鎴戜滑鍏堟潵鐪嬬湅10榪涘埗涓嬫槸濡備綍鎵嬪伐璁＄畻寮鏂圭殑銆?br>鍏堢湅涓嬮潰涓や釜綆楀紡錛?br>x = 10*p + q (1)
鍏紡(1)宸﹀彸騫蟲柟涔嬪悗寰楋細
x^2 = 100*p^2 + 20pq + q^2 (2)
鐜板湪鍋囪鎴戜滑鐭ラ亾x^2鍜宲錛屽笇鏈涙眰鍑簈鏉ワ紝姹傚嚭浜唓涔熷氨姹傚嚭浜唜^2鐨勫紑鏂箈浜嗐?br>鎴戜滑鎶婂叕寮?2)鏀瑰啓涓哄涓嬫牸寮忥細
q = (x^2 - 100*p^2)/(20*p+q) (3)
榪欎釜綆楀紡宸﹀彸閮芥湁q錛屽洜姝ゆ棤娉曠洿鎺ヨ綆楀嚭q鏉ワ紝鍥犳鎵嬪伐鐨勫紑鏂圭畻娉曞拰鎵嬪伐闄ゆ硶綆楁硶涓鏍鋒湁涓姝ラ渶瑕佺寽鍊箋?/p>
鎴戜滑鏉ヤ竴涓墜宸ヨ綆楃殑渚嬪瓙錛氳綆?234567890鐨勫紑鏂?/p>
棣栧厛鎴戜滑鎶婅繖涓暟涓や綅涓や綅涓緇勫垎寮錛岃綆楀嚭鏈楂樹綅涓?銆備篃灝辨槸(3)涓殑p錛屾渶涓嬮潰涓琛岀殑334涓轟綑鏁幫紝涔熷氨鏄叕寮?3)涓殑(x^2 - 100*p^2)榪戜技鍊?br> 3
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/ 12 34 56 78 90
9
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/ 3 34
涓嬮潰鎴戜滑瑕佹壘鍒頒竴涓?-9鐨勬暟q浣垮畠鏈鎺ヨ繎婊¤凍鍏紡(3)銆傛垜浠厛鎶妏涔樹互20鍐欏湪334宸﹁竟錛?br> 3 q
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/ 12 34 56 78 90
9
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(20*3+q)*q / 3 34
鎴戜滑鐪嬪埌q涓?鏃?60+q)*q鐨勫兼渶鎺ヨ繎334錛岃屼笖涓嶈秴榪?34銆備簬鏄垜浠緱鍒幫細
3 5
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/ 12 34 56 78 90
9
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65 / 3 34
3 25
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9 56
鎺ヤ笅鏉ュ氨鏄噸澶嶄笂闈㈢殑姝ラ浜嗭紝榪欓噷灝變笉鍐嶅暟鍡︿簡銆?
榪欎釜鎵嬪伐綆楁硶鍏跺疄鍜?0榪涘埗鍏崇郴涓嶅ぇ錛屽洜姝ゆ垜浠彲浠ュ緢瀹規槗鐨勬妸瀹冩敼涓轟簩榪涘埗錛屾敼涓轟簩榪涘埗涔嬪悗錛屽叕寮?3)灝卞彉鎴愪簡錛?br>q = (x^2 - 4*p^2)/(4*p+q) (4)
鎴戜滑鏉ョ湅涓涓緥瀛愶紝璁＄畻100(浜岃繘鍒?100100)鐨勫紑鏂癸細
1 0 1 0
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/ 1 10 01 00
1
-----------
100 / 0 10
0 00
-----------
1001 / 10 01
10 01
-----------
0 00
榪欓噷姣忎竴姝ヤ笉鍐嶆槸鎶妏涔樹互20浜嗭紝鑰屾槸鎶妏涔樹互4錛屼篃灝辨槸鎶妏鍙崇Щ涓や綅錛岃岀敱浜巕鐨勫煎彧鑳戒負0鎴栬?錛屾墍浠ユ垜浠彧闇瑕佸垽鏂綑鏁?x^2 - 4*p^2)鍜?4*p+1)鐨勫ぇ灝忓叧緋伙紝濡傛灉浣欐暟澶т簬絳変簬(4*p+q)閭ｄ箞璇ヤ笂涓涓?錛屽惁鍒欒涓婁竴涓?銆?/p>
涓嬮潰緇欏嚭瀹屾垚鐨凜璇█紼嬪簭錛屽叾涓璻oot琛ㄧずp錛宺em琛ㄧず姣忔璁＄畻涔嬪悗鐨勪綑鏁幫紝divisor琛ㄧず(4*p+1)錛岄氳繃a>>30鍙朼鐨勬渶楂?2浣嶏紝閫氳繃a<<=2灝嗚綆楀悗鐨勬渶楂?浣嶅墧闄ゃ傚叾涓璻oot鐨勪袱嬈?lt;<1鐩稿綋浜?*p銆傜▼搴忓畬鍏ㄦ槸鎸夌収鎵嬪伐璁＄畻鏀瑰啓鐨勶紝搴旇涓嶉毦鐞嗚В銆?br>unsigned short sqrt(unsigned long a){
unsigned long rem = 0;
unsigned long root = 0;
unsigned long divisor = 0;
for(int i=0; i<16; ++i){
root <<= 1;
rem = ((rem << 2) + (a >> 30));
a <<= 2;
divisor = (root<<1) + 1;
if(divisor <= rem){
rem -= divisor;
root++;
}
}
return (unsigned short)(root);
}