鍛靛懙錛屽彲鑳借繖涓棶棰樻瘮杈冪畝鍗曘備絾寮濮嬪垰鍒氭帴瑙︼紝铏界劧榪欎釜闂寰堢粡鍏革紝浣嗘垜鎯充簡(jiǎn)姣旇緝涔呮墠鎶婂畠寮勫嚭鏉ャ傚洜涓哄湪pow鍑芥暟閭ｉ噷鍗′綇浜?jiǎn)锛屼絾鍚庢潵鎱㈡參鐪嬩功锛尵l堜簬鎶婂畠緇欏紕鍑烘潵鍟︼紝鍚庢潵鍦ㄧ綉涓婃壘浜?jiǎn)鎵捐В娉曞Q屽彂鐜板拰鎴戠殑澶у悓灝忓紓錛岃繕鏄兂鎯蟲槸鍚︽湁鏇寸畝鍗曠殑瑙ｆ硶鍚с?/p>
#include<iostream.h>
#include<math.h>
void main()
{
int m,a,b,c,tmp;
cout<<"The Narcissistic Number is "<<endl;
for(m=100;m<=999;m++)
{a=m/100;
b=(m%100)/10;
c=m%10; //鎶婃暟鍒嗘垚涓変綅錛屽瓨鍦ㄤ笉鍚岀殑鍦版柟
tmp=pow(a,3)+pow(b,3)+pow(c,3); //姹傚嚭鍚勪綅鏁扮殑涓夋鏂逛箣鍜?o:p>
if(tmp==m)
cout<<m<<endl; //杈撳嚭璇ユ按浠欒姳鏁?o:p>
}
]]>
榪唬鍏紡鍏蜂綋涓篨n+1=(Xn+a/xn)/2 (n=0,1,2,3….;X0=a/2)錛岃繖鏄垜鐨勪竴嬈′綔涓氥?br>
#include<iostream.h>
#include<math.h>
void main()
{
float a,m,n;
cout<<"please input a positive integer"<<endl;
cout<<"a="<<endl;
cin>>a;
n=a/2;
m=(n+a/n)/2;
while(fabs(n-m)>1e-6)
{n=m;
m=(n+a/n)/2;
}
cout<<"The square root of a is"<<m<<endl;
}
鍛靛懙錛屽叧浜庣墰欏胯凱浠ｆ硶錛屼紬浜虹爺絀剁敋澶氥?br>TIP1:
鐗涢】榪唬娉曪紙Newton's method錛夊張縐頒負(fù)鐗涢】-鎷夊か閫婃柟娉曪紙Newton-Raphson method錛夛紝瀹冩槸鐗涢】鍦?7涓栫邯鎻愬嚭鐨勪竴縐嶅湪瀹炴暟鍩熷拰澶嶆暟鍩熶笂榪戜技姹傝В鏂圭▼鐨勬柟娉曘傚鏁版柟紼嬩笉瀛樺湪姹傛牴鍏紡錛屽洜姝ゆ眰綺劇‘鏍歸潪甯稿洶闅撅紝鐢氳嚦涓嶅彲鑳斤紝浠庤屽鎵炬柟紼嬬殑榪戜技鏍瑰氨鏄懼緱鐗瑰埆閲嶈銆傛柟娉曚嬌鐢ㄥ嚱鏁癴(x)鐨勬嘲鍕掔駭鏁扮殑鍓嶉潰鍑犻」鏉ュ鎵炬柟紼媐(x) = 0鐨勬牴銆傜墰欏胯凱浠ｆ硶鏄眰鏂圭▼鏍圭殑閲嶈鏂規(guī)硶涔嬩竴錛屽叾鏈澶т紭鐐規(guī)槸鍦ㄦ柟紼媐(x) = 0鐨勫崟鏍歸檮榪戝叿鏈夊鉤鏂規(guī)敹鏁涳紝鑰屼笖璇ユ硶榪樺彲浠ョ敤鏉ユ眰鏂圭▼鐨勯噸鏍廣佸鏍廣?
璁緍鏄痜(x) = 0鐨勬牴錛岄夊彇x0浣滀負(fù)r鍒濆榪戜技鍊鹼紝榪囩偣錛坸0,f(x0)錛夊仛鏇茬嚎y = f(x)鐨勫垏綰縇錛孡鐨勬柟紼嬩負(fù)y = f(x0)+f'(x0)(x-x0)錛屾眰鍑篖涓巟杞翠氦鐐圭殑妯潗鏍?x1 = x0-f(x0)/f'(x0)錛岀Оx1涓簉鐨勪竴嬈¤繎浼煎箋傝繃鐐癸紙x1,f(x1)錛夊仛鏇茬嚎y = f(x)鐨勫垏綰匡紝騫舵眰璇ュ垏綰夸笌x杞寸殑妯潗鏍?x2 = x1-f(x1)/f'(x1)錛岀Оx2涓簉鐨勪簩嬈¤繎浼煎箋傞噸澶嶄互涓婅繃紼嬶紝寰梤鐨勮繎浼煎煎簭鍒楋紝鍏朵腑x(n+1)=x(n)錛峟(x(n))/f'(x(n))錛岀О涓簉鐨刵+1嬈¤繎浼煎鹼紝涓婂紡縐頒負(fù)鐗涢】榪唬鍏紡銆?
瑙ｉ潪綰挎ф柟紼媐(x)=0鐨勭墰欏挎硶鏄妸闈炵嚎鎬ф柟紼嬬嚎鎬у寲鐨勪竴縐嶈繎浼兼柟娉曘傛妸f(x)鍦▁0鐐歸檮榪戝睍寮鎴愭嘲鍕掔駭鏁?f(x) = f(x0)+(x錛峹0)f'(x0)+(x錛峹0)^2*f''(x0)/2! +… 鍙栧叾綰挎ч儴鍒嗭紝浣滀負(fù)闈炵嚎鎬ф柟紼媐(x) = 0鐨勮繎浼兼柟紼嬶紝鍗蟲嘲鍕掑睍寮鐨勫墠涓ら」錛屽垯鏈塮(x0)+f'(x0)(x錛峹0)=f(x)=0 璁緁'(x0)≠0鍒欏叾瑙ｄ負(fù)x1=x0錛峟(x0)/f'(x0) 榪欐牱錛屽緱鍒扮墰欏挎硶鐨勪竴涓凱浠ｅ簭鍒楋細(xì)x(n+1)=x(n)錛峟(x(n))/f'(x(n))銆?/cn>
TIP2:
鐩稿叧錛氳凱浠ｇ畻娉曟槸鐢ㄨ綆楁満瑙ｅ喅闂鐨勪竴縐嶅熀鏈柟娉曘傚畠鍒╃敤璁＄畻鏈鴻繍綆楅熷害蹇侀傚悎鍋氶噸澶嶆ф搷浣滅殑鐗圭偣錛岃璁＄畻鏈哄涓緇勬寚浠わ紙鎴栦竴瀹氭楠わ級(jí)榪涜閲嶅鎵ц錛屽湪姣忔鎵ц榪欑粍鎸囦護(hù)錛堟垨榪欎簺姝ラ錛夋椂錛岄兘浠庡彉閲忕殑鍘熷兼帹鍑哄畠鐨勪竴涓柊鍊箋?br>渚嬪錛屽綋鎴戜滑瑕佽В鍐充竴涓浉鍏抽掑闂鏃訛紝鍒╃敤璁＄畻鏈虹殑浼樺娍鍙互璁捐鍑虹浉鍏崇殑紼嬪簭鏉ュ揩閫熸眰寰楄В銆?br>濡傞錛?涓涓ゲ鍏誨満寮曡繘涓鍙垰鍑虹敓鐨勬柊鍝佺鍏斿瓙錛岃繖縐嶅厰瀛愪粠鍑虹敓鐨勪笅涓涓湀寮濮嬶紝姣忔湀鏂扮敓涓鍙厰瀛愶紝鏂扮敓鐨勫厰瀛愪篃濡傛綣佹畺銆傚鏋滄墍鏈夌殑鍏斿瓙閮戒笉姝誨幓錛岄棶鍒扮 12 涓湀鏃訛紝璇ラゲ鍏誨満鍏辨湁鍏斿瓙澶氬皯鍙紵
鍛靛懙錛屽張鏄厰瀛愰棶棰橈紝榪欐槸涓濊礬姣旇緝娓呮錛岃В娉曟瘮杈冪畝鍗曠殑涓閬撻錛?br>榪欐槸涓涓吀鍨嬬殑閫掓帹闂銆傛垜浠笉濡ㄥ亣璁劇 1 涓湀鏃跺厰瀛愮殑鍙暟涓?u1 錛岀2涓湀鏃跺厰瀛愮殑鍙暟涓簎2,絎?涓湀鏃跺厰瀛愮殑鍙暟涓簎3錛?#8230;…鏍規(guī)嵁棰樻剰錛?#8220;榪欑鍏斿瓙浠庡嚭鐢熺殑涓嬩竴涓湀寮濮嬶紝姣忔湀鏂扮敓涓鍙厰瀛?#8221;錛屽垯鏈?
U1錛?,U 2錛漊1錛婾1×1錛?,U3錛漊2+U2×1錛?,……
鏍規(guī)嵁榪欎釜瑙勫緥錛屽彲浠ュ綊綰沖嚭涓嬮潰鐨勯掓帹鍏紡錛?nbsp;
U n 錛?nbsp;U (n-1)× 2 (n ≥ 2) ,瀵瑰簲 Un 鍜?nbsp;U n 錛?1 錛屽畾涔変袱涓凱浠ｅ彉閲?y 鍜?x 錛屽彲灝嗕笂闈㈢殑閫掓帹鍏紡杞崲鎴愬涓嬭凱浠ｅ叧緋伙細(xì)
y=x*2
x=y
璁╄綆楁満瀵硅繖涓凱浠ｅ叧緋婚噸澶嶆墽琛?11 嬈★紝灝卞彲浠ョ畻鍑虹 12 涓湀鏃剁殑鍏斿瓙鏁般?/p>