鍙戞槑鍗佸ぇ綆楁硶鐨勫叾涓嚑浣嶇畻娉曞ぇ甯?/p>
涓銆?946 钂欑壒鍗℃礇鏂規(guī)硶
[1946: John von Neumann, Stan Ulam, and Nick Metropolis, all at the Los Alamos Scientific Laboratory, cook up the Metropolis algorithm, also known as the Monte Carlo method.]
1946騫達(dá)紝緹庡浗鎷夋柉闃胯帿鏂浗瀹跺疄楠屽鐨勪笁浣嶇瀛﹀John von Neumann,Stan Ulam 鍜?Nick Metropolis
鍏卞悓鍙戞槑錛岃縐頒負(fù)钂欑壒鍗℃礇鏂規(guī)硶銆?/p>
瀹冪殑鍏蜂綋瀹氫箟鏄細(xì)
鍦ㄥ箍鍦轟笂鐢諱竴涓竟闀夸竴綾崇殑姝f柟褰紝鍦ㄦ鏂瑰艦鍐呴儴闅忔剰鐢ㄧ矇絎旂敾涓涓笉瑙勫垯鐨勫艦鐘訛紝
鐜板湪瑕佽綆楄繖涓笉瑙勫垯鍥懼艦鐨勯潰縐紝鎬庝箞璁$畻鍒?
钂欑壒鍗℃礇(Monte Carlo)鏂規(guī)硶鍛婅瘔鎴戜滑錛屽潎鍖鐨勫悜璇ユ鏂瑰艦鍐呮拻N錛圢 鏄竴涓緢澶х殑鑷劧鏁幫級(jí)涓粍璞嗭紝闅忓悗鏁版暟鏈夊灝戜釜榛勮眴鍦ㄨ繖涓笉瑙勫垯鍑犱綍褰㈢姸鍐呴儴錛屾瘮濡傝鏈塎涓紝
閭d箞錛岃繖涓鎬艦鐘剁殑闈㈢Н渚胯繎浼間簬M/N錛孨瓚婂ぇ錛岀畻鍑烘潵鐨勫間究瓚婄簿紜傚湪榪欓噷鎴戜滑瑕佸亣瀹氳眴瀛愰兘鍦ㄤ竴涓鉤闈笂錛岀浉浜掍箣闂存病鏈夐噸鍙犮?/p>
钂欑壒鍗℃礇鏂規(guī)硶鍙敤浜庤繎浼艱綆楀渾鍛ㄧ巼錛氳璁$畻鏈烘瘡嬈¢殢鏈虹敓鎴愪袱涓?鍒?涔嬮棿鐨勬暟錛岀湅榪欎袱涓疄鏁版槸鍚﹀湪鍗曚綅鍦嗗唴銆傜敓鎴愪竴緋誨垪闅忔満鐐癸紝緇熻鍗曚綅鍦嗗唴鐨勭偣鏁? 涓庢葷偣鏁幫紝錛堝渾闈㈢Н鍜屾鏂瑰艦闈㈢Н涔嬫瘮涓篜I:1錛孭I涓哄渾鍛ㄧ巼錛夛紝褰撻殢鏈虹偣鍙栧緱瓚婂錛堜絾鍗充嬌鍙?0鐨?嬈℃柟涓殢鏈虹偣鏃訛紝鍏剁粨鏋滀篃浠呭湪鍓?浣嶄笌鍦嗗懆鐜囧惢鍚堬級(jí) 鏃訛紝鍏剁粨鏋滆秺鎺ヨ繎浜庡渾鍛ㄧ巼銆?/p>
浜屻?947 鍗曠函褰㈡硶
[1947: George Dantzig, at the RAND Corporation, creates the simplex method for linear programming.]
1947騫達(dá)紝鍏板痙鍏徃鐨勶紝Grorge Dantzig錛屽彂鏄庝簡(jiǎn)鍗曠函褰㈡柟娉曘傚崟綰艦娉曪紝姝ゅ悗鎴愪負(fù)浜?jiǎn)绾挎ц鍒掑縐戠殑閲嶈鍩虹煶銆傛墍璋撶嚎鎬ц鍒掞紝綆鍗曠殑璇達(dá)紝灝辨槸緇欏畾涓緇勭嚎鎬э紙鎵鏈夊彉閲忛兘鏄竴嬈″箓錛夌害鏉? 鏉′歡錛堜緥濡俛1*x1+b1*x2+c1*x3>0)錛屾眰涓涓粰瀹氱殑鐩爣鍑芥暟鐨勬瀬鍊箋?/p>
榪欎箞璇翠技涔庝篃澶お澶娊璞′簡(jiǎn)錛屼絾鍦ㄧ幇瀹炰腑鑳芥淳涓婄敤鍦虹殑渚嬪瓙鍙笉緗曡鈥斺旀瘮濡傚浜庝竴涓叕鍙歌岃█錛屽叾鑳藉鎶曞叆鐢熶駭鐨勪漢鍔涚墿鍔涙湁闄愶紙鈥滅嚎鎬х害鏉熸潯浠垛濓級(jí)錛岃? 鍏徃鐨勭洰鏍囨槸鍒╂鼎鏈澶у寲錛堚滅洰鏍囧嚱鏁板彇鏈澶у尖濓級(jí)錛岀湅錛岀嚎鎬ц鍒掑茍涓嶆娊璞″惂錛佺嚎鎬ц鍒掍綔涓鴻繍絳瑰(operation research)鐨勪竴閮ㄥ垎錛屾垚涓虹鐞嗙瀛﹂鍩熺殑涓縐嶉噸瑕佸伐鍏楓傝孌antzig鎻愬嚭鐨勫崟綰艦娉曚究鏄眰瑙g被浼肩嚎鎬ц鍒掗棶棰樼殑涓涓瀬鍏舵湁鏁堢殑鏂規(guī)硶銆?/p>
涓夈?950 Krylov瀛愮┖闂磋凱浠f硶
[1950: Magnus Hestenes, Eduard Stiefel, and Cornelius Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods.]
1950騫達(dá)細(xì)緹庡浗鍥藉鏍囧噯灞鏁板煎垎鏋愮爺絀舵墍鐨勶紝椹牸鍔柉Hestenes錛岀埍寰峰崕鏂借拏璐瑰皵鍜岀灝煎埄鍘勬柉鐨凩anczos錛屽彂鏄庝簡(jiǎn)Krylov瀛愮┖闂? 榪唬娉曘侹rylov瀛愮┖闂磋凱浠f硶鏄敤鏉ユ眰瑙e艦濡侫x=b 鐨勬柟紼嬶紝A鏄竴涓猲*n 鐨勭煩闃碉紝褰搉鍏呭垎澶ф椂錛岀洿鎺ヨ綆楀彉寰楅潪甯稿洶闅撅紝鑰孠rylov鏂規(guī)硶鍒欏閥濡欏湴灝嗗叾鍙樹負(fù)Kxi+1=Kxi+b-Axi鐨勮凱浠e艦寮忔潵姹傝В銆傝繖閲岀殑K(鏉ユ簮浜庝綔 鑰呬縿鍥戒漢Nikolai Krylov濮撴皬鐨勯瀛楁瘝)鏄竴涓瀯閫犲嚭鏉ョ殑鎺ヨ繎浜嶢鐨勭煩闃碉紝鑰岃凱浠e艦寮忕殑綆楁硶鐨勫澶勫湪浜庯紝瀹冨皢澶嶆潅闂鍖栫畝涓洪樁孌墊х殑鏄撲簬璁$畻鐨勫瓙姝ラ銆?/p>
鍥涖?951 鐭╅樀璁$畻鐨勫垎瑙f柟娉?/strong>
[1951: Alston Householder of Oak Ridge National Laboratory formalizes the decompositional approach to matrix computations.]
1951騫達(dá)紝闃垮皵鏂氭鏍?wèi)宀浗瀹跺疄楠屽鐨凙lston Householder鎻愬嚭錛岀煩闃佃綆楃殑鍒嗚В鏂規(guī)硶銆傝繖涓畻娉曡瘉鏄庝簡(jiǎn)浠諱綍鐭╅樀閮藉彲浠ュ垎瑙d負(fù)涓夎銆佸瑙掋佹浜ゅ拰鍏朵粬鐗規(guī)畩褰㈠紡鐨勭煩闃碉紝璇ョ畻娉曠殑鎰忎箟浣垮緱寮鍙戠伒媧葷殑鐭╅樀璁$畻杞歡鍖呮垚涓哄彲鑳姐?/p>
浜斻?957 浼樺寲鐨凢ortran緙栬瘧鍣?/strong>
[1957: John Backus leads a team at IBM in developing the Fortran optimizing compiler.]
1957騫達(dá)細(xì)綰︾堪宸村簱鏂瀵煎紑鍙戠殑IBM鐨勫洟闃燂紝鍒涢犱簡(jiǎn)Fortran浼樺寲緙栬瘧鍣ㄣ侳ortran錛屼害璇戜負(fù)紱忎紶錛屾槸鐢盕ormula Translation涓や釜瀛楁墍緇勫悎鑰屾垚錛屾剰鎬濇槸鈥滃叕寮忕炕璇戔濄傚畠鏄笘鐣屼笂絎竴涓姝e紡閲囩敤騫舵祦浼犺嚦浠婄殑楂樼駭緙栫▼璇█銆傝繖涓璦鐜板湪錛屽凡緇忓彂灞曞埌 浜?jiǎn)锛孎ortran 2008錛屽茍涓轟漢浠墍鐔熺煡銆?/p>
鍏?959-61 璁$畻鐭╅樀鐗瑰緛鍊肩殑QR綆楁硶
[1959鈥?1: J.G.F. Francis of Ferranti Ltd, London, finds a stable method for computing eigenvalues, known as the QR algorithm.]
1959-61錛氫雞鏁﹁垂浼﹁拏鏈夐檺鍏徃鐨凧.G.F. Francis錛屾壘鍒頒簡(jiǎn)涓縐嶇ǔ瀹氱殑鐗瑰緛鍊肩殑璁$畻鏂規(guī)硶錛岃繖灝辨槸钁楀悕鐨凲R綆楁硶銆傝繖涔熸槸涓涓拰綰挎т唬鏁版湁鍏崇殑綆楁硶錛屽榪囩嚎鎬т唬鏁扮殑搴旇璁板緱鈥滅煩闃電殑鐗瑰緛鍊尖濓紝 璁$畻鐗瑰緛鍊兼槸鐭╅樀璁$畻鐨勬渶鏍稿績(jī)鍐呭涔嬩竴錛屼紶緇熺殑姹傝В鏂規(guī)娑夊強(qiáng)鍒伴珮?gòu)啤鏂菇E嬫眰鏍癸紝褰撻棶棰樿妯″ぇ鐨勬椂鍊欏崄鍒嗗洶闅俱俀R綆楁硶鎶婄煩闃靛垎瑙f垚涓涓浜ょ煩闃?甯屾湜璇繪鏂? 鐨勪綘錛岀煡閬撲粈涔堟槸姝d氦鐭╅樀銆?D銆?涓庝竴涓笂涓夎鐭╅樀鐨勭Н錛屽拰鍓嶉潰鎻愬埌鐨凨rylov 鏂規(guī)硶綾諱技錛岃繖鍙堟槸涓涓凱浠g畻娉曪紝瀹冩妸澶嶆潅鐨勯珮?gòu)啤鏂菇E嬫眰鏍歸棶棰樺寲綆涓洪樁孌墊х殑鏄撲簬璁$畻鐨勫瓙姝ラ錛屼嬌寰楃敤璁$畻鏈烘眰瑙eぇ瑙勬ā鐭╅樀鐗瑰緛鍊兼垚涓哄彲鑳姐傝繖涓畻娉曠殑浣滆? 鏄潵鑷嫳鍥戒雞鏁︾殑J.G.F. Francis銆?/p>
涓冦?962 蹇熸帓搴忕畻娉?/strong>
[1962: Tony Hoare of Elliott Brothers, Ltd., London, presents Quicksort.]
1962騫達(dá)細(xì)浼︽暒鐨勶紝鎵樺凹鍩冨埄濂ョ壒鍏勫紵鏈夐檺鍏徃錛岄湇灝?dāng)鎻愬囖Z簡(jiǎn)蹇熸帓搴忋傚搱鍝堬紝鎭枩浣狅紝緇堜簬鐪嬪埌浜?jiǎn)鍙兘鏄綘绗竴涓瘮杈冪啛鎮(zhèn)夌殑綆楁硶~銆傚揩閫熸帓搴忕畻娉曚綔涓? 鎺掑簭綆楁硶涓殑緇忓吀綆楁硶錛屽畠琚簲鐢ㄧ殑褰卞瓙闅忓鍙銆傚揩閫熸帓搴忕畻娉曟渶鏃╃敱Tony Hoare鐖靛+璁捐錛屽畠鐨勫熀鏈濇兂鏄皢寰呮帓搴忓垪鍒嗕負(fù)涓ゅ崐錛屽乏杈圭殑涓鍗婃繪槸鈥滃皬鐨勨濓紝鍙寵竟鐨勪竴鍗婃繪槸鈥滃ぇ鐨勨濓紝榪欎竴榪囩▼涓嶆柇閫掑綊鎸佺畫涓嬪幓錛岀洿鍒版暣涓簭鍒楁湁 搴忋傝璧瘋繖浣峊ony Hoare鐖靛+錛屽揩閫熸帓搴忕畻娉曞叾瀹炲彧鏄粬涓嶇粡鎰忛棿鐨勫皬灝忓彂鐜拌屽凡錛屼粬瀵逛簬璁$畻鏈鴻礎(chǔ)鐚富瑕佸寘鎷艦寮忓寲鏂規(guī)硶鐞嗚錛屼互鍙?qiáng)ALGOL60 緙栫▼璇█鐨勫彂鏄庣瓑錛屼粬涔熷洜榪欎簺鎴愬氨鑾峰緱1980 騫村浘鐏靛銆?/p>
========
鍏充簬蹇熸帓搴忕畻娉曠殑鍏蜂綋璁よ瘑涓庡簲鐢紝鍙弬鑰冩垜鍐欑殑涓綃囨枃绔狅紝
綺鵑氬叓澶ф帓搴忕畻娉曠郴鍒椼佷竴銆佸揩閫熸帓搴忕畻娉曪細(xì)
http://blog.csdn.net/v_JULY_v/archive/2011/01/04/6116297.aspx
------------------------------------------------------------
蹇熸帓搴忕殑騫沖潎鏃墮棿澶嶆潅搴︿粎浠呬負(fù)O(Nlog(N))錛岀浉姣斾簬鏅氶夋嫨鎺掑簭鍜屽啋娉℃帓搴忕瓑鑰岃█錛?/p>
瀹炲湪鏄巻鍙叉х殑鍒涗婦銆?/p>
鍏?965 蹇熷倕绔嬪彾鍙樻崲
[1965: James Cooley of the IBM T.J. Watson Research Center and John Tukey of Princeton University and AT&T Bell Laboratories unveil the fast Fourier transform.]
1965騫達(dá)細(xì)IBM 鍗庣敓鐮旂┒闄㈢殑James Cooley錛屽拰鏅灄鏂】澶у鐨凧ohn Tukey錛孉T錛員璐濆皵瀹為獙瀹ゅ叡鍚屾帹鍑轟簡(jiǎn)蹇熷倕绔嬪彾鍙樻崲銆傚揩閫熷倕绔嬪彾綆楁硶鏄鏁e倕绔嬪彾綆楁硶錛堣繖鍙槸鏁板瓧淇″彿澶勭悊鐨勫熀鐭籌級(jí)鐨勪竴縐嶅揩閫熺畻娉曪紝鍏舵椂闂村鏉傚害浠? 涓篛(Nlog(N))錛涙瘮鏃墮棿鏁堢巼鏇翠負(fù)閲嶈鐨勬槸錛屽揩閫熷倕绔嬪彾綆楁硶闈炲父瀹規(guī)槗鐢ㄧ‖浠跺疄鐜幫紝鍥犳瀹冨湪鐢?shù)瀛愭妧鏈鍩熷緱鍒版瀬鍏跺箍娉涚殑搴旂敤銆傛棩鍚庯紝鎴戜細(xì)鍦ㄦ垜鐨勭粡鍏哥畻 娉曠爺絀剁郴鍒楋紝鐫閲嶉槓榪版綆楁硶銆?/p>
涔?jié)銆?977 鏁存暟鍏崇郴鎺㈡祴綆楁硶
[1977: Helaman Ferguson and Rodney Forcade of Brigham Young University advance an integerrelation detection algorithm.]
1977騫達(dá)細(xì)Helaman Ferguson鍜?浼槑緲板ぇ瀛︾殑Rodney Forcade錛屾彁鍑轟簡(jiǎn)Forcade媯(gè)嫻嬬畻娉曠殑鏁存暟鍏崇郴銆傛暣鏁板叧緋繪帰嫻嬫槸涓彜鑰佺殑闂錛屽叾鍘嗗彶鐢氳嚦鍙互榪芥函鍒版鍑犻噷寰風(fēng)殑鏃朵唬銆傚叿浣撶殑璇?緇欏畾鈥旂粍瀹炴暟 X1,X2,...,Xn錛屾槸鍚﹀瓨鍦ㄤ笉鍏ㄤ負(fù)闆剁殑鏁存暟a1,a2,...an錛屼嬌寰?a1 x 1 +a2 x2 + . . . + an x n 錛??
榪欎竴騫碆righamYoung澶у鐨凥elaman Ferguson 鍜孯odney Forcade瑙e喅浜?jiǎn)杩欎竴闂銆傝綆楁硶搴旂敤浜庘滅畝鍖栭噺瀛愬満璁轟腑鐨凢eynman鍥劇殑璁$畻鈥濄俹k錛屽畠騫朵笉瑕佷綘鎳傦紝浜?jiǎn)瑙e崨_彲銆?/p>
鍗併?987 蹇熷鏋佺畻娉?/strong>
[1987: Leslie Greengard and Vladimir Rokhlin of Yale University invent the fast multipolealgorithm.]
1987騫達(dá)細(xì)鑾辨柉鍒╃殑Greengard錛屽拰鑰墮瞾澶у鐨凴okhlin鍙戞槑浜?jiǎn)蹇熷鏋佺畻娉曘?/p>
姝ゅ揩閫熷鏋佺畻娉曠敤鏉ヨ綆椻滅粡鐢卞紩鍔涙垨闈?rùn)鐢?shù)鍔涚浉浜掍綔鐢ㄧ殑N 涓矑瀛愯繍鍔ㄧ殑綺劇‘璁$畻鈥斺斾緥濡傞摱娌崇郴涓殑鏄熶綋錛屾垨鑰呰泲鐧借川涓殑鍘熷瓙闂寸殑鐩鎬簰浣滅敤鈥濄俹k錛屼簡(jiǎn)瑙e嵆鍙偮?/p>
鏈枃鏉ヨ嚜CSDN鍗氬錛岃漿杞借鏍囨槑鍑哄錛歨ttp://blog.csdn.net/v_JULY_v/archive/2011/01/10/6127953.aspx
#include<stdio.h>
#include<stdlib.h>
struct node
{
int data;
struct node *lh,*rh;
int ltag,rtag;
}*pr,*t,*s[30];
struct node* creat()
{
struct node *t,*q;
int i,x,j;
printf("i,x=");
scanf("%d%d",&i,&x);
while((i!=0)&&(x!=0))
{
q=(struct node *)malloc(sizeof(struct node));
q->data=x;
q->lh=NULL;
q->rh=NULL;
s[i ]=q;
if(i==1)
t=q;
else
{
j=i/2;
if((i%2)==0)
s[j]->lh=q;
else
s[j]->rh=q;
}
printf("i,x=");
scanf("%d%d",&i,&x);
}
return(t);
}
/*void inthread(struct node *p) //閫掑綊綆楁硶
{
if(p!=NULL)
{
inthread(p->lh);
printf("%6d\t",p->data);
if(p->lh!=NULL)
p->ltag=0;
else
{
p->ltag=1;
p->lh=pr;
} //寤虹珛P鑺傜偣鐨勫乏綰跨儲(chǔ)錛屾寚鍚戝墠瓚嬭妭鐐筆R
if(pr!=NULL)
{
if(pr->rh!=NULL)
pr->rtag=0;
else
{
pr->rtag=1;
pr->rh=p;
}//鍓嶈秼鑺傜偣PR寤虹珛宸︾嚎绱紝鎸囧悜鑺傜偣P
}
pr=p;//pr璺熶笂p,浠ヤ究p鍚戝悗縐誨姩
inthread(p->rh);
}
}*/
void inthread(struct node *t)//闈為掑綊綆楁硶
{
int top,bools;
struct node *p;
pr=NULL;p=t;top=0;bools=1;
do{
while(p!=NULL)
{
top++;
s[top]=p;
p=p->lh;
}
if(top==0)bools=0;
else
{
p=s[top];
top--;
printf("%6d",p->data);
if(p->lh!=NULL)
p->ltag=0;
else
{
p->ltag=1;
p->lh=pr;
} //寤虹珛P鑺傜偣鐨勫乏綰跨儲(chǔ)錛屾寚鍚戝墠瓚嬭妭鐐筆R
if(pr!=NULL)
{
if(pr->rh!=NULL)
pr->rtag=0;
else
{
pr->rtag=1;
pr->rh=p;
}//鍓嶈秼鑺傜偣PR寤虹珛宸︾嚎绱紝鎸囧悜鑺傜偣P
}
pr=p;//pr璺熶笂p,浠ヤ究p鍚戝悗縐誨姩
p=p->rh;
}//END else
}while(bools);
pr->rh=NULL;
}
main()
{
pr=NULL;
t=creat();
inthread(t);
pr->rh=NULL;
}
#include<stdio.h>
#include<malloc.h>
#include<iostream>
//瀹氫箟鑺傜偣
typedef struct BiNode{
char data;
struct BiNode *lch;
struct BiNode *rch;
}BiNode,*BiTree;
//鍏堝簭鎷撳睍搴忓垪寤虹珛浜屽弶鏍?
void Create(BiTree &T)
{
T =(BiNode*) malloc (sizeof(BiNode));
printf("Enter the data \n");
scanf(" %c",&T->data);
if(T->data=='#') T = NULL;
if(T){
printf("");
Create(T->lch);
Create(T->rch);
}
}
//鍏堝簭閬嶅巻 (閫掑綊)
void Preorder (BiTree T)
{
if (T) {
printf(" %c",T->data); // 璁塊棶鏍圭粨鐐?br>
Preorder(T->lch); // 閬嶅巻宸﹀瓙鏍?br> Preorder(T->rch);// 閬嶅巻鍙沖瓙鏍?br> }
}
//涓簭閬嶅巻 錛堥掑綊錛?br>void Inorder (BiTree T)
{
if(T) {
Inorder(T->lch);
printf(" %c",T->data);
Inorder(T->rch);
}
}
//鍚庡簭閬嶅巻 錛堥掑綊錛?br>void Postorder (BiTree T)
{
if(T) {
Postorder(T->lch);
Postorder(T->rch);
printf(" %c",T->data);
}
}
int main()
{
//寤烘爲(wèi)
printf("The fuction Create() is called.\n");
BiTree T;
Create(T);
//涓夌閬嶅巻閫掑綊綆楁硶
printf("\n");
printf("The fuction Preorder() is called.\n");
Preorder(T);
printf("\n");
printf("The fuction Inorder() is called.\n");
Inorder(T);
printf("\n");
printf("The fuction Postorder() is called.\n");
Postorder(T);
printf("\n");
system("pause");
}