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浜庡悗鍗婇儴鍒?灝變嬌寰楀墠鍗婇儴鍒嗙殑浠諱綍涓涓暟浠庢浠ュ悗閮戒笉鍐嶈窡鍚庡崐閮ㄥ垎鐨勬暟榪涜姣旇緝浜嗭紝澶уぇ鍑忓皯浜嗘暟瀛楅棿涓嶅繀瑕佺殑姣旇緝銆備絾鏌ユ壘鏁版嵁寰楀彟褰撳埆璁轟簡銆? 蹇熸帓搴忛噰鐢ㄤ簡涓縐嶅垎娌葷殑絳栫暐錛岄氬父縐板叾涓哄垎娌繪硶錛屽叾鍩烘湰鎬濇兂鏄細灝嗗師闂鍒嗚В涓鴻嫢騫蹭釜瑙勬ā鏇村皬浣嗙粨鏋勪笌鍘熼棶棰樼浉浼肩殑瀛愰棶棰樸傞掑綊鍦拌В榪欎簺瀛愰棶棰橈紝鐒跺悗灝嗚繖浜涘瓙闂鐨勮В緇勫悎涓哄師闂鐨勮В銆?br /> 蹇熸帓搴忕殑鍏蜂綋榪囩▼濡備笅錛?br /> 絎竴姝ワ紝鍦ㄥ緟鎺掑簭鐨刵涓褰曚腑浠誨彇涓涓褰曪紝浠ヨ璁板綍鐨勬帓搴忕爜涓哄噯錛屽皢鎵鏈夎褰曞垎鎴愪袱緇勶紝絎?緇勫悇璁板綍鐨勬帓搴忕爜閮藉皬浜庣瓑浜庤鎺掑簭鐮侊紝絎?緇勫悇璁板綍鐨勬帓搴忕爜閮藉ぇ浜庤鎺掑簭鐮侊紝騫舵妸璇ヨ褰曟帓鍦ㄨ繖涓ょ粍涓棿銆?br /> 絎簩姝ワ紝閲囩敤鍚屾牱鐨勬柟娉曪紝瀵瑰乏杈圭殑緇勫拰鍙寵竟鐨勭粍榪涜鎺掑簭錛岀洿鍒版墍鏈夎褰曢兘鎺掑埌鐩稿簲鐨勪綅緗負姝€?br /> ================================== 鍥?褰掑茍鎺掑簭 =================================== 鎬葷粨鎬葷粨錛?/font> 鎸夊鉤鍧囨椂闂村皢鎺掑簭鍒嗕負鍥涚被錛?br /> ======================================= =========鍙︿竴鐗?======================== ======================================= 閫夋嫨鎺掑簭 鍦ㄨ鎺掑簭鐨勪竴緇勬暟涓紝閫夊嚭鏈灝忕殑涓涓暟涓庣涓涓綅緗殑鏁頒氦鎹紱 閫夋嫨鎺掑簭鏄笉紼沖畾鐨勩傜畻娉曞鏉傚害O(n2)--[n鐨勫鉤鏂筣 void select_sort(int *x, int n) for (i=0; i<n-1; i++) /*瑕侀夋嫨鐨勬鏁幫細0~n-2鍏眓-1嬈?/ 鐩存帴鎻掑叆鎺掑簭 鍦ㄨ鎺掑簭鐨勪竴緇勬暟涓紝鍋囪鍓嶉潰(n-1) [n>=2] 涓暟宸茬粡鏄帓 void insert_sort(int *x, int n) for (i=1; i<n; i++) /*瑕侀夋嫨鐨勬鏁幫細1~n-1鍏眓-1嬈?/ *(x+j+1) = t; /*鎵懼埌涓嬫爣涓篿鐨勬暟鐨勬斁緗綅緗?/ 鍐掓場鎺掑簭 鍦ㄨ鎺掑簭鐨勪竴緇勬暟涓紝瀵瑰綋鍓嶈繕鏈帓濂藉簭鐨勮寖鍥村唴鐨勫叏閮ㄦ暟錛岃嚜涓?br />鑰屼笅瀵圭浉閭葷殑涓や釜鏁頒緷嬈¤繘琛屾瘮杈冨拰璋冩暣錛岃杈冨ぇ鐨勬暟寰涓嬫矇錛岃緝 鍐掓場鎺掑簭鏄ǔ瀹氱殑銆傜畻娉曟椂闂村鏉傚害O(n2)--[n鐨勫鉤鏂筣 void bubble_sort(int *x, int n) 甯屽皵鎺掑簭鏄笉紼沖畾鐨勩?/strong> void shell_sort(int *x, int n) for (h=n/2; h>0; h=h/2) /*鎺у埗澧為噺*/ 蹇熸帓搴忔槸瀵瑰啋娉℃帓搴忕殑涓縐嶆湰璐ㄦ敼榪涖傚畠鐨勫熀鏈濇兂鏄氳繃涓瓚?br />鎵弿鍚庯紝浣垮緱鎺掑簭搴忓垪鐨勯暱搴﹁兘澶у箙搴﹀湴鍑忓皯銆傚湪鍐掓場鎺掑簭涓紝涓嬈?br />鎵弿鍙兘紜繚鏈澶ф暟鍊肩殑鏁扮Щ鍒版紜綅緗紝鑰屽緟鎺掑簭搴忓垪鐨勯暱搴﹀彲鑳藉彧 蹇熸帓搴忔槸涓嶇ǔ瀹氱殑銆傛渶鐞嗘兂鎯呭喌綆楁硶鏃墮棿澶嶆潅搴(nlog2n)錛屾渶鍧廜(n2) if (low < high) /*瑕佹帓搴忕殑鍏冪礌璧鋒涓嬫爣錛屼繚璇佸皬鐨勬斁鍦ㄥ乏杈癸紝澶х殑鏀懼湪鍙寵竟銆傝繖閲屼互涓嬫爣涓簂ow鐨勫厓绱犱負鍩哄噯鐐?/ while (i<j) /*寰幆鎵弿*/ if (i<j) while (i<j && *(x+i)<=t) /*鍦ㄥ乏杈圭殑鍙灝忎簬絳変簬鍩哄噯鐐逛粛鏀懼湪宸﹁竟*/ if (i<j) *(x+i) = t; /*涓閬嶆壂鎻忓畬鍚庯紝鏀懼埌閫傚綋浣嶇疆*/ 鍫嗘帓搴?/strong> 鍫嗘帓搴忔槸涓縐嶆爲褰㈤夋嫨鎺掑簭錛屾槸瀵圭洿鎺ラ夋嫨鎺掑簭鐨勬湁鏁堟敼榪涖?br />鍫嗙殑瀹氫箟濡備笅錛氬叿鏈塶涓厓绱犵殑搴忓垪錛坔1,h2,...,hn),褰撲笖浠呭綋 鐢卞爢鐨勫畾涔夊彲浠ョ湅鍑猴紝鍫嗛《鍏冪礌錛堝嵆絎竴涓厓绱狅級蹇呬負鏈澶ч」銆傚畬鍏ㄤ簩鍙夋爲鍙互 浠庣畻娉曟弿榪版潵鐪嬶紝鍫嗘帓搴忛渶瑕佷袱涓繃紼嬶紝涓鏄緩绔嬪爢錛屼簩鏄爢欏朵笌鍫嗙殑鏈鍚庝竴涓厓绱?br />浜ゆ崲浣嶇疆銆傛墍浠ュ爢鎺掑簭鏈変袱涓嚱鏁扮粍鎴愩備竴鏄緩鍫嗙殑娓楅忓嚱鏁幫紝浜屾槸鍙嶅璋冪敤娓楅忓嚱鏁?br />瀹炵幇鎺掑簭鐨勫嚱鏁般?/strong> 鍫嗘帓搴忔槸涓嶇ǔ瀹氱殑銆傜畻娉曟椂闂村鏉傚害O(nlog2n)銆?/strong> 娓楅忓緩鍫?/strong> t = *(x+s); /*鏆傚瓨寮濮嬪厓绱?/ while (j<n) if (t<*(x+j)) /*璋冩暣*/ 鍫嗘帓搴?/strong> for (i=n/2-1; i>=0; i--) =============================================================================== /*嫻嬭瘯閫夋嫨鎺掑簭*/ /* /* /*嫻嬭瘯蹇熸帓搴?/ /* /*嫻嬭瘯鍫嗘帓搴?/ /* for (p=a, i=0; i<MAX; i++)int Fabonacci(int n){ if(n <= 2) return n - 1; else return (Fabonacci(n - 1) + Fabonacci(n - 2));}int _Fabonacci(int n)//杈撳嚭鍓?n 涓暟{ int i, a, b, c; a = 0; b = 1; printf("%10d%10d", a, b);/*杈撳嚭鍓嶄袱涓暟*/ for(i = 3; i <= n; i ++) { c = a + b; printf("%10d", c); if(i % 5 == 0) printf("\n");/*姣忚杈撳嚭 5 涓?/ a = b; b = c;/*欏圭Щ鍔?/ } printf("\n");}
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閲嶅2鍙鋒楠わ紝鐩磋嚦鍘熸暟鍒椾負絀恒?
鎻掑叆鎺掑簭鐨勫鉤鍧囨椂闂村鏉傚害涓哄鉤鏂圭駭鐨勶紝鏁堢巼涓嶉珮錛屼絾鏄鏄撳疄鐜般傚畠鍊熷姪浜?閫愭鎵╁ぇ鎴愭灉"鐨勬濇兂錛屼嬌鏈夊簭鍒楄〃鐨勯暱搴﹂愭笎澧炲姞錛岀洿鑷沖叾闀垮害絳変簬鍘熷垪琛ㄧ殑闀垮害銆?/font>
鎺ユ彃鍏ユ帓搴忕殑榪囩▼涓猴細鍦ㄦ彃鍏ョi涓褰曟椂錛孯1,R2,..Ri-1宸茬粡鎺掑ソ搴忥紝灝嗙i涓褰曠殑鎺掑簭鐮並i渚濇鍜孯1,R2,..,Ri-1鐨勬帓搴忕爜閫愪釜榪涜姣旇緝錛屾壘鍒伴傚綋鐨勪綅緗備嬌鐢ㄧ洿鎺ユ彃鍏ユ帓搴忥紝瀵逛簬鍏鋒湁n涓褰曠殑鏂囦歡錛岃榪涜n-1瓚熸帓搴忋?br />
浠g爜濡備笅:
void Dir_Insert(int A[],int N) //鐩存帴鎻掑叆鎺掑簭
{
int j,t;
for(int i=1;i<N;i++)
{
t=A[i];
j=i-1;
while(A[j]>t)
{
A[j+1]=A[j];
j--;
}
A[j+1]=t;
}
}
②.甯屽皵鎺掑簭(涓嶇ǔ瀹?錛?br />
甯屽皵(Shell)鎺掑簭鐨勫熀鏈濇兂鏄細鍏堝彇涓涓皬浜巒鐨勬暣鏁癲1浣滀負絎竴涓閲忔妸鏂囦歡鐨勫叏閮ㄨ褰曞垎鎴恉1涓粍銆傛墍鏈夎窛紱諱負d1鐨勫嶆暟鐨勮褰曟斁鍦ㄥ悓涓涓粍
涓傚厛鍦ㄥ悇緇勫唴榪涜鐩存帴鎻掑叆鎺掑簭錛涚劧鍚庯紝鍙栧緱絎簩涓閲廳2<d1閲嶅涓婅堪鐨勫垎緇勫拰鎺掑簭錛岀洿鑷蟲墍鍙栫殑澧為噺di=1錛屽嵆鎵鏈夎褰曟斁鍦ㄥ悓涓緇勪腑榪涜鐩存帴
鎻掑叆鎺掑簭涓烘銆傝鏂規硶瀹炶川涓婃槸涓縐嶅垎緇勬彃鍏ユ柟娉曘?br /> 涓鑸彇d1=n/2錛宒i+1=di/2銆傚鏋滅粨鏋滀負鍋舵暟錛屽垯鍔?錛屼繚璇乨i涓哄鏁般?br /> 甯屽皵鎺掑簭鏄笉紼沖畾鐨勶紝甯屽皵鎺掑簭鐨勬墽琛屾椂闂翠緷璧栦簬澧為噺搴忓垪錛屽叾騫沖潎鏃墮棿澶嶆潅搴︿負O(n^1.3).
浠g爜濡備笅:
void Shell(int A[],int n) //Shell鎺掑簭
{
int i,j,k,t;
(n/2)%2 == 0 ? k = n/2+1 : k = n/2; //淇濊瘉澧為噺涓哄鏁?br /> while(k > 0)
{
for(j=k;j<n; j++)
{
t = A[j];
i = j - k;
while(i>=0 && A[i]>t)
{
A[i+k]=A[i];
i=i-k;
}
A[i+k]=t;
}
if(k == 1) break;
(k/2)%2 ==0 ? k=k/2+1 : k=k/2;
}
}
i=1
浠庢暟緇勭殑絎琲涓厓绱犲紑濮嬪埌絎琻涓厓绱狅紝瀵繪壘鏈灝忕殑鍏冪礌銆?
灝嗕笂涓姝ユ壘鍒扮殑鏈灝忓厓绱犲拰絎琲浣嶅厓绱犱氦鎹€?
濡傛灉i=n錛?綆楁硶緇撴潫錛屽惁鍒欏洖鍒扮3姝?
鐩存帴閫夋嫨鎺掑簭鐨勮繃紼嬫槸錛氶鍏堝湪鎵鏈夎褰曚腑閫夊嚭搴忕爜鏈灝忕殑璁板綍錛屾妸瀹冧笌絎?涓褰曚氦鎹紝鐒跺悗鍦ㄥ叾浣欑殑璁板綍鍐呴夊嚭鎺掑簭鐮佹渶灝忕殑璁板綍錛屼笌絎?涓褰曚氦鎹?.....渚濇綾繪帹錛岀洿鍒版墍鏈夎褰曟帓瀹屼負姝€?br />
鏃犺鏂囦歡鍒濆鐘舵佸浣曪紝鍦ㄧi瓚熸帓搴忎腑閫夊嚭鏈灝忓叧閿瓧鐨勮褰曪紝闇瑕佸仛n-i嬈℃瘮杈冿紝鍥犳錛屾葷殑姣旇緝嬈℃暟涓簄(n-1)/2=O(n^2)銆傚綋鍒濆鏂囦歡涓烘
搴忔椂錛岀Щ鍔ㄦ鏁頒負0錛涙枃浠跺垵鎬佷負鍙嶅簭鏃訛紝姣忚稛鎺掑簭鍧囪鎵ц浜ゆ崲鎿嶄綔錛屾葷殑縐誨姩嬈℃暟鍙栨渶澶у?(n-1)銆傜洿鎺ラ夋嫨鎺掑簭鐨勫鉤鍧囨椂闂村鏉傚害涓篛(n^2)銆傜洿
鎺ラ夋嫨鎺掑簭鏄笉紼沖畾鐨勩?br />
浠g爜濡備笅:
void Dir_Choose(int A[],int n) //鐩存帴閫夋嫨鎺掑簭
{
int k,t;
for(int i=0;i<n-1;i++)
{
k=i;
for(int j=i+1;j<n;j++)
{
if(A[j]<A[k]) k=j;
}
if(k!=i)
{
t=A[i];
A[i]=A[k];
A[k]=t;
}
}
}
②.鍫嗘帓搴?涓嶇ǔ瀹?
棣?
鍏堟柊寤轟竴涓┖鍒楄〃錛屼綔鐢ㄤ笌鎻掑叆鎺掑簭涓殑"鏈夊簭鍒楄〃"鐩稿悓銆?銆鎵懼埌鏁板垪涓渶澶х殑鏁板瓧錛屽皢鍏跺姞鍦?鏈夊簭鍒楄〃"鐨勬湯灝撅紝騫跺皢鍏朵粠鍘熸暟鍒椾腑鍒犻櫎銆?
閲嶅2鍙鋒楠わ紝鐩磋嚦鍘熸暟鍒椾負絀恒?
鍫嗘帓搴忕殑騫沖潎鏃墮棿澶嶆潅搴︿負nlogn,鏁堢巼楂橈紙鍥犱負鏈夊爢榪欑鏁版嵁緇撴瀯浠ュ強瀹冨濡欑殑鐗瑰緛錛屼嬌寰?鎵懼埌鏁板垪涓渶澶х殑鏁板瓧"榪欐牱鐨勬搷浣滃彧闇瑕丱(1)鐨勬椂闂村鏉?
搴︼紝緇存姢闇瑕乴ogn鐨勬椂闂村鏉傚害錛夛紝浣嗘槸瀹炵幇鐩稿澶嶆潅錛堝彲浠ヨ鏄繖閲?縐嶇畻娉曚腑姣旇緝闅懼疄鐜扮殑錛夈?
鐪嬭搗鏉ヤ技涔庡爢鎺掑簭涓庢彃鍏ユ帓搴忔湁浜涚浉鍍忥紝浣嗕粬浠叾瀹炴槸鏈川涓嶅悓鐨勭畻娉曘傝嚦灝戯紝浠栦滑鐨勬椂闂村鏉傚害宸簡涓涓暟閲忕駭錛屼竴涓槸騫蟲柟綰х殑錛屼竴涓槸瀵規暟綰х殑銆?
K1,K2,...,Kn
縐頒負鍫嗭紝褰撲笖浠呭綋璇ュ簭鍒楁弧瓚?Ki<=K2i涓擪i<=K2i+1)鎴?Ki>=K2i涓擪i>=K2i+1),(1&
lt;=i<=n/2)銆傛牴緇撶偣(鍫嗛《)鐨勫叧閿瓧鏄爢閲屾墍鏈夌粨鐐瑰叧閿瓧涓渶灝忚咃紝縐頒負灝忔牴鍫嗭紱鏍圭粨鐐圭殑鍏抽敭瀛楁槸鍫嗛噷鎵鏈夌粨鐐瑰叧閿瓧涓渶澶ц咃紝縐頒負澶?
鏍瑰爢銆?br /> 鑻ュ皢姝ゅ簭鍒楁墍瀛樺偍鐨勫悜閲廟[1..n]鐪嬩綔鏄竴媯靛畬鍏ㄤ簩鍙夋爲鐨勫瓨鍌ㄧ粨鏋勶紝鍒欏爢瀹炶川涓婃槸婊¤凍濡備笅鎬ц川鐨勫畬鍏ㄤ簩鍙夋爲錛氭爲涓換涓闈炲彾緇撶偣鐨勫叧閿瓧鍧囦笉澶т簬(鎴栦笉灝忎簬)鍏跺乏鍙沖瀛?鑻ュ瓨鍦?緇撶偣鐨勫叧閿瓧銆?br />
鍫嗘帓搴忕殑鍏抽敭姝ラ鏈変袱涓細涓鏄浣曞緩绔嬪垵濮嬪爢錛涗簩鏄綋鍫嗙殑鏍圭粨鐐逛笌鍫嗙殑鏈鍚庝竴涓粨鐐逛氦鎹㈠悗錛屽浣曞灝戜簡涓涓粨鐐瑰悗鐨勭粨鐐瑰簭鍒楀仛璋冩暣錛屼嬌涔嬮噸鏂版垚涓哄爢銆傚爢鎺?
搴忕殑鏈鍧忔椂闂村鏉傚害涓篛(nlog2n),鍫嗘帓搴忕殑騫沖潎鎬ц兘杈冩帴榪戜簬鏈鍧忔ц兘銆傜敱浜庡緩鍒濆鍫嗘墍闇鐨勬瘮杈?
嬈℃暟杈冨錛屾墍浠ュ爢鎺掑簭涓嶉傚疁浜庤褰曡緝灝戠殑鏂囦歡銆傚爢鎺掑簭鏄氨鍦版帓搴忥紝杈呭姪絀洪棿涓篛(1)錛屽畠鏄笉紼沖畾鐨勬帓搴忔柟娉曘?br />
浠g爜鐣?.
①.鍐掓場鎺掑簭(紼沖畾鐨?
棣?
鍏堝皢鎵鏈夊緟鎺掑簭鐨勬暟瀛楁斁鍏ュ伐浣滃垪琛ㄤ腑銆?浠庡垪琛ㄧ殑絎竴涓暟瀛楀埌鍊掓暟絎簩涓暟瀛楋紝閫愪釜媯鏌ワ細鑻ユ煇涓浣嶄笂鐨勬暟瀛楀ぇ浜庝粬鐨勪笅涓浣嶏紝鍒欏皢瀹冧笌瀹冪殑涓嬩竴浣嶄氦鎹€?
閲嶅2鍙鋒楠わ紝鐩磋嚦鍐嶄篃涓嶈兘浜ゆ崲銆?鍐掓場鎺掑簭鐨勫鉤鍧囨椂闂村鏉傚害涓庢彃鍏ユ帓搴忕浉鍚岋紝涔熸槸騫蟲柟綰х殑錛屼絾涔熸槸闈炲父瀹規槗瀹炵幇鐨勭畻娉曘?nbsp;
絎竴姝ワ紝鍏堟瘮杈僰1鍜宬2錛岃嫢k1>k2錛屽垯浜ゆ崲k1鍜宬2鎵鍦ㄧ殑璁板綍錛屽惁鍒欎笉浜ゆ崲銆傜戶緇k2鍜宬3閲嶅涓婅堪榪囩▼錛岀洿鍒板鐞嗗畬kn-1鍜宬n銆傝繖鏃舵渶澶х殑鎺掑簭鐮佽褰曡漿鍒頒簡鏈鍚庝綅緗紝縐扮1嬈¤搗娉★紝鍏辨墽琛宯-1嬈℃瘮杈冦?br /> 涓庣涓姝ョ被浼鹼紝浠巏1鍜宬2寮濮嬫瘮杈冿紝鍒発n-2鍜宬n-1涓烘錛屽叡鎵цn-2嬈℃瘮杈冦?br /> 渚濇綾繪帹錛屽叡鍋歯-1嬈¤搗娉★紝瀹屾垚鏁翠釜鎺掑簭榪囩▼銆?br /> 鑻ユ枃浠剁殑鍒濆鐘舵佹槸姝e簭鐨勶紝涓瓚熸壂鎻忓嵆鍙畬鎴愭帓搴忋傛墍闇鍏抽敭瀛楁瘮杈冩鏁頒負n-1嬈★紝璁板綍縐誨姩嬈℃暟涓?銆傚洜姝わ紝鍐掓場鎺掑簭鏈濂界殑鏃墮棿澶嶆潅搴︿負O(n)銆?br />
鑻ュ垵濮嬫枃浠舵槸鍙嶅簭鐨勶紝闇瑕佽繘琛宯-1瓚熸帓搴忋傛瘡瓚熸帓搴忚榪涜n-i嬈″叧閿瓧鐨勬瘮杈?1<=i<=n-1),涓旀瘡嬈℃瘮杈冮兘蹇呴』縐誨姩璁板綍涓夋鏉ヨ揪
鍒頒氦鎹㈣褰曚綅緗傚湪榪欑鎯呭喌涓嬶紝姣旇緝嬈℃暟杈懼埌鏈澶у糿(n-1)/2=O(n^2),縐誨姩嬈℃暟涔熻揪鍒版渶澶у?n(n-1)/2=O(n^2)銆傚洜姝わ紝鍐掓場
鎺掑簭鐨勬渶鍧忔椂闂村鏉傚害涓篛(n^2)銆?br /> 铏界劧鍐掓場鎺掑簭涓嶄竴瀹氳榪涜n-1瓚燂紝浣嗙敱浜庡畠鐨勮褰曠Щ鍔ㄦ鏁拌緝澶氾紝鏁呭鉤鍧囨ц兘姣旂洿鎺ユ彃鍏ユ帓搴忚宸緱澶氥傚啋娉℃帓搴忔槸灝卞湴鎺掑簭錛屼笖瀹冩槸紼沖畾鐨勩?br />
浠g爜濡備笅:
void QP(int A[],int n) //浼樺寲鐨勫啋娉℃帓搴?
{
int count=0,t,flag;
for(int i=0;i<n-1;i++)
{
flag=0;
for(int j=0;j<n-i;j++)
{
if(A[j+1]<A[j])
{
t=A[j];
A[j]=A[j+1];
A[j+1]=t;
flag=1;
count+=3;
}
}
if(flag==0) break;
}
}
②.蹇熸帓搴忥細(涓嶇ǔ瀹氱殑)
浠g爜濡備笅:
void Quick_Sort(int A[],int low,int high) //low鍜宧igh鏄暟緇勭殑涓嬫爣
{
if(low<high)
{
int temp,t=A[low];
int l=low,h=high;
while(l<h)
{
while(A[l]<t) l++;
while(A[h]>=t) h--;
if(h>l)
{
temp=A[l];
A[l]=A[h];
A[h]=temp;
}
}
Quick_Sort(A,low,l-1);
Quick_Sort(A,l+1,high);
}
}
褰掑茍鎺掑簭鏄皢涓や釜鎴栦袱涓互涓婄殑鏈夊簭瀛愯〃鍚堝茍鎴愪竴涓柊鐨勬湁搴忚〃銆傚垵濮嬫椂錛屾妸鍚湁n涓粨鐐圭殑寰呮帓搴忓簭鍒楃湅浣滅敱n涓暱搴﹂兘涓?鐨勬湁搴忓瓙琛ㄧ粍鎴愶紝灝嗗畠浠緷嬈′袱涓ゅ綊騫跺緱鍒伴暱搴︿負2鐨勮嫢騫叉湁搴忓瓙琛紝鍐嶅瀹冧滑涓や袱鍚堝茍銆傜洿鍒板緱鍒伴暱搴︿負n鐨勬湁搴忚〃錛屾帓搴忕粨鏉熴?br />
褰掑茍鎺掑簭鏄竴縐嶇ǔ瀹氱殑鎺掑簭錛屽彲鐢ㄩ『搴忓瓨鍌ㄧ粨鏋勶紝涔熸槗浜庡湪閾捐〃涓婂疄鐜幫紝瀵歸暱搴︿負n鐨勬枃浠訛紝闇榪涜log2n瓚熶簩璺綊騫訛紝姣忚稛褰掑茍鐨勬椂闂翠負O(n),鏁呭叾鏃墮棿
澶嶆潅搴︽棤璁烘槸鍦ㄦ渶濂芥儏鍐典笅榪樻槸鍦ㄦ渶鍧忔儏鍐典笅鍧囨槸O(nlog2n)銆傚綊騫舵帓搴忛渶瑕佷竴涓緟鍔╁悜閲忔潵鏆傚瓨涓や釜鏈夊簭瀛愭枃浠跺綊騫剁殑緇撴灉錛屾晠鍏惰緟鍔╃┖闂村鏉傚害涓?
O(n),鏄劇劧瀹冧笉鏄氨鍦版帓搴忋?br />
浠g爜鐣?..
=================================
浜?鍩烘暟鎺掑簭
璁懼崟鍏抽敭瀛楃殑姣忎釜鍒嗛噺鐨勫彇鍊艱寖鍥村潎鏄疌0<=Kj<=Crd-1(0<=j<=rd),鍙兘鐨勫彇鍊間釜鏁皉d縐頒負鍩烘暟錛庡熀鏁扮殑閫夋嫨鍜屽叧閿瓧鐨勫垎瑙e洜鍏抽敭瀛楃殑綾誨瀷鑰屽紓錛?br />銆銆(1).鑻ュ叧閿瓧鏄崄榪涘埗鏁存暟錛屽垯鎸変釜銆佸崄絳変綅榪涜鍒嗚В錛屽熀鏁皉d=10,C0=0,C9=9,d涓烘渶闀挎暣鏁扮殑浣嶆暟錛?br />銆銆(2).鑻ュ叧閿瓧鏄皬鍐欑殑鑻辨枃瀛楃涓詫紝鍒檙d=26,C0='a',C25='z',d涓烘渶闀垮瓧絎︿覆鐨勯暱搴︼紟
銆銆鍩烘暟鎺掑簭鐨勫熀鏈濇兂鏄細浠庝綆浣嶅埌楂樹綅渚濇瀵瑰緟鎺掑簭鐨勫叧閿爜榪涜鍒嗛厤鍜屾敹闆嗭紝緇忚繃d瓚熷垎閰嶅拰鏀墮泦錛屽氨鍙互寰楀埌涓涓湁搴忓簭鍒楋紟
錛?錛夊鉤鏂歸樁(O(n2))鎺掑簭
銆涓鑸О涓虹畝鍗曟帓搴忥紝渚嬪鐩存帴鎻掑叆銆佺洿鎺ラ夋嫨鍜屽啋娉℃帓搴忥紱
錛?錛夌嚎鎬у鏁伴樁(O(nlgn))鎺掑簭
銆濡傚揩閫熴佸爢鍜屽綊騫舵帓搴忥紱
錛?錛塐(n1+錕?闃舵帓搴?br /> 銆錕℃槸浠嬩簬0鍜?涔嬮棿鐨勫父鏁幫紝鍗?<錕?lt;1錛屽甯屽皵鎺掑簭錛?br />錛?錛夌嚎鎬ч樁(O(n))鎺掑簭
銆濡傚熀鏁版帓搴忋?br />
鍚勭鎺掑簭鏂規硶姣旇緝
綆鍗曟帓搴忎腑鐩存帴鎻掑叆鏈濂斤紝蹇熸帓搴忔渶蹇紝褰撴枃浠朵負姝e簭鏃訛紝鐩存帴鎻掑叆鍜屽啋娉″潎鏈浣熾?br />
褰卞搷鎺掑簭鏁堟灉鐨勫洜绱?/strong>
銆鍥犱負涓嶅悓鐨勬帓搴忔柟娉曢傚簲涓嶅悓鐨勫簲鐢ㄧ幆澧冨拰瑕佹眰錛屾墍浠ラ夋嫨鍚堥傜殑鎺掑簭鏂規硶搴旂患鍚堣冭檻涓嬪垪鍥犵礌錛?br />銆銆①寰呮帓搴忕殑璁板綍鏁扮洰n錛?br />銆銆②璁板綍鐨勫ぇ灝?瑙勬ā)錛?br />銆銆③鍏抽敭瀛楃殑緇撴瀯鍙婂叾鍒濆鐘舵侊紱
銆銆④瀵圭ǔ瀹氭х殑瑕佹眰錛?br />銆銆⑤璇█宸ュ叿鐨勬潯浠訛紱
銆銆⑥瀛樺偍緇撴瀯錛?br />銆銆⑦鏃墮棿鍜岃緟鍔╃┖闂村鏉傚害絳夈?br />
涓嶅悓鏉′歡涓嬶紝鎺掑簭鏂規硶鐨勯夋嫨
(1)鑻杈冨皬(濡俷≤50)錛屽彲閲囩敤鐩存帴鎻掑叆鎴栫洿鎺ラ夋嫨鎺掑簭銆?br /> 銆褰撹褰曡妯¤緝灝忔椂錛岀洿鎺ユ彃鍏ユ帓搴忚緝濂斤紱鍚﹀垯鍥犱負鐩存帴閫夋嫨縐誨姩鐨勮褰曟暟灝戜簬鐩存帴鎻掍漢錛屽簲閫夌洿鎺ラ夋嫨鎺掑簭涓哄疁銆?br />(2)鑻ユ枃浠跺垵濮嬬姸鎬佸熀鏈湁搴?鎸囨搴?錛屽垯搴旈夌敤鐩存帴鎻掍漢銆佸啋娉℃垨闅忔満鐨勫揩閫熸帓搴忎負瀹滐紱
(3)鑻杈冨ぇ錛屽垯搴旈噰鐢ㄦ椂闂村鏉傚害涓篛(nlgn)鐨勬帓搴忔柟娉曪細蹇熸帓搴忋佸爢鎺掑簭鎴?br />褰掑茍鎺掑簭銆?br /> 蹇熸帓搴忔槸鐩墠鍩轟簬姣旇緝鐨勫唴閮ㄦ帓搴忎腑琚涓烘槸鏈濂界殑鏂規硶錛屽綋寰呮帓搴忕殑鍏抽敭瀛楁槸闅忔満鍒嗗竷鏃訛紝蹇熸帓搴忕殑騫沖潎鏃墮棿鏈鐭紱
鍫嗘帓搴忔墍闇鐨勮緟鍔╃┖闂村皯浜庡揩閫熸帓搴忥紝騫朵笖涓嶄細鍑虹幇蹇熸帓搴忓彲鑳藉嚭鐜扮殑鏈鍧忔儏鍐點傝繖涓ょ鎺掑簭閮芥槸涓嶇ǔ瀹氱殑銆?br />
鑻ヨ姹傛帓搴忕ǔ瀹氾紝鍒欏彲閫夌敤褰掑茍鎺掑簭銆備絾浠庡崟涓褰曡搗榪涜涓や袱褰掑茍鐨?nbsp;
鎺掑簭綆楁硶騫朵笉鍊煎緱鎻愬★紝閫氬父鍙互灝嗗畠鍜岀洿鎺ユ彃鍏ユ帓搴忕粨鍚堝湪涓璧蜂嬌鐢ㄣ傚厛鍒╃敤鐩存帴鎻掑叆鎺掑簭姹傚緱杈冮暱鐨勬湁搴忓瓙鏂囦歡錛岀劧鍚庡啀涓や袱褰掑茍涔嬨傚洜涓虹洿鎺ユ彃鍏ユ帓搴忔槸紼沖畾
鐨勶紝鎵浠ユ敼榪涘悗鐨勫綊騫舵帓搴忎粛鏄ǔ瀹氱殑銆?/font>
鐒跺悗鍦ㄥ墿涓嬬殑鏁板綋涓啀鎵炬渶灝忕殑涓庣浜屼釜浣嶇疆鐨勬暟浜ゆ崲錛屽姝ゅ驚鐜?br />鍒板掓暟絎簩涓暟鍜屾渶鍚庝竴涓暟姣旇緝涓烘銆?
{
int i, j, min, t;
{
min = i; /*鍋囪褰撳墠涓嬫爣涓篿鐨勬暟鏈灝忥紝姣旇緝鍚庡啀璋冩暣*/
for (j=i+1; j<n; j++)/*寰幆鎵懼嚭鏈灝忕殑鏁扮殑涓嬫爣鏄摢涓?/
{
if (*(x+j) < *(x+min))
{
min = j; /*濡傛灉鍚庨潰鐨勬暟姣斿墠闈㈢殑灝忥紝鍒欒涓嬪畠鐨勪笅鏍?/
}
}
if (min != i) /*濡傛灉min鍦ㄥ驚鐜腑鏀瑰彉浜嗭紝灝遍渶瑕佷氦鎹㈡暟鎹?/
{
t = *(x+i);
*(x+i) = *(x+min);
*(x+min) = t;
}
}
}
濂介『搴忕殑錛岀幇鍦ㄨ鎶婄n涓暟鎻掑埌鍓嶉潰鐨勬湁搴忔暟涓紝浣垮緱榪檔涓暟
涔熸槸鎺掑ソ欏哄簭鐨勩傚姝ゅ弽澶嶅驚鐜紝鐩村埌鍏ㄩ儴鎺掑ソ欏哄簭銆?br />
鐩存帴鎻掑叆鎺掑簭鏄ǔ瀹氱殑銆傜畻娉曟椂闂村鏉傚害O(n2)--[n鐨勫鉤鏂筣
{
int i, j, t;
{
/*
鏆傚瓨涓嬫爣涓篿鐨勬暟銆傛敞鎰忥細涓嬫爣浠?寮濮嬶紝鍘熷洜灝辨槸寮濮嬫椂
絎竴涓暟鍗充笅鏍囦負0鐨勬暟錛屽墠闈㈡病鏈変換浣曟暟錛屽崟鍗曚竴涓紝璁や負
瀹冩槸鎺掑ソ欏哄簭鐨勩?br /> */
t=*(x+i);
for (j=i-1; j>=0 && t<*(x+j); j--) /*娉ㄦ剰錛歫=i-1錛宩--錛岃繖閲屽氨鏄笅鏍囦負i鐨勬暟錛屽湪瀹冨墠闈㈡湁搴忓垪涓壘鎻掑叆浣嶇疆銆?/
{
*(x+j+1) = *(x+j); /*濡傛灉婊¤凍鏉′歡灝卞線鍚庢尓銆傛渶鍧忕殑鎯呭喌灝辨槸t姣斾笅鏍囦負0鐨勬暟閮藉皬錛屽畠瑕佹斁鍦ㄦ渶鍓嶉潰錛宩==-1錛岄鍑哄驚鐜?/
}
}
}
灝忕殑寰涓婂啋銆傚嵆錛氭瘡褰撲袱鐩擱偦鐨勬暟姣旇緝鍚庡彂鐜板畠浠殑鎺掑簭涓庢帓搴忚
姹傜浉鍙嶆椂錛屽氨灝嗗畠浠簰鎹€?br />
涓嬮潰鏄竴縐嶆敼榪涚殑鍐掓場綆楁硶錛屽畠璁板綍浜嗘瘡涓閬嶆壂鎻忓悗鏈鍚庝笅娌夋暟鐨?br />浣嶇疆k錛岃繖鏍峰彲浠ュ噺灝戝灞傚驚鐜壂鎻忕殑嬈℃暟銆?/strong>
{
int j, k, h, t;
for (h=n-1; h>0; h=k) /*寰幆鍒版病鏈夋瘮杈冭寖鍥?/
{
for (j=0, k=0; j<h; j++) /*姣忔棰勭疆k=0錛屽驚鐜壂鎻忓悗鏇存柊k*/
{
if (*(x+j) > *(x+j+1)) /*澶х殑鏀懼湪鍚庨潰錛屽皬鐨勬斁鍒板墠闈?/
{
t = *(x+j);
*(x+j) = *(x+j+1);
*(x+j+1) = t; /*瀹屾垚浜ゆ崲*/
k = j; /*淇濆瓨鏈鍚庝笅娌夌殑浣嶇疆銆傝繖鏍穔鍚庨潰鐨勯兘鏄帓搴忔帓濂戒簡鐨勩?/
}
}
}
}
甯屽皵鎺掑簭
鍦ㄧ洿鎺ユ彃鍏ユ帓搴忕畻娉曚腑錛屾瘡嬈℃彃鍏ヤ竴涓暟錛屼嬌鏈夊簭搴忓垪鍙鍔?涓妭鐐癸紝
騫朵笖瀵規彃鍏ヤ笅涓涓暟娌℃湁鎻愪緵浠諱綍甯姪銆傚鏋滄瘮杈冪浉闅旇緝榪滆窛紱伙紙縐頒負
澧為噺錛夌殑鏁幫紝浣垮緱鏁扮Щ鍔ㄦ椂鑳借法榪囧涓厓绱狅紝鍒欒繘琛屼竴嬈℃瘮杈冨氨鍙兘娑堥櫎
澶氫釜鍏冪礌浜ゆ崲銆侱.L.shell浜?959騫村湪浠ヤ粬鍚嶅瓧鍛藉悕鐨勬帓搴忕畻娉曚腑瀹炵幇
浜嗚繖涓鎬濇兂銆傜畻娉曞厛灝嗚鎺掑簭鐨勪竴緇勬暟鎸夋煇涓閲廳鍒嗘垚鑻ュ共緇勶紝姣忕粍涓?br />璁板綍鐨勪笅鏍囩浉宸甦.瀵規瘡緇勪腑鍏ㄩ儴鍏冪礌榪涜鎺掑簭錛岀劧鍚庡啀鐢ㄤ竴涓緝灝忕殑澧為噺
瀵瑰畠榪涜錛屽湪姣忕粍涓啀榪涜鎺掑簭銆傚綋澧為噺鍑忓埌1鏃訛紝鏁翠釜瑕佹帓搴忕殑鏁拌鍒嗘垚
涓緇勶紝鎺掑簭瀹屾垚銆?br />
涓嬮潰鐨勫嚱鏁版槸涓涓笇灝旀帓搴忕畻娉曠殑涓涓疄鐜幫紝鍒濇鍙栧簭鍒楃殑涓鍗婁負澧為噺錛?br />浠ュ悗姣忔鍑忓崐錛岀洿鍒板閲忎負1銆?/strong>
{
int h, j, k, t;
{
for (j=h; j<n; j++) /*榪欎釜瀹為檯涓婂氨鏄笂闈㈢殑鐩存帴鎻掑叆鎺掑簭*/
{
t = *(x+j);
for (k=j-h; (k>=0 && t<*(x+k)); k-=h)
{
*(x+k+h) = *(x+k);
}
*(x+k+h) = t;
}
}
}
蹇熸帓搴?/strong>
鍑忓皯1銆傚揩閫熸帓搴忛氳繃涓瓚熸壂鎻忥紝灝辮兘紜繚鏌愪釜鏁幫紙浠ュ畠涓哄熀鍑嗙偣鍚э級
鐨勫乏杈瑰悇鏁伴兘姣斿畠灝忥紝鍙寵竟鍚勬暟閮芥瘮瀹冨ぇ銆傜劧鍚庡張鐢ㄥ悓鏍風殑鏂規硶澶勭悊
瀹冨乏鍙充袱杈圭殑鏁幫紝鐩村埌鍩哄噯鐐圭殑宸﹀彸鍙湁涓涓厓绱犱負姝€傚畠鏄敱
C.A.R.Hoare浜?962騫存彁鍑虹殑銆?br />
鏄劇劧蹇熸帓搴忓彲浠ョ敤閫掑綊瀹炵幇錛屽綋鐒朵篃鍙互鐢ㄦ爤鍖栬В閫掑綊瀹炵幇銆備笅闈㈢殑
鍑芥暟鏄敤閫掑綊瀹炵幇鐨勶紝鏈夊叴瓚g殑鏈嬪弸鍙互鏀規垚闈為掑綊鐨勩?/strong>
void quick_sort(int *x, int low, int high)
{
int i, j, t;
{
i = low;
j = high;
t = *(x+low); /*鏆傚瓨鍩哄噯鐐圭殑鏁?/
{
while (i<j && *(x+j)>t) /*鍦ㄥ彸杈圭殑鍙姣斿熀鍑嗙偣澶т粛鏀懼湪鍙寵竟*/
{
j--; /*鍓嶇Щ涓涓綅緗?/
}
{
*(x+i) = *(x+j); /*涓婇潰鐨勫驚鐜鍑猴細鍗沖嚭鐜版瘮鍩哄噯鐐瑰皬鐨勬暟錛屾浛鎹㈠熀鍑嗙偣鐨勬暟*/
i++; /*鍚庣Щ涓涓綅緗紝騫朵互姝や負鍩哄噯鐐?/
}
{
i++; /*鍚庣Щ涓涓綅緗?/
}
{
*(x+j) = *(x+i); /*涓婇潰鐨勫驚鐜鍑猴細鍗沖嚭鐜版瘮鍩哄噯鐐瑰ぇ鐨勬暟錛屾斁鍒板彸杈?/
j--; /*鍓嶇Щ涓涓綅緗?/
}
}
quick_sort(x,low,i-1); /*瀵瑰熀鍑嗙偣宸﹁竟鐨勬暟鍐嶆墽琛屽揩閫熸帓搴?/
quick_sort(x,i+1,high); /*瀵瑰熀鍑嗙偣鍙寵竟鐨勬暟鍐嶆墽琛屽揩閫熸帓搴?/
}
}
婊¤凍錛坔i>=h2i,hi>=2i+1錛夋垨錛坔i<=h2i,hi<=2i+1錛?i=1,2,...,n/2)
鏃剁О涔嬩負鍫嗐傚湪榪欓噷鍙璁烘弧瓚沖墠鑰呮潯浠剁殑鍫嗐?/strong>
寰堢洿瑙傚湴琛ㄧず鍫嗙殑緇撴瀯銆傚爢欏朵負鏍癸紝鍏跺畠涓哄乏瀛愭爲銆佸彸瀛愭爲銆?br />鍒濆鏃舵妸瑕佹帓搴忕殑鏁扮殑搴忓垪鐪嬩綔鏄竴媯甸『搴忓瓨鍌ㄧ殑浜屽弶鏍戯紝璋冩暣瀹冧滑鐨勫瓨鍌ㄩ『搴忥紝
浣夸箣鎴愪負涓涓爢錛岃繖鏃跺爢鐨勬牴鑺傜偣鐨勬暟鏈澶с傜劧鍚庡皢鏍硅妭鐐逛笌鍫嗙殑鏈鍚庝竴涓妭鐐?br />浜ゆ崲銆傜劧鍚庡鍓嶉潰(n-1)涓暟閲嶆柊璋冩暣浣夸箣鎴愪負鍫嗐備緷姝ょ被鎺紝鐩村埌鍙湁涓や釜鑺傜偣
鐨勫爢錛屽茍瀵瑰畠浠綔浜ゆ崲錛屾渶鍚庡緱鍒版湁n涓妭鐐圭殑鏈夊簭搴忓垪銆?/strong>
void sift(int *x, int n, int s)
{
int t, k, j;
k = s; /*寮濮嬪厓绱犱笅鏍?/
j = 2*k + 1; /*鍙沖瓙鏍戝厓绱犱笅鏍?/
{
if (j<n-1 && *(x+j) < *(x+j+1))/*鍒ゆ柇鏄惁婊¤凍鍫嗙殑鏉′歡錛氭弧瓚沖氨緇х畫涓嬩竴杞瘮杈冿紝鍚﹀垯璋冩暣銆?/
{
j++;
}
{
*(x+k) = *(x+j);
k = j; /*璋冩暣鍚庯紝寮濮嬪厓绱犱篃闅忎箣璋冩暣*/
j = 2*k + 1;
}
else /*娌℃湁闇瑕佽皟鏁翠簡錛屽凡緇忔槸涓爢浜嗭紝閫鍑哄驚鐜?/
{
break;
}
}
*(x+k) = t; /*寮濮嬪厓绱犳斁鍒板畠姝g‘浣嶇疆*/
}
void heap_sort(int *x, int n)
{
int i, k, t;
int *p;
{
sift(x,n,i); /*鍒濆寤哄爢*/
}
for (k=n-1; k>=1; k--)
{
t = *(x+0); /*鍫嗛《鏀懼埌鏈鍚?/
*(x+0) = *(x+k);
*(x+k) = t;
sift(x,k,0); /*鍓╀笅鐨勬暟鍐嶅緩鍫?/
}
}
void main()
{
#define MAX 4
int *p, i, a[MAX];
/*褰曞叆嫻嬭瘯鏁版嵁*/
p = a;
printf("Input %d number for sorting :\n",MAX);
for (i=0; i<MAX; i++)
{
scanf("%d",p++);
}
printf("\n");
p = a;
select_sort(p,MAX);
/**/
/*嫻嬭瘯鐩存帴鎻掑叆鎺掑簭*/
p = a;
insert_sort(p,MAX);
*/
/*嫻嬭瘯鍐掓場鎺掑簭*/
p = a;
insert_sort(p,MAX);
*/
p = a;
quick_sort(p,0,MAX-1);
*/
p = a;
heap_sort(p,MAX);
*/
{
printf("%d ",*p++);
}
printf("\n");
system("pause");
]]>