锘??xml version="1.0" encoding="utf-8" standalone="yes"?>色婷婷狠狠久久综合五月,亚洲国产欧美国产综合久久,日韩欧美亚洲综合久久http://www.shnenglu.com/hello-world/zh-cnWed, 07 May 2025 00:51:28 GMTWed, 07 May 2025 00:51:28 GMT60Waterloo local 2002.09.21http://www.shnenglu.com/hello-world/archive/2009/03/03/75466.htmlhello_worldhello_worldTue, 03 Mar 2009 15:22:00 GMThttp://www.shnenglu.com/hello-world/archive/2009/03/03/75466.htmlhttp://www.shnenglu.com/hello-world/comments/75466.htmlhttp://www.shnenglu.com/hello-world/archive/2009/03/03/75466.html#Feedback0http://www.shnenglu.com/hello-world/comments/commentRss/75466.htmlhttp://www.shnenglu.com/hello-world/services/trackbacks/75466.htmlWaterloo local 2002.09.21


Trains

DP錛屽浘璁?/td>
   
 Square  鎼滅儲
Blocks  鏆村姏
Faucet Flow


Trains錛?==)

Square錛?br>榪欓亾鎼滅儲棰樹笌pku1011鏈夌浉浼肩殑瑙f硶錛屽壀鏋濋兘涓鏍風殑錛屽叧浜?011宸茬粡寰堢粡鍏鎬簡http://www.acrush.cn/?cat=9榪欓噷鏈夊緢璇︾粏鐨勫壀鏋濓紒鍩烘湰涓婃敼鏀瑰氨鑳借繃浜唦錛?br>
blocks錛氭毚鍔涘姞涓晫鑳借窇0ms
榪欓亾棰樼被浼?a >Grocery store




Faucet Flow
榪欐槸涓閬撳緢浼樼編鐨勯錛屾帹鑽?br>棣栧厛鎴戜滑鏉ュ垽鏂竴涓嬫按鍒板簳浼氫粠宸﹁竟婕忚繕鏄粠鍙寵竟婕忥紝鍋囪宸﹁竟鏈楂樼殑楂樺害鏄痯錛?鍙寵竟鏈楂樼殑楂樺害鏄痲
鑻 > q 嫻佸線鍙寵竟
鑻 < q 嫻佸線宸﹁竟
鑻==q 閭e氨瑕佺湅閭h竟鑳借涓嬫洿澶氱殑姘?br>鍓嶄袱縐嶉偅鍧楁渶楂樼殑鎸℃澘涓嶅彲閫捐秺錛屾兂鎯沖氨浼氭槑鐧斤紝鍚庝竴縐嶆按嫻佷細鍒嗘垚涓よ偂錛屽乏鍙崇瓑閲忥紝閭e氨瑕佺湅閭h竟鍧氭寔鐨勪箙浜?br>澶ф鎰忔濆氨鏄繖鏍鳳紝鑰冪偣灝辨槸鍙兘浼氭湁鐩哥瓑楂樺害鐨勬尅鏉匡紝榪欐棤鐤戝姞澶ч毦搴︼紝姝ら鐨勫叿浣撳疄鐜頒篃闇瑕佽垂浜涘姛澶?br>鍐嶆帹鑽愪竴閬撶被浼肩殑棰橈紝璇寸被浼煎彧鏄儗鏅被浼鹼紝瑙f硶鍚勫紓錛屽悗涓縐嶇殑浠g爜瀹炵幇鏂規硶涔熸槸寰堜笉閿欑殑             Artificial Lake




]]>
Waterloo local contest 1998http://www.shnenglu.com/hello-world/archive/2009/03/01/75268.htmlhello_worldhello_worldSun, 01 Mar 2009 15:17:00 GMThttp://www.shnenglu.com/hello-world/archive/2009/03/01/75268.htmlhttp://www.shnenglu.com/hello-world/comments/75268.htmlhttp://www.shnenglu.com/hello-world/archive/2009/03/01/75268.html#Feedback0http://www.shnenglu.com/hello-world/comments/commentRss/75268.htmlhttp://www.shnenglu.com/hello-world/services/trackbacks/75268.htmlWaterloo local 1998.10.17
Prime Distance
綆鍗曞埛琛?br>
 Yahtzee  DP
 Request for Proposal  綆鍗曢
 Australian Voting  妯℃嫙
Chocolate Chip Cookies geometry


 Prime Distance

 棰樼洰澶ф剰灝辨槸緇欎綘涓涓尯闂碵l錛宺]錛屾壘鍑鴻繖閲岀浉閭葷礌鏁扮殑鏈澶ц窛紱誨拰鏈灝忚窛紱?
 鍒瘋〃鏄粡鍏歌屽疄鐢ㄧ殑鏂規硶


Yahtzee
緇欏崄涓夌5涓瀛愮殑鐘舵侊紝鍗佷笁縐嶈鍒欙紝姣忕瑙勫垯涓嬫瘡涓姸鎬佹湁涓涓緱鍒嗭紝闂庢牱鍒嗛厤瑙勫垯涓庣姸鎬佷箣闂寸殑瀵瑰簲鍏崇郴錛岃寰楀垎鏈澶э紝鍚屾椂瑕佹敞鎰忕殑鏄鏋滃墠鍏瑙勫垯涓嬬殑寰楀垎濡傛灉>=63錛岄偅涔堟誨緱鍒嗚鍔犱笂35錛?br>棣栧厛棰勫鐞嗗嚭姣忕瑙勫垯涓嬫瘡涓姸鎬佺殑寰楀垎鎯呭喌錛?br>濡傛灉娌℃湁鏈鍚庝竴涓檺鍒訛紝閭d箞鎴戜滑鍙互鏈変袱縐嶅仛娉曪細1錛屼簩鍒嗗浘鐨勬渶澶ф潈鍖歸厤錛?錛孌P錛佷絾鏄湁浜嗘渶鍚庝竴涓檺鍒訛紝鐢ㄥ尮閰嶇殑璇濅笉鐭ユ庝箞涓嬫墜錛屾垜鍙兘鎯沖埌dp錛乨p[i][j][k]琛ㄧず鍓峣縐嶉瀛愮姸鎬佸凡緇忓垎閰嶅ソ錛屽垎閰嶇殑鎯呭喌鍘嬬緝鎴愪竴涓暣鏁癹錛屽茍涓斿墠鍏瑙勫垯鐨勫緱鍒嗘槸k鐨勭姸鎬侊紝閭d箞鐘舵佽漿縐誨氨鏄?dp[i][j][k] = {max(dp[ i - 1 ][ j - (1<<h) ][ k - score[h][i] ] ) (0<=h<=6)錛宮ax(max(dp[ i - 1 ][ j - (1<<h) ][ k ])( 7<=h<13) } (j鐨勭h浣嶄負1) ! 澶嶆潅搴﹀ぇ姒傛槸13*2^13*64 ; 涓棿璁板綍鍓嶄竴涓姸鎬侊紝 鏈鍚庨掑綊杈撳嚭灝卞ソ浜唦
 
Request for Proposal錛?br>
Australian Voting錛?br>鎸夌収棰樻剰妯℃嫙灝卞ソ浜唦

 Chocolate Chip Cookies

 棰樼洰澶ф剰灝辨槸鏈変竴浜涚偣錛?00涓級錛?鐢ㄤ竴涓粰瀹氬崐寰勶紙r==5cm錛夌殑鍦嗭紝鏈澶氳兘緗╀綇澶氬皯涓偣
 200涓偣鐨勮瘽 o ( n^3 )鑳借繃錛岃繖鏍鋒垜浠湁浜嗙畻娉曪紝瑕佺僵浣忔渶澶氱殑鐐癸紝閭d釜鍦嗗繀欏昏嚦灝戣鍗?/span>浣忎袱涓偣
 鏋氫婦姣忎袱涓偣紜畾鍦嗗績錛屽湪媯鏌ユ墍鏈夌殑鐐規槸鍚﹀湪鍦嗗唴銆傛兂娉曞緢鑷劧
 緇嗚妭闂涓婂氨鏄浣曟壘鍒板渾蹇冿紙紜畾鍗婂緞鍜屼袱涓渾涓婄殑鐐癸級榪欐槸鍩烘湰鍔?/span>
 
 濡傛灉璇寸洿鎺ヨВ鏂圭▼鏈変簺綣佺悙榪欓噷鏈夊ソ鏂規硶錛?br>
 
 榪欐牱鍙瑙d簩鍏冧竴嬈℃柟紼嬶紝鍙弬鑰冧互涓嬩唬鐮侊細
 1 struct point {double x, y;};
 2 
 3 bool centre(point p, point q, double r,point &o1, point &o2)
 4 //涓ょ偣涓鍗婂緞浼氱‘瀹氫袱涓渾蹇?nbsp;o1 o2
 5 {
 6    double rise,run,theta;
 7    double chordlen, perplen;
 8    double tantheta,tantheta1;
 9  
10    chordlen = sqrt( (p.x-q.x)*(p.x-q.x) + (p.y-q.y)*(p.y-q.y) );
11    if (chordlen > 2*r) { return false; }
12    tantheta = sqrt(r*r*4 - chordlen*chordlen)/(chordlen);
13    //鍦嗗績瑙?lt;poq鐨勫崐瑙掔殑姝e垏鍊?nbsp;
14 
15    run = (p.x-q.x)/2;
16    rise = (p.y-q.y)/2;
17    o1.x= (p.x+q.x)/2 + rise * tantheta;
18    o1.y= (p.y+q.y)/2 + -run * tantheta;
19    o2.x= (p.x+q.x)/2 + -rise * tantheta;
20    o2.y = (p.y+q.y)/2 + run * tantheta;
21   //緇撳悎鐐圭Н灝辮兘寰楀嚭涓婂紡
22    return true;
23 }
24 



]]>
Waterloo Local 2001.09.29 && 2002.01.26 && 2002.07.01http://www.shnenglu.com/hello-world/archive/2009/02/13/73738.htmlhello_worldhello_worldFri, 13 Feb 2009 11:36:00 GMThttp://www.shnenglu.com/hello-world/archive/2009/02/13/73738.htmlhttp://www.shnenglu.com/hello-world/comments/73738.htmlhttp://www.shnenglu.com/hello-world/archive/2009/02/13/73738.html#Feedback0http://www.shnenglu.com/hello-world/comments/commentRss/73738.htmlhttp://www.shnenglu.com/hello-world/services/trackbacks/73738.htmlWaterloo local 2001.09.29
  棰樼洰鍒嗙被
 Adventures in Moving - Part IV DP
 Pairsumonious Numbers  鎼滅儲
 Snow Clearing  綆鍗曢
Stack 'em Up 妯℃嫙

Adventures in Moving - Part IV錛?br>榪欓DP鐨勯樁孌靛拰鍐崇瓥閮介潪甯告槑鏄俱俫[i][j]=min( g[i-1][j+dis[i]-dis[i-1]-buy]+buy*pirce[i] )
g[i][j]琛ㄧず灝嗚紱誨紑絎琲涓姞娌圭珯鏃訛紝鏈塲鍗囨苯娌癸紝鎵瑕佽姳璐圭殑鏈灝戠殑閽便?br>
Pairsumonious Numbers 錛?br>棣栧厛 n==3 鏃跺緢瀹規槗姹傚嚭絳旀錛宎1+a2, a1+a3, a2+a3,涓や袱鐩稿姞鍐嶅噺鍘誨彟涓涓?br>鐒跺悗 n > 3 鏃墮鍏堟垜浠帓搴忥紝鏈夐『搴忓氨鏄垚鍔熺殑涓鍗婏紝
濡傛灉閭?n 涓暟鐨勫ぇ灝忔槸 a1 < a2 < a3 < ... < an
閭d箞鏈灝忕殑鏄?nbsp; a1+a2, 嬈″皬鐨勬槸 a1+a3錛屽鏋滄垜浠煡閬?a2+a3 鍦ㄥ摢 閭h澶氬ソ鍟?br>騫歌繍鐨勬槸 a2+a3鍙彲鑳藉嚭鐜板湪絎?3 浣嶅埌絎?n 浣嶄箣闂達紝n鍙堟槸灝忎簬10鐨勬暟錛岄偅鎴戜滑鍙鏋氫婦
姣忕鎯呭喌灝卞彲浠ヤ簡
榪欐牱鎴戜滑灝辮兘姹傚嚭a1 , a2, a3 閭e瑙i鏈変粈涔堢敤鍛紵
榪欐椂鎴戜滑鎶?a1+a2, a1+a3, a2+a3 鍒犳帀錛屽墿涓嬬殑鏈灝忕殑鏄笉鏄偗瀹氬彧鏈?a1+a4,閭f槸涓嶆槸
a4涔熸眰鍑烘潵浜?br>鎺ョ潃鎴戜滑鎶?a1+a4, a2+a4, a3+a4閮藉垹鎺夛紝鍓╀笅鏈灝忕殑涓嶅氨鏄?a1+a5浜嗗悧
涓嶆柇榪涜涓婅堪榪囩▼灝辮兘姹傚嚭絳旀
鑷充簬鏈夌浉鍚屽厓绱犵殑鏃跺欙紝寰堝鏄撳氨鐭ラ亾涔熺鍚堜笂榪板仛娉曪紝姝e洜涓烘湁鐩稿悓鍏冪礌錛屼腑闂村彲鐢╩ultiset
瀹炵幇涓婅堪鍔熻兘

Snow Clearing錛?br>鍙渶瑕佹妸姣忔潯琛楀姞璧鋒潵鍐嶄箻浠?灝辨槸鎬葷殑璺濈錛岄櫎浠ラ熷害鐒跺悗鍖栨垚鏃墮棿鍗沖彲錛?br>
Stack 'em Up錛?br>榪欓鍙鎶婇鎰忕湅鎳備箣鍚庯紝灝辨病闂浜嗐傞鍏堢粰浣爊縐嶆礂鐗岀瓥鐣ワ紝鐒跺悗鍐嶇粰浣犺嫢騫蹭釜k錛屽湪鍓嶄竴嬈℃礂濂界殑鐗岀殑鍩虹涓婏紝鎸夌収絎琸縐嶆礂鐗岀瓥鐣ユ礂銆傛瘡媧椾竴嬈★紝杈撳嚭鐩墠鐨勭墝鐨勯『搴忋?br>
Waterloo Local 2002.01.26
棰樼洰鍒嗙被 
   
Discrete Logging    姹傜鏁e鏁?/td>
Hardwood Species  綆鍗曢
Forests
姘撮錛坰tl榪愮敤錛?br>
A Star not a Tree? 鐗涢】榪唬娉?br>


Discrete Logging 錛?br>姹備互b涓哄熀妯′簬n鐨勭鏁e鏁版垜浠湁O(n^0.5*logn)鐨勭畻娉?br>鏈夊叴瓚h呭彲鏌ョ湅Shank's Baby-Step-Gaint-Step Algorithm



A Star not a Tree? 錛?br>緇欎綘騫抽潰涓?n ( n < 100)涓偣錛?瑕佹眰涓涓偣p錛屼嬌寰?p 鍒板悇涓偣鐨勮窛紱諱箣鍜屾渶灝?br>鐢ㄧ墰欏胯凱浠o紝鑳借瘉鏄巟,y鍋忓涓?鏃訛紝鏈夋渶灝忓鹼紝浣嗘垜涓嶄細璇?img src="http://www.shnenglu.com/CuteSoft_Client/CuteEditor/images/emembarrassed.gif" align="absmiddle" border="0">錛?span style="color: red;">鍥炲幓瀛﹂珮鏁?/span>錛?br>鏃㈢劧鐭ラ亾鏂圭▼x錛寉鍋忓涓?鏃舵湁鏈灝忓鹼紝閭e氨濂藉姙浜嗭紝鍙栧鉤鍧囧間負鍒濆鹼紝鐒跺悗涓嶆柇榪唬錛?br>浣嗘垜綺懼害璋冨埌 1e-4 鎵嶈兘榪囷紝榪欐牱鎴戠殑榪唬璺戜簡300ms錛屽埆浜洪兘璺?ms錛屾繪劅瑙夋湁闂
璐村嚭榪唬浠g爜錛屽笇鏈涘ぇ瀹剁粰鎴戞寚姝?br>
 while!( zero(x1 - x0) && zero(y1 - y0) ) )
         { 
             x0
=x1, y0=y1;
             
for( fx=0, i=0; i < n; i++)
                 fx
+= (x0 - p[i][0])/ sqrt( (x0 - p[i][0])*(x0 - p[i][0]) + (y0 - p[i][1])*(y0 - p[i][1]) );
             
for(fxx=0, i =0; i < n; i++)
                 fxx
+=2*(x0 - p[i][0])*(x0 - p[i][0]) + (y0 - p[i][1])*(y0 - p[i][1]) ) / ( (x0 - p[i][0])*(x0 - p[i][0]) + (y0 - p[i][1])*(y0 - p[i][1]) );
             x1 
= x0 - fx/fxx;
             
for(fy=0, i=0; i < n; i++)
                 fy
+=(y0 - p[i][1])/ sqrt( (x0 - p[i][0])*(x0 - p[i][0]) + (y0 - p[i][1])*(y0 - p[i][1]) );
             
for(fyy=0, i=0; i < n; i++)
                 fyy
+=( (x0 - p[i][0])*(x0 - p[i][0]) + 2*(y0 - p[i][1])*(y0 - p[i][1]) ) / ( (x0 - p[i][0])*(x0 - p[i][0]) + (y0 - p[i][1])*(y0 - p[i][1]) );
             y1
=y0 - fy/fyy;
         }





Waterloo local 2002.07.01


棰樼洰鍒嗙被
 Hay Points  綆鍗曢
 Jogging Trails  鍥捐錛屼腑鍥介偖璺棶棰?/td>
 Beavergnaw  綆鍗曢
 Power Strings  姘撮
Relatives
嬈ф媺鍑芥暟
Jogging Trails錛?br>棰樼洰鎰忔濇槸緇欏畾涓浜涚偣錛岀劧鍚庝竴浜涜竟錛屽茍涓斾袱涓偣涔嬮棿鍙兘鏈夊鏉¤竟錛岄棶浠庝竴涓偣鍑哄彂錛岄亶鍘嗗畬鎵鏈夌殑杈硅嚦灝戜竴嬈′笖鏈鍚庡湪鍥炲埌鍑哄彂鐐歸渶瑕佽蛋鐨勬渶灝戣窛紱伙紒
濡傛灉榪欎釜鍥炬槸嬈ф媺鍥撅紝閭d箞璺濈灝辨槸杈逛箣鍜岋紝涓涓浘瀛樺湪嬈ф媺鍥劇殑鍏呰鏉′歡鏄瘡涓畾鐐圭殑搴︿負鍋舵暟錛?br>浣嗘槸濡傛灉涓嶆槸嬈ф媺鍥撅紝閭d箞鎴戜滑灝辮鎶婅繖涓浘鍙樻垚嬈ф媺鍥撅紝鍙渶瑕佹坊鍔犱竴浜涜竟錛岄《鐐圭殑搴﹀叏閮ㄤ負鍋舵暟灝卞ソ浜嗭紝鍥犱負涓涓浘涓鏁板害欏剁偣涓瀹氭湁鍋舵暟涓紒鎵浠ュ彧瑕佹灇涓捐繖鏍風殑濂囨暟搴﹂《鐐癸紝娣誨姞杈逛嬌鍏跺害涓哄伓鏁幫紝寰堟槑鏄炬坊鍔犵殑杈逛笉浼氬獎鍝嶅叾浠栧伓鏁板害欏剁偣鐨勫鍋舵э紒騫朵笖鐢變簬瑕佽窛紱繪渶灝忥紝鎵浠ユ坊鍔犵殑杈逛竴瀹氭槸榪欎袱涓《鐐圭殑鏈鐭窛紱伙紒榪欎竴姝ュ彲浠ョ敤璁板繂鍖栨悳绱㈠疄鐜幫紒


嬈ф媺鍑芥暟鐨勪竴浜涢鐩紙
杞?span style="font-size: 10pt;">http://hi.baidu.com/wuxyy/blog/item/33957f1ee03a1cf51bd5761d.html
錛?br>

嬈ф媺鍑芥暟鍏ラ棬棰樼洰錛?/font>poj3090 Visible Lattice Points  poj2407 Relatives
poj2478 Farey Sequence
嬈ф媺鍑芥暟楂樼駭搴旂敤錛?font color="#000000">poj2480 Longge's problem  poj1091 璺寵殼

璺寵殼棰樼洰寰堟湁鎰忔濓紝鎺ㄨ崘




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Waterloo local 2001.09.22http://www.shnenglu.com/hello-world/archive/2009/02/12/73668.htmlhello_worldhello_worldThu, 12 Feb 2009 15:08:00 GMThttp://www.shnenglu.com/hello-world/archive/2009/02/12/73668.htmlhttp://www.shnenglu.com/hello-world/comments/73668.htmlhttp://www.shnenglu.com/hello-world/archive/2009/02/12/73668.html#Feedback0http://www.shnenglu.com/hello-world/comments/commentRss/73668.htmlhttp://www.shnenglu.com/hello-world/services/trackbacks/73668.htmlWaterloo local 2001.09.22
  棰樼洰鍒嗙被
 Average Speed  綆鍗曢
 Subway  鍥捐錛屾渶鐭礬
Babelfish  Map
Bounding box  鍑犱綍
A multiplication game
鍗氬紙錛屽眬闈?br>

Subway錛?br>鎶妌涓湴閾佺珯鎶借薄涓虹偣錛岃搗鐐逛負瀹訛紝緇堢偣涓哄鏍★紒涓鍏眓+2涓偣錛屼粎褰撲袱涓湴閾佺珯鍦ㄤ竴鏉$嚎璺笂涓旂浉閭諱粬浠殑璺濈鎵嶆槸瀹為檯璺濈鐨?/4, 鍚勪釜鐐逛箣闂寸殑璺濈灝變負瀹為檯璺濈錛岀劧鍚庢眰璧風偣鍒扮粓鐐圭殑鏈鐭窛紱誨嵆鍙紝鐒跺悗鎹㈢畻鎴愭椂闂達紝娉ㄦ剰鐨勬槸铏界劧棰樼洰娌℃湁璇翠絾鏄瘡鏉$嚎璺笂鐨勭珯鐐規槸鍚勪笉鐩稿悓鐨勶紒涓嶇敤鑰冭檻寰楀お楹葷儲錛?br>
Babelfish錛?br>姝ら鍋鋒噿鍋氬彲浠ョ敤C++涓殑map錛屼笉榪囨晥鐜囦笉鏄緢楂樸傚鏋滄兂鍔犲揩鏁堢巼錛屽彲浠ョ敤Trie鏍戞潵鍋氥?br>
bounding box錛?br>姹傚嚭鍦嗗績鐒跺悗涓嶆柇鏃嬭漿

a multiplication game錛?br>鎵懼繀鑳滃眬涓庡繀璐熷眬錛岄掕姹傝В

鐤插姵ing~~







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Waterloo local 2001.06.02http://www.shnenglu.com/hello-world/archive/2009/02/12/73667.htmlhello_worldhello_worldThu, 12 Feb 2009 14:34:00 GMThttp://www.shnenglu.com/hello-world/archive/2009/02/12/73667.htmlhttp://www.shnenglu.com/hello-world/comments/73667.htmlhttp://www.shnenglu.com/hello-world/archive/2009/02/12/73667.html#Feedback0http://www.shnenglu.com/hello-world/comments/commentRss/73667.htmlhttp://www.shnenglu.com/hello-world/services/trackbacks/73667.htmlWaterloo local 2001.06.02
  棰樼洰鍒嗙被
 No Tipping  浜岃繘鍒惰〃紺虹姸鎬侊紝DFS
Sumsets  鏌ユ壘錛屾悳绱?/td>
Zipf's Law 瀛楃涓插鐞?br>
Ones 綆鍗曢
No Tipping:
棰樼洰瑕佹眰鎶婁竴涓湁涓や釜鏀偣鐨勬潬鏉嗕笂鐨勯噸鐗╂嬁鎺夛紝浣垮緱鏉犳潌濮嬬粓淇濇寔騫寵 錛岀劧鍚庤緭鍑烘煇涓彲琛岀殑欏哄簭銆傛樉鐒訛紝鐘舵佺殑琛ㄧず鍜岀墿浣撴嬁璧扮殑欏哄簭鏈夊叧錛屾棰樹粠姝i潰鍏ユ墜錛岀姸鎬佽〃紺烘瘮杈冨洶闅俱傚叾瀹炲彲浠ユ崲涓搴︾湅錛屽氨鏄湪涓鍧楃┖鐨勬潬鏉嗕笂錛屼緷嬈℃斁涓婇噸鐗╋紝鏉犳潌瑕佸緇堜繚鎸佸鉤琛★紝榪欎釜欏哄簭灝辨槸鎷胯蛋鐨勯『搴忋傜敤浜岃繘鍒跺彲浠ユ柟渚跨殑琛ㄧず鐘舵侊紝濡傛灉錛坰|1<<i錛夎繖涓姸鎬佸彲琛岋紝灝辮鏄庡湪s鐨勭姸鎬佷笅錛屾斁涓婄墿浣搃涓嶄細浣挎潬鏉嗗炬枩銆傚垽鏂槸鍚﹀鉤琛$殑鏉′歡錛岃鐢ㄥ埌鐗╃悊鐭ヨ瘑錛屽姏鐭?鍔涢伩 x 鍔涳紝 閲嶅績鐨勫潗鏍囷紝涔熷彲浠ラ氳繃(鍔涚煩/閲嶅姏)姹傚嚭銆傚彧瑕侀噸蹇冨潗鏍囧湪涓や釜鏀偣涔嬮棿灝辮兘淇濇寔騫寵 銆?br>
Sumsets錛?br>棰樼洰瑕佹眰姹傚嚭緇欏畾闆嗗悎涓渶澶х殑涓涓暟錛岃繖涓暟瑕佹弧瓚蟲槸闆嗗悎涓叾浠栦笁涓暟鐨勫拰錛屽嵆姹?a+b+c=d 錛?br>鎴戠殑鍋氭硶錛氬厛瀵歸泦鍚堟帓搴忥紝鏆村姏綆楀嚭闆嗗悎涓換鎰忎袱涓暟鐨勫拰鍗砤+b錛岀劧鍚庡鍜屾帓搴忥紝瀵歸泦鍚堜腑鐨勬暟浠庡ぇ鍒板皬鏋氫婦d錛岀湅鏄惁瀛樺湪c錛屼嬌d-c鍦ㄥ拰鐨勯泦鍚堜腑錛佸洜涓哄拰鐨勯泦鍚堟槸鏈夊簭鐨勶紝鎵浠ュ彲浠ヤ簩鍒嗘煡鎵撅紝鍚屾椂娉ㄦ剰榪欏洓涓暟涓嶈兘鐩稿悓灝卞彲浠ヤ簡錛?br>
Zipf's Law錛?br>瀛楃涓插鐞嗭紝鎸夌収棰樼洰鎰忔濆仛灝卞ソ浜嗭紝浣跨敤string浼氬緢鏂逛究錛屽鐞嗗叏閮ㄧ殑鍗曡瘝錛岀劧鍚庢帓搴忓鐞唦

Ones錛?br>浠?寮濮嬩笉鏂殑妯錛岀劧鍚庡緇撴灉*10+1錛屽驚鐜洿鍒頒負0鍗沖彲~


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