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Longest Prefix
闂鎻忚堪錛?/span>
緇欏畾涓鍫嗙煭瀛楃涓詫紝鍜屼竴鏉¢暱瀛楃涓詫紝姹傜敤鐭瓧絎︿覆緇勬垚鐨勯暱瀛楃涓茬殑鏈闀垮墠緙闀垮害銆?/span>
鍒嗘瀽錛?/span>
鐪嬪畬棰樼洰棣栧厛鎯沖埌鐨勬槸DFS錛屽啓瀹屾彁浜や笂鍘誨悗鍒扮涓夌粍鏁版嵁灝辮秴鏃朵簡銆傘傘傜湅浜嗗埆浜虹殑棰樿В錛屽師鏉ヨ鐢ㄥ姩瑙勶紝鐢?/span>dp[i]琛ㄧず褰撳墠鑳芥嫾鍒扮殑鏈闀垮墠緙錛岀劧鍚庡湪鐭瓧絎﹂噷闈㈠鎵炬渶闀跨殑鑳藉拰闀垮瓧絎︿覆緇х畫鍖歸厤鐨勶紝鐒跺悗i+1錛佹湰鏉ユ兂絎竴嬈¤瘯璇?/span>Hash錛屼絾鍐欏埌涓鍗婅寰楀嚱鏁板啓寰椾笉澶熷ソ錛屽厛璁頒綇浜嗭紝鏈夌┖浜嗙敤Hash浼樺寲涓閬嶃?/span>
Cow Pedigrees
闂鎻忚堪錛?/span>
緇欏畾涓棰楁爲鐨勮妭鐐規暟鍜屽害錛岄棶鍏惰兘鏋勬垚澶氬皯縐嶄笉鍚岀殑鏁般?/span>
鍒嗘瀽錛?/span>
榪欓铏界劧鏄庣煡閬撹鐢ㄥ姩瑙勶紝浣嗘兂浜嗕竴涓嬪崍閮芥病鎯沖嚭鐘舵佽漿縐繪柟紼嬫潵錛屽洤~銆傜湅浜嗙綉涓婄殑瀹樻柟棰樿В錛屼竴棰楁爲鏄劇劧瑕佺敱涓棰楀皬鏍戯紙鏍硅妭鐐癸級鏋勬垚錛屽彲浠ユ槸宸﹀瓙鏍戯紝涔熷彲浠ユ槸鍙沖瓙鏍戯紝鍒嗕笁縐嶆儏鍐碉紝宸﹂暱錛屽彸闀匡紝宸﹀彸鍚岄暱銆傜姸鎬佽漿縐繪柟紼嬪涓嬶細
table[i][j] += smalltrees[i-2][k]*table[i-1][j-1-k];
// 宸﹀瓙鏍戞繁搴﹀皬浜?/span>i-1錛屽彸瀛愭爲娣卞害涓?/span>i-1
table[i][j] += table[i-1][k]*smalltrees[i-2][j-1-k];
// 宸﹀瓙鏍戞繁搴︿負i-1錛屽彸瀛愭爲娣卞害灝忎簬i-1
table[i][j] += table[i-1][k]*table[i-1][j-1-k];
// 宸﹀彸瀛愭爲娣卞害閮戒負i-1
Zero Sum
闂鎻忚堪錛?/span>
璇瘋冭檻涓涓敱1鍒?/span>N錛?/span>N=3, 4, 5 ... 9錛夌殑鏁板瓧緇勬垚鐨勯掑鏁板垪錛?/span>1 2 3 ... N銆傜幇鍦ㄨ鍦ㄦ暟鍒椾腑鎻掑叆“+”琛ㄧず鍔狅紝鎴栬?#8220;-”琛ㄧず鍑忥紝“ ”琛ㄧず絀虹櫧(渚嬪1-2 3灝辯瓑浜?/span>1-23)錛屾潵灝嗘瘡涓瀵規暟瀛楃粍鍚堝湪涓璧鳳紙璇蜂笉鍦ㄧ涓涓暟瀛楀墠鎻掑叆絎﹀彿錛夈傝綆楄琛ㄨ揪寮忕殑緇撴灉騫跺垽鏂叾鍊兼槸鍚︿負0銆傝浣犲啓涓涓▼搴忔壘鍑烘墍鏈変駭鐢熷拰涓洪浂鐨勯暱搴︿負N鐨勬暟鍒椼?/span>
鍒嗘瀽錛?/span>
榪欓鍦ㄥ煿璁殑鏃跺欒榪囷紝鍒涘緩涓涓瓧絎︿覆“1 2 3 4 5 6 7 8 9 ”鏁板瓧闂撮殧鐫絀烘牸錛岀劧鍚庡湪絀烘牸浣嶇疆鏋氫婦鍐欏叆‘ ’錛?#8216;+’錛?#8216;-’閫掑綊錛堝叾瀹炰篃灝辨槸綆鍗曠殑DFS錛夈傛妸瀛楃涓茶漿鎴愭暟瀛楄繍綆楋紝鑻ョ粨鏋滀負0鍒欒緭鍑恒?/span>
Money Systems
闂鎻忚堪錛?/span>
緇欏嚭涓濂楅挶甯佺殑闈㈠鹼紝姹傜粍鎴愭煇鏁?/span>N鏈夊灝戠鏂規銆?/span>
鍒嗘瀽錛?/span>
榪欐槸涓畝鍗曠殑鍔ㄨ錛岀敤dp[ i ] [ j ]琛ㄧず浠呯敤鍓?/span>i縐嶉挶甯佹嫾鎴?/span>j鐨勬柟妗堟暟錛岄偅涔堜粎鐢ㄥ墠i-1縐嶉挶甯佹嫾鎴?/span>j鐨勬柟妗?/span>dp[i-1][j]涔熸弧瓚籌紝濡傛灉鐢ㄤ簡涓鏋氶潰鍊間負i鐨勯挶甯侊紝鍒?/span>dp[i][j]+=dp[i-1][j-v[i]]鍏朵腑v[i]涓?/span>i鐨勯潰鍊鹼紝鍚岀悊錛岀敤浜嗕袱鏋?/span>dp[i][j]+=dp[i-1][j-2*v[i]]錛屼竴鐩村埌j-k*v[i]<=0涓烘銆?/span>
娉ㄦ剰錛屽綋j鍙互琚?/span>v[i]鏁撮櫎鏃訛紝dp[i][j]++;鍒濆鍖?/span>dp[1][k*v[1]]=1,(k*v[i]<=N)
鐘舵佽漿縐繪柟紼嬩負錛?/span>
dp[i][j] =鈭?/span>dp[i-1][j-k*v[i]];錛?/span>k=1..j/v[i]錛?/span>
Controlling Companies
闂鎻忚堪錛?/span>
鏈変簺鍏徃鏄叾浠栧叕鍙哥殑閮ㄥ垎鎷ユ湁鑰咃紝鍥犱負浠栦滑鑾峰緱浜嗗叾浠栧叕鍙稿彂琛岀殑鑲$エ鐨勪竴閮ㄥ垎銆傚鏋滆嚦灝戞弧瓚充簡浠ヤ笅涓変釜鏉′歡涔嬩竴錛屽叕鍙?/span>A灝卞彲浠ユ帶鍒跺叕鍙?/span>B浜嗭細
1.鍏徃A = 鍏徃B銆?/span>
2.鍏徃A鎷ユ湁澶т簬50%鐨勫叕鍙?/span>B鐨勮偂紲ㄣ?/span>
3.鍏徃A鎺у埗K(K >= 1)涓叕鍙革紝璁頒負C1, ..., CK錛屾瘡涓叕鍙?/span>Ci鎷ユ湁xi%鐨勫叕鍙?/span>B鐨勮偂紲紝騫朵笖x1+ .... + xK > 50%銆?/span>
緇欎綘涓涓〃錛屾瘡琛屽寘鎷笁涓暟(i,j,p)錛涜〃鏄庡叕鍙?/span>i浜湁鍏徃j鐨?/span>p%鐨勮偂紲ㄣ傝綆楁墍鏈夌殑鏁板(h,s)錛岃〃鏄庡叕鍙?/span>h鎺у埗鍏徃s銆傝嚦澶氭湁100涓叕鍙搞?/span>
鍐欎竴涓▼搴忚鍏ヤ笁瀵規暟(i,j,p)錛?/span>i,j鍜?/span>p鏄兘鍦ㄨ寖鍥?/span>(1..100)鐨勬鏁存暟錛屽茍涓旀壘鍑烘墍鏈夌殑鏁板(h,s)錛屼嬌寰楀叕鍙?/span>h鎺у埗鍏徃s銆?/span>
鍒嗘瀽錛?/span>
榪欓浼間箮寰堥夯鐑︼紝褰撲綘鎺у埗浜嗕竴瀹舵柊鍏徃鍚庯紝鏂板叕鍙稿張鏈夊彲鑳芥帶鍒剁潃鍙︿竴瀹跺叕鍙革紝鏋勬垚涓灞傛帴涓灞傜殑榪唬鍏崇郴銆傘傘傚垰寮濮嬬敤DFS鐨勬椂鍊欐濊礬灝辨瘮杈冩販涔憋紝緇撴灉鍙氳繃浜嗗墠鍏釜嫻嬭瘯錛岃屼笖鏁堢巼寰堜綆錛屽悗鏉ョ粏緇嗗垎鏋愪簡涓涓嬶紝鍏跺疄榪欐湁鐐圭被浼煎浘鐨勭粨鏋勶紝棰樼洰緇欏嚭鐨勮〃鍙互鐪嬪仛閭繪帴鐭╅樀銆傞棶棰樺氨杞寲涓猴紝浠ユ煇鐐逛綔涓哄師鐐瑰嚭鍙戯紝濡傛灉鍘熺偣鍒版煇鐐?/span>s鐨勮窛紱昏秴榪?/span>50錛岄偅涔堟妸s綰沖叆鍘熺偣鎵鍦ㄩ泦鍚?/span>P錛屾壘涓?/span>s璺濈瓚呰繃50鐨勭偣錛屽啀嬈$撼鍏?/span>P錛屼笉鏂洿鏂板師鐐瑰埌榪欎簺鐐圭殑璺濈銆傛渶鍚庡垪鍑烘墍鏈夊埌鍘熺偣璺濈瓚呰繃50鐨勭偣銆?/span>
Preface Numbering
闂鎻忚堪錛?/span>
鍏堟槸浠嬬粛緗楅┈鏁板瓧涔﹀啓錛堢暐錛夛紝緇欏嚭涓涓暟瀛楋紝姹?/span>1鍒拌繖涓暟瀛椾箣闂存墍鏈夋暟瀛楃殑緗楅┈琛ㄧず涓叡鍑虹幇鍑犱釜I錛?/span>V錛?/span>X錛?/span>L錛?/span>C錛?/span>D錛?/span>M銆?/span>
鍒嗘瀽錛?/span>
鏈鍒濈殑鎬濊礬鏄竴涓釜鍦版ā鎷燂細瑙傚療鍚庡彲浠ュ彂鐜幫紝46鍙互琛ㄧず涓?/span>XLVI錛屼互鏁扮粍s[1…7]琛ㄧずI…M錛屽垯47涓?/span>2111000錛岃?/span>4涓?/span>1100000錛?/span>7涓?/span>21000000錛屾葷粨鍙煡s[n][1]=s[n%10][1];s[n][2]=s[n%10][2];錛堟敞鎰?/span>n%10==9鐨勮瘽錛?/span>s[n][3]+=s[9][3]錛夈?/span>2<=i<=7鏃訛紝 s[n][i]=s[n/10][i-2]銆?/span>
鍏跺疄瀹屽叏鍙互鍒嗘緇熻錛屾瘮濡?/span>234錛屼釜浣嶅嚭鐜頒簡23涓?/span>0~9錛?/span>1涓?/span>0~4錛屽崄浣嶅嚭鐜頒簡20涓?/span>0~9錛?/span>1涓?/span>0~3錛岀櫨浣嶅嚭鐜頒簡1銆?/span>2錛?/span>
Subset Sums
闂鎻忚堪錛?/span>
瀵逛簬浠?/span>1鍒?/span>N (1 <= N <= 39) 鐨勮繛緇暣鏁伴泦鍚堬紝鑳藉垝鍒嗘垚涓や釜瀛愰泦鍚堬紝涓斾繚璇佹瘡涓泦鍚堢殑鏁板瓧鍜屾槸鐩哥瓑鐨勩傜粰鍑?/span>N錛屼綘鐨勭▼搴忓簲璇ヨ緭鍑哄垝鍒嗘柟妗堟繪暟錛屽鏋滀笉瀛樺湪榪欐牱鐨勫垝鍒嗘柟妗堬紝鍒欒緭鍑?/span>0銆?/span>
鍒嗘瀽錛?/span>
鐪嬪畬棰樼洰鏈鍏堟兂鍒扮殑鏄繁鎼滐紝鏋氫婦鎵鏈夊彲鑳斤紝褰撳叾鍜岀瓑浜庢誨拰涓鍗婄殑鏃跺欏垯璁板綍銆備絾鎻愪氦鍚庡彂鐜幫紝褰?/span>N涓?/span>31錛岀▼搴忕畻浜?/span>7銆?/span>8縐掓墠鍑虹瓟妗堛傜湅鏉ユ繁鎼滄槸涓嶈浜嗭紝鍦ㄧ綉涓婄湅浜嗗埆浜虹殑瑙f硶鎵嶇煡閬撹鍔ㄦ佽鍒掋傚叾瀹炲簲璇ョ畻閫掓帹錛屼護ans[i][j]琛ㄧず鍓?/span>i涓暟閲岄潰鍜屼負j鐨勬柟妗堟暟錛屽垯ans[i][j]鍙互絳変簬鍓?/span>i-1涓暟瀛楅噷闈㈠拰涓?/span>j鐨勬柟妗堟暟錛堝嵆涓嶅惈鏁板瓧j鐨勬柟妗堬級錛屽姞涓婂墠i-1涓暟瀛楅噷鍜屼負j-i鐨勬柟妗堟暟錛堝嵆鏈緇堝惈鏈夋暟瀛?/span>j錛?/span>,ans[N][N*(N+1)/4]鍗充負鏈緇堣В銆傜姸鎬佽漿縐繪柟紼嬩負錛?/span>
ans[i][j]=ans[i-1][j]+ans[i-1][j-i];
Runaround Numbers
闂鎻忚堪錛?/span>
瀵繪壘寰幆鏁?/span>----浠庢渶鍙崇殑鏁板瓧鍑哄彂錛岃蛋鏁板瓧瀵瑰簲鐨勬鏁幫紝鐒跺悗浠庢墍鍋滅殑鏁板瓧緇х畫鍑哄彂錛屽啀璧板垰鎵嶆墍鍋滄暟瀛楀搴旀鏁幫紝鐩村埌鍥炲埌鍑哄彂鐐廣?/span>
鍒嗘瀽錛?/span>
寰幆鏁版湁鐐圭被浼肩害鐟熷か鐜紝鐩存帴妯℃嫙鍗沖彲錛屼粠棰樼洰鎵緇欐暟瀛楀紑濮嬩竴涓釜鏋氫婦銆傛敞鎰忥細鏁板瓧涓嶅惈0錛涘洖鍒拌搗濮嬬偣鍓嶏紝姣忎竴浣嶉兘蹇呴』鍋滅暀榪囦竴嬈′笖蹇呴』鍙仠涓嬈°?/span>
Party Lamps
闂鎻忚堪錛?/span>
鏈夊洓涓寜閽帶鍒?/span>N鐩忕伅錛?/span>10<=N<=100
鎸夐挳1錛氬綋鎸変笅姝ゆ寜閽紝灝嗘敼鍙樻墍鏈夌殑鐏細鏈潵浜潃鐨勭伅灝辯唲鐏紝鏈潵鏄叧鐫鐨勭伅琚偣浜?/span>
鎸夐挳2錛氬綋鎸変笅姝ゆ寜閽紝灝嗘敼鍙樻墍鏈夊鏁板彿鐨勭伅銆?/span>
鎸夐挳3錛氬綋鎸変笅姝ゆ寜閽紝灝嗘敼鍙樻墍鏈夊伓鏁板彿鐨勭伅銆?/span>
鎸夐挳4錛氬綋鎸変笅姝ゆ寜閽紝灝嗘敼鍙樻墍鏈夊簭鍙鋒槸3*K+1(K>=0)鐨勭伅銆備緥濡傦細1,4,7...
涓涓鏃跺櫒璁板綍鎸変笅鎸夐挳鐨勬鏁?/span>C錛岀幇緇欏嚭C錛屽拰鏌愪簺鐏殑鏈緇堝紑鍏崇姸鎬侊紝姹傛墍鏈夌殑鐏渶緇堝彲鑳界殑鎵鏈夌姸鎬併?/span>
鍒嗘瀽錛?/span>
榪欓寰堜箙浠ュ墠灝辮榪囦簡錛岃寰楁瘮杈冮夯鐑︼紝灝變竴鐩存病鍔紝鐜板湪涓嶅姩涓嶈浜嗐傚湪綰鎬笂鍒嗘瀽鍚庝細鍙戠幇錛岀伅鐨勭姸鎬佹槸鍏釜涓緇勫驚鐜嚭鐜扮殑錛屾晠鍙渶寰楀嚭鍓嶅叚涓伅鐨勭姸鎬侊紝鍚庨潰鐨勭伅鐨勭姸鎬佸氨鍙煡浜嗐傛瘡鐩忕伅鏈夊紑鍏充袱縐嶇姸鎬侊紝鍥涗釜寰幆鏋氫婦鍗沖彲銆傚湪緗戜笂鐪嬩簡涓涓嬪埆浜虹殑瑙f硶錛岀敤浜岃繘鍒惰〃紺虹姸鎬佹槸姣旇緝鏂逛究鐨勶紝浜庢槸鎴戝喅瀹氱涓嬈″皾璇曚綅榪愮畻瑙i銆?/span>
鐢變簬寮傛垨榪愮畻絎︾殑鐗圭偣錛?/span>0鍜?/span>1寮傛垨1浠ュ悗鍙栧弽錛屽紓鎴?/span>0涓嶅彉銆傜涓縐嶆搷浣滃彲浠ョ敤n^(111111)2瀹炵幇錛岀浜岀鎿嶄綔鐢?/span>n^(101010)2瀹炵幇錛岀涓夌鐢?/span>n^(10101)2瀹炵幇錛岀鍥涚鐢?/span>n^(100100)2瀹炵幇銆?/span>
瀵逛簬鐘舵佺殑璇誨彇錛屾垜鎯充笉鍑轟粈涔堝ソ鍔炴硶銆傚彧濂借繖鏍蜂簡錛?/span>
渚嬪錛屾祴璇曟暟鎹粰鍑?/span>2鍙風伅浜紝鍒欐渶緇堢姸鎬侀噷2浣嶄笂鐨勫繀涓?/span>1錛岃〃紺轟負錛?/span>010000 銆傝鍏ヤ笉浜殑鐏殑鍑芥暟鍋氱浉搴斾慨鏀瑰嵆鍙?/span>
鍒ゆ柇褰撳墠鏋氫婦寰楀埌鐨勭姸鎬佹槸鍚︽弧瓚寵姹傚彲鐢ㄤ互涓嬫柟娉曪細
絎簲琛屽鏋?/span>state鏄?/span>0鍗抽兘涓嶄寒錛岃?/span>On涔熶負0錛屾湰鏉ュ簲璇ユ槸絎﹀悎鐨勶紝浣嗙敱浜?/span>0&0=1錛?/span>=0.鎵浠ュ湪鍚庨潰琛ヤ笂銆?/span>