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涓涓暟錛屽鏋滃彧鏈?鍜屽畠鏈韓涓や釜鍥犳暟錛岃繖鏍風殑鏁板彨鍋氳川鏁幫紝鍙堢О绱犳暟銆?/p>
鍦ㄤ笂鏂?銆?a target=_blank>绱犳暟綆楁硶澶у叏錛屽強C紼嬪簭瀹炵幇浼樺寲璇﹁В (涓) 璇曢櫎娉?/a>銆嬩腑鎴戜滑宸茬粡鎺㈣浜嗘眰瑙g礌鏁扮殑涓綾葷畻娉曪紝騫朵笖灝嗚瘯闄ゆ硶浠庢渶鍒濈殑浣庢晥鐗堟湰浼樺寲鐨勯珮鏁堢殑V2銆傞偅涔堬紝榪樻湁娌℃湁鍏跺畠鏇翠匠綆楁硶鍛紵榪欏氨鏄笅闈笁钘忚鍜屽ぇ瀹舵帰璁ㄧ殑鍐呭
鍚堟暟榪囨護絳涢夋硶
綆楁硶鎻忚堪錛氭垜浠煡閬擄紝绱犳暟N涓嶈兘琚?~(N-1)闂寸殑浠諱綍鏁版暣闄わ紱鍙嶈繃鏉ョ湅錛屽彧瑕佽兘琚?~(N-1)闂寸殑浠諱綍鏁版暣闄ょ殑N錛岄兘涓嶆槸绱犳暟銆傛墍浠ユ垜浠彲浠ラ噰鐢ㄤ竴涓畝鍗曠殑鎺掗櫎娉曪細灝辨槸瀵筃浠ュ唴鐨勬墍鏈夋暟錛屽彧瑕侀愪釜鍘婚櫎鍊間負2~(N-1)鐨勫嶆暟鐨勬暟錛屽墿涓嬬殑灝辨槸绱犳暟銆?/p>
C璇█瀹炵幇
// 鍚堟暟榪囨護絳涢夋硶 Ver1
// 鍙傛暟錛歯 姹傝Вn浠ュ唴(鍖呮嫭n)鐨勭礌鏁?br>// 榪斿洖鍊鹼細n浠ュ唴绱犳暟涓暟
int CompositeNumFilterV1(int n)
{
int i, j;
// 绱犳暟鏁伴噺緇熻
int count = 0;
// 鍒嗛厤绱犳暟鏍囪絀洪棿錛岀粨鍚堝悗鏂囨濊冧負浣?1
char* flag = (char*)malloc( n+1 );
// 鍒濆鍖栫礌鏁版爣璁?
for (i=2; i<=n; i++)
{
// 涓轟粈涔?(p+i)瑕佸啓鎴恌lag[i]鍛紵鍙鎬ф洿浣沖皵
flag[i] = 1;
}
// 鍐欑▼搴忚娉ㄦ剰鎺掔増鍜岀暀絀猴紝鏂逛究闃呰錛屼篃鍙噺灝戝嚭閿欏嚑鐜?br> // 浠?~(N-1)涓哄洜瀛愯繃婊ゅ悎鏁?
for (i=2; i < n; i++)
{
for (j=2; i*j <= n; j++)
{
// i*j鏄敱i,j涓ゆ暣鏁扮浉涔樿屽緱錛屾樉鐒朵笉鏄礌鏁?br> flag[i*j] = 0;
}
}
// 緇熻绱犳暟涓暟
for (i=2; i<=n; i++)
{
// 鍏跺疄if(flag)灝卞叾鍚屾牱浣滅敤浜嗭紝浣嗚繖涔堝啓鏄湁鐣欒█鐨?
// 璇峰弬闃呫奀璇█紼嬪簭璁捐甯歌閿欒鍓栨瀽鍙婅В鍐充箣閬撱嬩竴鏂?
if (1 == flag[i]) count++;
}
// 鍥犺緭鍑鴻垂鏃訛紝涓斿拰綆楁硶鏍稿績鐩稿叧涓嶅ぇ錛屾晠鐣?br>
// 閲婃斁鍐呭瓨錛屽埆蹇樹簡浼犺涓殑鍐呭瓨娉勬紡
free(flag);
return count;
}
鍦ㄤ笂鏂囩粰鍑虹殑main鍑芥暟涓互涓嶅悓鍙傛暟璋冪敤CompositeNumFilterV1鍑芥暟錛屽緱鍒版墽琛岀粨鏋滃涓嬶細
[100000]浠ュ唴绱犳暟涓暟錛?592, 璁$畻鐢ㄦ椂錛?5姣
[1000000]浠ュ唴绱犳暟涓暟錛?8498, 璁$畻鐢ㄦ椂錛?25姣
[5000000]浠ュ唴绱犳暟涓暟錛?48513, 璁$畻鐢ㄦ椂錛?578姣
[10000000]浠ュ唴绱犳暟涓暟錛?64579, 璁$畻鐢ㄦ椂錛?281姣
娉細鍥犵▼搴忔槸闈炵嫭鍗犳ц繍琛岀殑錛屾墍浠ユ椂闂翠笉鏄畬鍏ㄧ簿紜殑錛屼絾鍩烘湰鑳藉弽鏄犲疄鎯?/p>
鏄劇劧錛屾瘮涓婃枃涓殑璇曢櫎娉曡蹇紝鑰屼笖璋侀兘鍙互鐪嬪埌涓婁緥鏄竴涓湭緇忎紭鍖栫殑綺楅檵鐗堟湰錛屽ソ澶氬湴鏂規槸涓夎棌鏁呮剰閲囩敤姣旇緝浣庢晥鍋氭硶錛屼負浜嗕笌鍚庢枃鐨勪紭鍖栫増姣旇緝錛屽嚫鏄句紭鍖栦箣閲嶈錛屼篃涓轟簡鍒濆鑰呰浣忓埆閲囩敤綾諱技浣庢晥鍋氭硶錛屼笅闈㈡垜浠紑濮嬩紭鍖栦箣鏃?/p>
浼樺寲鍒嗘瀽
涓婇潰CompositeNumFilterV1鍑芥暟瀛樺湪鐨勯棶棰樻湁錛?/p>
鎹笂榪板垎鏋愶紝鎴戜滑鍙皢紼嬪簭浼樺寲濡備笅錛?/p>
// 鍚堟暟榪囨護絳涢夋硶 Ver2
// 鍙傛暟錛歯 姹傝Вn浠ュ唴(鍖呮嫭n)鐨勭礌鏁?br>// 榪斿洖鍊鹼細n浠ュ唴绱犳暟涓暟
int CompositeNumFilterV2(int n)
{
int i, j;
// 绱犳暟鏁伴噺緇熻
int count = 0;
// 鍒嗛厤绱犳暟鏍囪絀洪棿錛屾槑鐧?1鍘熷洜浜嗗惂錛屽洜涓烘氮璐逛簡涓涓猣lag[0]
char* flag = (char*)malloc( n+1 );
// 鍒濆鍖栫礌鏁版爣璁幫紝瑕侀珮鏁堢偣鍜?br> flag[2] = 1;
// 娉ㄦ剰鏄痠<n涓嶆槸涓婁緥涓殑i<=n浜嗭紝鐞嗙敱鑷?
for (i=3; i<n; i++)
{
flag[i++] = 1;
// 鍋舵暟鑷劧涓嶆槸绱犳暟錛岀洿鎺ョ疆0濂戒簡
flag[i] = 0;
}
// n涓哄鏁?
if (n%2 != 0)
{
flag[n] = 1;
}
// 浠?寮濮媐ilter錛屽洜涓?鐨勫嶆暟鏃╁湪鍒濆鍖栨椂浠e氨騫叉帀浜?br> // 鍒皀/2姝㈢殑鐞嗙敱榪樿璇村悧
for (i=3; i <= n/2; i++)
{
// i鏄悎鏁幫紝璇鋒瓏鐫鍚э紝鍥犱負鎮ㄧ殑宸ヤ綔鏃╂湁鎮ㄧ殑璐ㄥ洜瀛愪唬鍔充簡
if (0 == flag[i]) continue;
// 浠巌鐨?鍊嶅紑濮嬭繃婊わ紝鍙樹箻娉曚負鍔犳硶
for (j=i+i; j <= n; j+=i)
{
flag[j] = 0;
}
}
// 緇熻绱犳暟涓暟
for (i=2; i<=n; i++)
{
if (flag[i]) count++;
}
// 鍥犺緭鍑鴻垂鏃訛紝涓斿拰綆楁硶鏍稿績鐩稿叧涓嶅ぇ錛屾晠鐣?br>
// 閲婃斁鍐呭瓨錛屽埆蹇樹簡浼犺涓殑鍐呭瓨娉勬紡
free(flag);
return count;
}
鍐嶆潵璋冪敤CompositeNumFilterV2寰楀埌鎵ц緇撴灉錛?/p>
[100000]浠ュ唴绱犳暟涓暟錛?592, 璁$畻鐢ㄦ椂錛歯澶皬錛屾椂闂寸簿搴︿笉澶?br>[1000000]浠ュ唴绱犳暟涓暟錛?8498, 璁$畻鐢ㄦ椂錛?1姣
[5000000]浠ュ唴绱犳暟涓暟錛?48513, 璁$畻鐢ㄦ椂錛?53姣
[10000000]浠ュ唴绱犳暟涓暟錛?64579, 璁$畻鐢ㄦ椂錛?062姣
[100000000]浠ュ唴绱犳暟涓暟錛?761455, 璁$畻鐢ㄦ椂錛?2973姣
鍝囧搰錛屾瘮鏄ㄥぉ鐨勮瘯闄ゅ彂蹇簡濂藉鍊嶏紝鍙綆楁硶鐨勫▉鍔涳紝鍊煎緱濂藉ソ瀛︿範錛屽埆璇村綆楁硶娌$敤鍜?/p>
涓婁緥鐫閭d釜璁$畻涓浜夸互鍐呯殑绱犳暟鍙綰?3縐掞紝搴旇綆椾笉閿欎簡錛屼粖澶╂槸鍚﹀彲浠ヤ紤鎭簡鍛紵No錛屾垜浠榪芥眰鏋侀檺錛?/p>
int CompositeNumFilterV3(int n)
{
int i, j;
// 绱犳暟鏁伴噺緇熻
int count = 0;
// 鍒嗛厤绱犳暟鏍囪絀洪棿錛屾槑鐧?1鍘熷洜浜嗗惂錛屽洜涓烘氮璐逛簡涓涓猣lag[0]
char* flag = (char*)malloc( n+1 );
// 騫插槢鐢ㄧ殑錛岃浠旂粏鐮旂┒涓嬫枃
int mpLen = 2*3*5*7*11*13;
char magicPattern[mpLen];
// 濂囨殑浠g爜錛寃hy錛屾濊冩棤娉曚唬鍔籌紝鎯籌紒
for (i=0; i<mpLen; i++)
{
magicPattern[i++] = 1;
magicPattern[i++] = 0;
magicPattern[i++] = 0;
magicPattern[i++] = 0;
magicPattern[i++] = 1;
magicPattern[i] = 0;
}
for (i=4; i<=mpLen; i+=5)
magicPattern[i] = 0;
for (i=6; i<=mpLen; i+=7)
magicPattern[i] = 0;
for (i=10; i<=mpLen; i+=11)
magicPattern[i] = 0;
for (i=12; i<=mpLen; i+=13)
magicPattern[i] = 0;
// 鏂扮殑鍒濆鍖栨柟娉?灝?,3,5,7,11,13鐨勫嶆暟鍏ㄥ共鎺?br> // 鑰屼笖閲囩敤memcpy浠pLen闀跨殑magicPattern鏉ユ壒閲忓鐞?
int remainder = n%mpLen;
char* p = flag+1;
char* pstop = p+n-remainder;
while (p < pstop)
{
memcpy(p, magicPattern, mpLen);
p += mpLen;
}
if (remainder > 0)
{
memcpy(p, magicPattern, remainder);
}
flag[2] = 1;
flag[3] = 1;
flag[5] = 1;
flag[7] = 1;
flag[11] = 1;
flag[13] = 1;
// 浠?7寮濮媐ilter錛屽洜涓?,3,5,7,11,13鐨勫嶆暟鏃╄kill浜?
// 鍒皀/13姝㈢殑錛屽搱鍝堬紝灝戜簡濂藉鍚?br> int stop = n/13;
for (i=17; i <= stop; i++)
{
// i鏄悎鏁幫紝璇鋒瓏鐫鍚э紝鍥犱負鎮ㄧ殑宸ヤ綔鏃╂湁鎮ㄧ殑璐ㄥ洜瀛愪唬鍔充簡
if (0 == flag[i]) continue;
// 浠巌鐨?7鍊嶅紑濮嬭繃婊?br> int step = i*2;
for (j=i*17; j <= n; j+=step)
{
flag[j] = 0;
}
}
// 緇熻绱犳暟涓暟
for (i=2; i<=n; i++)
{
if (flag[i]) count++;
}
// 鍥犺緭鍑鴻垂鏃訛紝涓斿拰綆楁硶鏍稿績鐩稿叧涓嶅ぇ錛屾晠鐣?br>
// 閲婃斁鍐呭瓨錛屽埆蹇樹簡浼犺涓殑鍐呭瓨娉勬紡
free(flag);
return count;
}
鍐嶇湅CompositeNumFilterV3鎵ц緇撴灉錛?/p>
[1000000]浠ュ唴绱犳暟涓暟錛?8498, 璁$畻鐢ㄦ椂錛?5姣
[5000000]浠ュ唴绱犳暟涓暟錛?48513, 璁$畻鐢ㄦ椂錛?03姣
[10000000]浠ュ唴绱犳暟涓暟錛?64579, 璁$畻鐢ㄦ椂錛?15姣
[100000000]浠ュ唴绱犳暟涓暟錛?761455, 璁$畻鐢ㄦ椂錛?421姣
鍐嶆浼樺寲鍚庨熷害鎻愬崌浜嗗張涓鍊嶅乏鍙籌紝涓夎棌涓嶇鏈夌偣婊¤凍浜嗭紝鐫¤涔燂紒
璐ㄦ暟鐨勫畾涔?/strong>
涓涓暟錛屽鏋滃彧鏈?鍜屽畠鏈韓涓や釜鍥犳暟錛岃繖鏍風殑鏁板彨鍋氳川鏁幫紝鍙堢О绱犳暟銆?nbsp;
璇曢櫎鍒ゆ柇娉?/strong>
綆楁硶鎻忚堪錛氫粠涓婅堪瀹氫箟鍙煡錛岀礌鏁頒笉鑳借1鍜屽畠鏈韓涔嬪鐨勬暟鏁撮櫎錛屾墍浠ワ紝鍒ゆ柇涓涓暟x鏄惁绱犳暟鍙鐪嬪畠鏄惁鑳借2~sqrt(x)闂寸殑鏁版暣闄ゅ嵆鍙紱鑰屾眰N鍐呮墍鏈夌礌鏁板垯鏄驚鐜噸澶嶄笂榪拌繃紼嬨?/p>
C璇█瀹炵幇錛?/p>
#include <time.h>
#include <malloc.h>
#define N 100000
// 綆鍗曡瘯闄ゅ垽鏂硶 Ver1
int SimpleDivisionV1(int n)
{
int i,j;
// 绱犳暟鏁伴噺緇熻
int count = 0;
// 鍒嗛厤瀛樻斁緇撴灉鐨勭┖闂?
int* primes = (int*)malloc( sizeof(int)*n );
// 2鏄礌鏁拌皝閮界煡閬擄紝涓嶇畻浜?
primes[count++] = 2;
// 寰幆璁$畻3~n闂寸殑鏁?
for (i=3; i<=n; i++)
{
// 涓轟粈涔堟槸sqrt(i)錛屾濊冧竴涓?
for (j=2; j<=sqrt(i); j++)
{
// i琚玧鏁撮櫎錛屾樉鐒朵笉鏄礌鏁頒簡
if (i%j == 0) break;
}
// i涓嶈兘琚?~sqrt(i)闂寸殑鏁版暣闄?绱犳暟涔?
if (j > sqrt(i))
{
primes[count++] = i;
}
}
// 鍥犺緭鍑鴻垂鏃訛紝涓斿拰綆楁硶鏍稿績鐩稿叧涓嶅ぇ錛屾晠鐣?br>
// 閲婃斁鍐呭瓨錛屽埆蹇樹簡浼犺涓殑鍐呭瓨娉勬紡
free(primes);
return count;
}
void main()
{
int count;
clock_t start, end;
// time鍑芥暟涓嶅綺劇‘錛岀敤clock鍑戝悎涓涓嬪惂
start = clock();
count = SimpleDivisionV1(N);
end = clock();
printf("[%d]浠ュ唴绱犳暟涓暟錛?d, 璁$畻鐢ㄦ椂錛?d姣\n", N, count, end-start);
getch();
}
璁$畻緇撴灉錛?br>[100000]浠ュ唴绱犳暟涓暟錛?592, 璁$畻鐢ㄦ椂錛?68姣
[1000000]浠ュ唴绱犳暟涓暟錛?8498, 璁$畻鐢ㄦ椂錛?0859姣
[5000000]浠ュ唴绱犳暟涓暟錛?48513, 璁$畻鐢ㄦ椂錛?03560姣
鍣㈠櫌錛岀畻綆楀崄涓囪繕琛岋紝鐧句竾灝?0縐掑浜嗭紝鑰屼笖鏃墮棿澧為暱寰堝揩錛岃繖涓嶈錛屽緱浼樺寲涓涓嬶紒
浼樺寲鍒嗘瀽錛?/p>
浠旂粏鐮旂┒涓涓婼impleDivisionV1鎴戜滑鍙互鍙戠幇浠ヤ笅鍑犱釜闂錛?/p>
鏍規嵁涓婇潰涓ょ偣錛屾垜浠彲灝哠impleDivisionV1鍗囩駭涓篠impleDivisionV2錛屽涓?/p>
// 綆鍗曡瘯闄ゅ垽鏂硶 Ver2
int SimpleDivisionV2(int n)
{
int i, j, k, stop;
// 绱犳暟鏁伴噺緇熻
int count = 0;
// 鍒嗛厤瀛樻斁緇撴灉鐨勭┖闂?
int* primes = (int*)malloc( sizeof(int)*n );
// 2鏄礌鏁拌皝閮界煡閬擄紝涓嶇畻浜?
primes[count++] = 2;
stop = count;
// 寰幆璁$畻3~n闂寸殑鏁?
for (i=3; i<=n; i++)
{
k = sqrt(i);
// 鍦ㄥ驚鐜潯浠朵腑閲嶅璋冪敤sqrt鏄綆鏁堝仛娉曪紝鏁呭紩鍏
while (primes[stop] <= k && stop < count)
stop++;
// stop騫蹭粈涔堢敤錛屾濊冧竴涓?br> for (j=0; j<stop; j++)
{
if (i%primes[j] == 0) break;
}
// i涓嶈兘琚?~sqrt(i)闂寸殑绱犳暟鏁撮櫎錛岃嚜鐒朵篃涓嶈兘琚叾浠栨暟鏁撮櫎,绱犳暟涔?
if (j == stop)
{
primes[count++] = i;
}
}
// 鍥犺緭鍑鴻垂鏃訛紝涓斿拰綆楁硶鏍稿績鐩稿叧涓嶅ぇ錛屾晠鐣?br>
// 閲婃斁鍐呭瓨錛屽埆蹇樹簡浼犺涓殑鍐呭瓨娉勬紡
free(primes);
return count;
}
鐒跺悗灝唌ain涓皟鐢ㄧ殑鍑芥暟鏇挎崲涓篠impleDivisionV2錛屽湪鐪嬩竴涓嬫墽琛岀粨鏋滐細
[100000]浠ュ唴绱犳暟涓暟錛?592, 璁$畻鐢ㄦ椂錛?6姣
[1000000]浠ュ唴绱犳暟涓暟錛?8498, 璁$畻鐢ㄦ椂錛?46姣
[5000000]浠ュ唴绱犳暟涓暟錛?48513, 璁$畻鐢ㄦ椂錛?515姣
[10000000]浠ュ唴绱犳暟涓暟錛?64579, 璁$畻鐢ㄦ椂錛?000姣
寰堝紑蹇冪殑鐪嬪埌錛岀粡榪囦紭鍖栵紝閫熷害鎻愰珮浜嗗嚑鍗佸嶏紝灝ゅ叾鏄椂闂村闀挎洸綰跨殑鍧″害鍙樺皬浜嗭紝N鍊艱秺澶э紝V2鍑芥暟姣擵1鐨勬晥鐜囧氨瓚婇珮
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綰挎ц〃鈥斺旈潤鎬侀摼琛?009.7.30
綰挎ц〃鈥斺旈摼琛ㄧ殑鍐呴儴綾誨疄鐜?008.8
綰挎ц〃鈥斺旈摼琛ㄧ殑鍙嬪厓綾誨疄鐜?008.8
綰挎ц〃鈥斺斿弻鍚戦摼琛?009.8.11
綰挎ц〃鈥斺旈『搴忚〃2009.8.3
綰挎ц〃鈥斺斿弸鍏冩ā鏉跨被2009.8
綰︾憻澶棶棰樷斺斿洓縐嶈В娉?009.8.11錛堟暟緇勶紝閾捐〃錛屽驚鐜摼琛ㄧ瓑錛?br>闃熷垪鈥斺旈槦鍒楃殑欏哄簭琛ㄧず寰幆闃熷垪2009.8.11
闃熷垪鈥斺旈摼闃熷垪2009.8.11
鏍堚斺旀眽璇哄2009.8.6
鏍堚斺旇繘鍒惰漿鎹?009.8.6
鏍堚斺旀嫭鍙峰尮閰?009.8.6
鏍堚斺旀ā鏉塊摼鏍?009.8.3
鏍堚斺旀ā鏉塊『搴忔爤2009.7
鏍堚斺旈『搴忔爤2009.8.6
鏍堚斺旂畻鏈〃杈懼紡姹傚?009.7.13
鏍堚斺旇緙栬緫2009.8.6
浜屽弶鏍戔斺斾簩鍙夋爲鐨勫父瑙佹搷浣?009.9.3
2010.3.9 鏇存柊
鏍戠殑搴旂敤鈥斾豢DOS鏂囦歡澶圭鐞嗙▼搴?/p>
200浣嶅ぇ鏁頒箻娉?rar
200浣嶅ぇ鏁板姞娉?rar
榪炶繛鐪嬪崟鏈虹▼搴廙FC