴戜滑涓嶆兂鐮旂┒鍒板簳鍏堟墜涓鴻儨榪樻槸涓鴻礋錛屾垜鍙兂闂ぇ瀹訛細(xì)
鈥斺?#8220;鍏堟墜鐨勪漢濡傛灉鎯寵耽錛岀涓姝ユ湁鍑犵閫夋嫨鍛紵”
Input
杈撳叆鏁版嵁鍖呭惈澶氫釜嫻嬭瘯鐢ㄤ緥錛屾瘡涓祴璇曠敤渚嬪崰2琛岋紝棣栧厛涓琛屽寘鍚竴涓暣鏁癕(1<M<100)錛岃〃紺烘墤鍏嬬墝鐨勫爢鏁幫紝绱ф帴鐫涓琛屽寘鍚玀涓暣鏁癗i(1<=Ni<=1000000錛宨=1…M)錛屽垎鍒〃紺篗鍫嗘墤鍏嬬殑鏁伴噺銆侻涓?鍒欒〃紺鴻緭鍏ユ暟鎹殑緇撴潫銆?br>
Output
濡傛灉鍏堟墜鐨勪漢鑳借耽錛岃杈撳嚭浠栫涓姝ュ彲琛岀殑鏂規(guī)鏁幫紝鍚﹀垯璇瘋緭鍑?錛屾瘡涓疄渚嬬殑杈撳嚭鍗犱竴琛屻?br>
Sample Input
3
5 7 9
0
Sample Output
1
棰樼洰鍒嗘瀽 :
MiYu鍘熷垱, 杞笘璇鋒敞鏄?: 杞澆鑷?______________鐧界櫧銇眿
涓.
濡傛灉a1^a2^a3^...^an=0 ( 鍗?: nim-sum=0 ) , 璇存槑鍏堟墜娌℃湁蹇呰耽絳栫暐, 鏂規(guī)硶鏁拌偗瀹氫負(fù) 0;
浜?
鍋囪鍏堟墜鐨勪漢鏈夊繀璧㈢瓥鐣ャ?/p>
闂鍒欒漿鍖栦負(fù)=>鍦ㄤ換鎰忎竴鍫嗘嬁浠繪剰K寮犵墝錛屽茍涓斿墿涓嬫墍鏈夊爢鐨刵im-sum=0(P-position)鐨勬柟妗堟繪暟銆?/p>
1. 鐜板湪鎴戜滑鍏堢湅涓涓緥瀛?5,7,9)錛屽茍鍋囪浠庣涓鍫嗗彇浠繪剰K寮犵墝銆?/p>
鎺掗櫎絎竴鍫嗙墝鐨刵im-sum涓?7^9=14
0111
^1001
-------
1110
濡傛灉瑕佷嬌鎵鏈夊爢鐨刵im-sum=0鎴愮珛錛屽垯絎竴鍫嗗彇鎺塊寮犱互鍚庡繀瀹氫負(fù)1110錛屽洜涓篨^X=0銆?/p>
鎵浠ヨ瑙傚療 5-k=14 k>0 鎴愮珛,姝や緥瀛?鍦ㄧ涓鍫嗗彇浠繪剰K寮犵墝)鏄庢樉鐨勪笉鎴愮珛銆備絾騫朵笉浠ｈ〃鍦ㄧ浜屾垨絎笁鍫嗗彇浠繪剰K寮犵墝鐨勮В涓嶆垚绔嬨?/p>
2. 鐜板湪鐪嬬浜屼釜渚嬪瓙(15,7,9)錛屽茍鍋囪浠庣涓鍫嗗彇浠繪剰K寮犵墝銆?/p>
鎺掗槦絎竴鍫嗙墝鐨刵im-sum涓?^9=14錛屽拰絎竴涓緥瀛愮浉鍚岋紝鎵浠ラ棶棰樺彉?shù)给櫑傚?15-k=14 k>0 鏄惁鎴愮珛銆?/p>
褰撶劧榪欎釜渚嬪瓙鏄垚绔嬬殑銆?/p>
涓?
鎬葷粨寰楀嚭錛?/p>
鍦ㄤ換鎰忎竴鍫嗘嬁浠繪剰K寮犵墝錛屽茍涓旀墍鏈夊爢鐨刵im-sum=0 鎴愮珛鐨勬潯浠朵負(fù)錛氭帓闄ゅ彇鎺塊寮犵墝鐨勯偅涓鍫嗙殑nim-sum蹇呴』灝戜簬璇ュ爢鐗屼笂鐨勬暟閲?渚嬪瓙浜?錛屽惁鍒欎笉鑳藉湪姝ゅ爢涓婂彇浠繪剰K寮犵墝浣挎墍鏈夊爢鐨刵im-sum=0鎴愮珛(渚嬪瓙涓)銆?/p>
鏁呮繪柟妗堟暟涓?( 鍦ㄤ換鎰忎竴鍫嗘嬁浠繪剰K寮犵墝錛屽茍涓旀墍鏈夊爢鐨刵im-sum=0 鎴愮珛 ) 鐨勬繪暟銆?/p>
浠ｇ爜濡備笅 :
#include <iostream>
int heap[101];
int main ()
{
int T;
while ( scanf ( "%d",&T ), T )
{
int res = 0 , nCount = 0;
for ( int i = 0; i != T; ++ i )
{
scanf ( "%d",heap + i );
res ^= heap[i];
}
if ( res == 0 )
{
puts ( "0" );
continue;
}
int cmp = 0;
for ( int i = 0; i != T; ++ i )
{
cmp = res ^ heap[i];
if ( cmp < heap[i] )
{
nCount ++;
}
}
printf ( "%d\n",nCount );
}
return 0;
}
]]>
棰樼洰鍦板潃:
http://acm.hdu.edu.cn/showproblem.php?pid=2897
棰樼洰鎻忚堪:
褰撴棩閬囧埌鏈堬紝浜庢槸鏈変簡(jiǎn)鏄庛傚綋鎴戦亣鍒頒簡(jiǎn)浣狅紝渚挎垚浜?jiǎn)淝G銆?br>閭ｅぉ錛屾棩鏈堢浉浼?xì)锛屾垜瑙佸堫C簡(jiǎn)浣犮傝屼笖錛屽ぇ鍦板け鍘諱簡(jiǎn)鍏夎緣錛屼綘鎴戞槸鍚︽垚渚ｏ紵榪欐敞瀹氭槸涓噭緹庣殑鏁呬簨銆傦紙浠ヤ笂鏄簾璇濓級(jí)
灝弔鍜屾墍鏈変笘淇楃殑浜轟滑涓鏍鳳紝鏈熷緟閭ｇ櫨騫撮毦閬囩殑鏃ラ銆傞┗瓚寵澶寸湅澶╋紝鐪嬫棩鏈堟笎娓愯蛋榪戯紝灝弔鐨勮剸瀛愰偅涓吀鍛錛堜粬鍧氭寔榪欎釜濮垮娍宸茬粡鏈夊崐涓灝忔椂鍟︼級(jí)銆備粬浣庝笅浠拌搗鐨勫ご錛岀幆欏懼洓鍛ㄣ傚拷鐒跺彂鐜拌韓杈圭珶绔欑潃浣嶆紓浜殑mm銆傚ぉ娓愭笎鏆椾笅錛岃繖mm鍦ㄨ繖琛楀ご绔熺劧濡傛鑰鐪鹼紝濂規(guī)槸澶╀嬌鍚楋紵绔欑潃灝弔韜竟鐨勫ぉ浣褲?br>灝弔瀵筸m鎯婂懠錛?#8220;緙樺垎鍛?/span>~~”銆俶m鍗存涓嶅惈緋婏細(xì)“鏄晩錛?00騫翠竴閬囧摝錛?#8221;錛堟鍚庣渷鐣?000瀛?#8230;.錛?br>灝弔璧剁揣鍚憁m瑕佽仈緋繪柟寮忥紝鍙痬m璇達(dá)細(xì)“鎴戝拰浣犵帺涓父鎴忓惂錛岃耽浜?jiǎn)锛屾垜灏辨妸鎴戠殑鎵嬫満鍙峰憡璇変綘銆?#8221;灝弔錛屽績(jī)鎯沖ぉ涓嬪摢鏈夐鐩兘闅懼掓垜鍛紝渚挎弧鍙ｇ瓟搴斾笅鏉ャ俶m寮濮嬭娓告垙瑙勫垯錛?#8220;鎴戞湁涓鍫嗙‖甯侊紝涓鍏?鏋氾紝浠庤繖涓‖甯佸爢閲屽彇紜竵錛屼竴嬈℃渶灝戝彇2鏋氾紝鏈澶?鏋氾紝濡傛灉鍓╀笅灝戜簬2鏋氬氨瑕佷竴嬈″彇瀹屻傛垜鍜屼綘杞祦鍙栵紝鐩村埌鍫嗛噷鐨勭‖甯佸彇瀹岋紝鏈鍚庝竴嬈″彇紜竵鐨勭畻杈撱傛垜鐜╄繃榪欎釜娓告垙濂藉嬈′簡(jiǎn)錛屽氨璁╄浣狅紝璁╀綘鍏堝彇鍚?/span>~”
灝弔鎺愭寚涓綆楋紝涓嶅鍛錛岃繖鏄笉鍙兘鐨勪換鍔′箞銆傚皬t闇插嚭寰楁剰鐨勭瑧錛?#8220;榪樻槸mm浼樺厛鍟︼紝鍛靛懙~”mm闇庢椂鎰ｄ綇浜?jiǎn)锛屾兿x(chóng)槸瀵瑰皬t鐨勫弽搴斿嚭涔庢剰鏂欏惂銆?br>濂瑰嵈涔熶笉鐢熸皵錛?#8220;濂藉皬瀛愶紝鎸鴻仾鏄庡憿錛岃涓嶈繖鏍峰惂錛屼綘鎶婃垜鐨勯偖綆辯粰鎴戯紝鎴戠粰浣犲彂涓枃鏈紝姣忚鏈変笁涓暟瀛梟錛宲錛宷錛岃〃紺轟竴鍫嗙‖甯佷竴鍏辨湁n鏋氾紝浠庤繖涓‖甯佸爢閲屽彇紜竵錛屼竴嬈℃渶灝戝彇p鏋氾紝鏈澶歲鏋氾紝濡傛灉鍓╀笅灝戜簬p鏋氬氨瑕佷竴嬈″彇瀹屻備袱浜鴻疆?huà)箒鍙栧Q岀洿鍒板爢閲岀殑紜竵鍙栧畬錛屾渶鍚庝竴嬈″彇紜竵鐨勭畻杈撱傚浜庢瘡涓琛岀殑涓変釜鏁板瓧錛岀粰鍑哄厛鍙栫殑浜烘槸鍚︽湁蹇呰儨絳栫暐錛屽鏋滄湁鍥炵瓟WIN錛屽惁鍒欏洖絳擫OST銆備綘鎶婂搴旂殑絳旀鍙戠粰鎴戯紝濡傛灉浣犺兘鍦ㄤ粖澶╂櫄涓?鐐逛互鍓嶅彂緇欐垜姝ｇ‘絳旀錛屾垨璁告垜浠槑澶╀笅鍗堝彲浠ュ啀瑙併?#8221;
灝弔浜岃瘽娌¤錛屽皢鑷繁鐨勯偖綆辯粰浜?jiǎn)mm銆傚綋浠栧叴鍐插啿寰楄刀鍥炲錛屼笂緗戠湅閭錛屽搰錛乵m鐨勯偖浠跺凡緇忓埌浜?jiǎn)銆備粬鍙戠幇鏂囨湰闀胯揪100000琛岋紝姣忚鐨勪笁涓暟瀛楅兘寰堝ぇ錛屼絾鏄兘鏄笉瓚呰繃65536鐨勬暣鏁般傚皬t鐪嬭〃宸茬粡涓嬪崍6鐐逛簡(jiǎn)錛岃鎯蟲(chóng)墜宸ョ畻鍑烘墍鏈夌粨鏋滐紝鐪嬫潵鏄笉鍙兘浜?jiǎn)銆備綘鑳藉府甯粬錛岃浠栧啀瑙佸埌閭ｄ釜mm鍚楋紵
Input
涓嶈秴榪?00000琛岋紝姣忚涓変釜姝ｆ暣鏁皀錛宲錛宷銆?br>
Output
瀵瑰簲姣忚杈撳叆錛屾寜鍓嶉潰浠嬬粛鐨勬父鎴忚鍒欙紝鍒ゆ柇鍏堝彇鑰呮槸鍚︽湁蹇呰儨絳栫暐銆傝緭鍑篧IN鎴栬匧OST銆?br>
Sample Input
7 2 4
6 2 4
Sample Output
LOST
WIN
鍗氬紙鐨勫叆闂ㄩ, 宸翠粈鍗氬(Bash Game), 鍏蜂綋浜?jiǎn)瑙ｈL(fēng)偣鍑?nbsp; 鍗氬紙鍏ラ棬 .
浠ｇ爜濡備笅:
#include <iostream>
int main ()
{
int N, p, q;
while ( scanf ( "%d%d%d",&N, &p, &q ) != EOF )
{
int res = N % ( p + q );
puts ( res ? res <= p ? "LOST" : "WIN" : "WIN" );
}
return 0;
}
鍙﹀縐縐鑷繁鐨勪竴琛屼唬鐮?:
main(p,q){int N,res;while(~scanf("%d%d%d",&N,&p,&q)){res=N%(p+q);puts(res?res<=p?"LOST":"WIN":"WIN");}}
]]>
瀵繪壘騫寵 鐘舵侊紙涔熺О蹇呰觸鎬侊紝 濂囧紓灞鍔匡級(jí)錛岋紙婊¤凍錛氫換鎰忛潪騫寵 鎬佺粡榪囦竴嬈℃搷浣滃彲浠ュ彉?shù)负邈^琛℃侊級(jí)
(涓)宸翠粈鍗氬(Bash Game):
鍙湁涓鍫?/span>n涓墿鍝?/span>,涓や釜浜鴻疆?huà)箒浠帢q欏爢鐗╁搧涓彇鐗?/span>,瑙勫畾姣忔鑷沖皯鍙栦竴涓?/span>,鏈澶氬彇m涓?/span>.鏈鍚庡彇鍏夎呭緱鑳?/span>.
n = (m+1)r+s , (r涓轟換鎰忚嚜鐒舵暟,s≤m), 鍗?/span>n%(m+1) != 0, 鍒欏厛鍙栬呰偗瀹氳幏鑳?/span>
(浜?/span>)濞佷綈澶崥濂?/span>(Wythoff Game):
,,,,.
(ak,bk)(ak ≤ bk ,k=0,1,2,...,n)琛ㄧず濂囧紓灞鍔?/span>
姹傛硶錛?/span>
ak =[k(1+√5)/2], bk= ak + k (k=0,1,2,...,n 鏂規(guī)嫭鍙瘋〃紺哄彇鏁村嚱鏁?/span>)
鍒ゆ柇錛?/span>
Gold=(1+sqrt(5.0))/2.0錛?/span>
1錛夊亣璁撅紙a錛?/span>b錛変負(fù)絎?/span>k縐嶅寮傚眬鍔?/span>(k=0,1,2...) 閭ｄ箞k=b-a;
2錛夊垽鏂叾a==(int)(k*Gold),鐩哥瓑鍒欎負(fù)濂囧紓灞鍔?/span>
錛堟敞錛氶噰鐢ㄩ傚綋鐨勬柟娉?/span>,鍙互灝嗛潪濂囧紓灞鍔垮彉?shù)负濂囧紓灞鍔?/span>.
鍋囪闈㈠鐨勫眬鍔挎槸(a,b)
鑻?/span> b = a,鍒欏悓鏃朵粠涓ゅ爢涓彇璧?/span> a 涓墿浣?/span>,灝卞彉?shù)皋Z簡(jiǎn)濂囧紓灞鍔?/span>(0,0)錛?/span>
1. 濡傛灉a = ak,
1.1 b > bk, 閭ｄ箞,鍙栬蛋b - bk涓墿浣?/span>,鍗沖彉?shù)负濂囧紓灞鍔?/span>(ak, bk)錛?/span>
1.2 b < bk 鍒欏悓鏃朵粠涓ゅ爢涓嬁璧?/span> ak – a[b – ak]涓墿浣?/span>,鍙樹(shù)負(fù)濂囧紓灞鍔?/span>( a[b – ak] , a[b – ak]+ b - ak)錛?/span>
2 濡傛灉a = bk ,
2.1 b > ak ,鍒欎粠絎簩鍫嗕腑鎷胯蛋澶氫綑鐨勬暟閲?/span>b – ak
2.2 b < ak ,鍒?/span> 鑻?/span>b = aj (j < k) 浠庣涓鍫嗕腑鎷胯蛋澶氫綑鐨勬暟閲?/span>a– bj; (a > bj)
鑻?/span>b = bj (j < k) 浠庣涓鍫嗕腑鎷胯蛋澶氫綑鐨勬暟閲?/span>a– aj; ( a > aj)
錛?/span>
渚嬮錛?/span>pku 1067
(涓?/span>)灝煎鍗氬(Nimm Game):
n,,,,.
浠諱綍濂囧紓灞鍔?/span>(a1, a2, … , an)閮芥湁a1(+)a2(+)…(+)an =0. ( (+)涓?/span> 鎸変綅^)
Nim娓告垙綆浠嬶細(xì)
錛?錛夋湁涓や釜鐜╁錛?/p>
錛?錛夋湁涓夊爢鎵戝厠鐗岋紙姣斿錛氬彲浠ュ垎鍒槸5錛?錛?寮狅級(jí)錛?/p>
錛?錛夌帺瀹剁殑姣忔鎿嶄綔鏄夋嫨鍏朵腑鏌愪竴鍫嗙墝錛岀劧鍚庝粠涓彇璧頒換鎰忓紶錛?/p>
nim娓告垙鐨勫畾鐞嗕竴錛?/p>
瀵逛簬nim娓告垙鐨勬煇涓綅緗?x1,x2,x3),褰撲笖浠呭綋瀹冨悇閮ㄥ垎鐨刵im-sum絳変簬0鏃訛紙鍗硏1⊕x2⊕x3=0錛夛紙x1錛寈2錛寈3鍋氬紓鎴栨搷浣淾錛夛紝鍒欏綋鍓嶄綅浜庡繀璐ョ偣銆?/p>
渚嬮錛?/span>pku 2234 渚嬮錛?/span>hdu 1730 渚嬮錛?/span>pku 1740 渚嬮錛?/span>pku 1704 渚嬮錛?/span>pku 1082 (澶ч噺鍒嗘瀽… 緇撹寰堢畝鍗曘?/span> 涔熷彲浠ユ牴鎹畝鍗曠殑鎺ㄨ妯℃嫙瀹炵幇銆?/span>)
瀹氫箟: 鍋囪 (xm · · · x0)2 鍜?ym · · · y0)2 鐨刵im-sum鏄?zm · · · z0)2,鍒欐垜浠〃紺烘垚 (xm · · · x0)2 ⊕ (ym · · · y0)2 = (zm · · · z0)2,
榪欓噷錛寊k = xk + yk (mod 2)錛坘=0…m錛? 
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