C语言程序填空练习题(二).docx
将下面的程序补充完整，以完成指定的功能。1 .尼科彻斯定理ThisprogramistoverifyTheoremofNicoqish.Thatisthecubeofanyintegercanberepresentedasthesumofsomecontinueoddnumbers.Forexample,83=512=57+59+61+63+65+67+69+71.include<iostream>usingnamespacestd;intmain()(intn,a,i;while(1)(cout<<"Pleaseinputaintegertoverify(Otoquit):"cin>>n;if(n=O);/(D/输出等差数列，首项为a*a-a+1,公差为2,项数为na=n*n-n+1;cout<<n<<,'*,'<<n<<"*"<<n<<,'="<<n*n*n<<"=,'<<a;for(i=1;i+)/(2)cout<<"+,<</(3)cout<<endl;)returnO;)2 .角谷猜想ThisprogramistoverifyJiaoguGuess.Thatisgivenanynaturalnumber,ifitisaneven,divides2,ifitisanodd,multiple3andadd1,theresultcontinuestobecalculatedanalogously.Aftersometimes,theresultisalways1.#include<iostream>usingnamespacestd;intmain()(intn,a,i,cnt;while(1)(cout<<"Pleaseinputaintegertoverify(Otoquit):"cin>>n;if(n=O)break;/(1)cnt=O;cout<<"Resultsofverification:n"doif(/(2)n=n*3+1;cout<<',StepNo."<<+cnt<<",<<(n-1)3<<"*3+1="<<n<<endl;)else(n=2;cout<<"StepNo."<<+cnt<<"'<<2*n<<72="<<n<<endl;)while();/(3)cout<<endl;)return0;)3 .四方定理ThisprogramistoverifyTheoremofFourSquares.Thatisallnaturalnumberscanberepresentedassumofnomorethan4squaresofthenumbers.e.g.,123=7*7+7*7+4*4+3*3.#include<iostream>usingnamespacestd;intmain()(inti,j,kJ,number;while(1)cout<<"Pleaseinputanumbertoverify(0toquit):"cin>>number;if(number=O);/(1)cout<<"Resultsofverification:n"for(i=1;i<=number/2;i+)for0=O;j<=i;j+)for(k=0;k<=j;k+)for(l=0;l<=k;l+)if()/(2)(cout<<number<<"="<<i<<"*"<<i<<',+"<<j<<"*"<<j<<"+"<<k<<"*,<<k<<"+"<<l<<"*"<<<<endl;gotoexit;)exit:cout<<"n"returnO;)4 .亲密数Thisisaprogramtofindfriendlynumberspair.WhichmeansthesumofintegerA'sallfactors(exceptA)equalstothesumofintegerB'sallfactors(exceptB)<e.g.sumofinteger220'sallfactorsare:1+2+4+5+10+11+20+22+44+55+110=284,andsumofinteger284'sallfactorsare:1+2+4+71+142=220>#include<iostream>usingnamespacestd;intmain()(inta,i,b,n,m;cout<<"Pleaseinputthescaleyouwanttofindn:"cin>>n;cout<<"nTherearefollowingfriendly-numberspairsmallerthan"<<n<<endl;for(a=1;a<n;a+)(for(;i<=a/2;i+)/(1)if(!(a%i)b+=i;for(;i<=b/2;i+)/(2)if(!(b%i)m+=i;if(&&a<b)/(3)cout<<a<<".,'<<b<<"m;)cout<<endl;return0;)5 .自守数Thisprogramwillfindtheautomorphicnumbers.Thedefinationofaautomorphicnumberis:themantissaofanaturalnumber'ssquareequalstoitself.e.g.,52=25,762=5776,93762=87909376.#include<iostream>usingnamespacestd;intmain()(intmul,number,k,kk;for(number=0;number<1OOOOjnumber+)(for(mul=number,k=1;k*=10);/(1)kk=k*10;mul=number*number%kk;if()/(2)cout<<number<<")cout<<endl;return0;)6 .特殊的四位数Thisprogramwillfindthefourfigureswhichhavethecharacteristicasfollows:abcd=(ab+cd)2.e.g.,3025=(30+25)*(30+25).#include<iostream>usingnamespacestd;intmain()intn,a,b;for(n=1000;n<10000;n+)(;/(1);/(2)if(a+b)*(a+b)=n)cout<<n<<"',;)cout<<endl;return0;)7 .求方程COS(X)x=0的根Thisprogramistofindtherealrootoffunctioncos(x)-x=0.include<iostream>include<cmath>usingnamespacestd;intmain()float×0,x1=0.0;while(1)(; /(1); /(2)if(fabs(x-x1)<1e-6)break;)cout<<"Therealrootis,<<x1<<endl;return0;)8 .特殊的3位数ThisprogramistofindthePerfectSquareNumbers.whichhave3digits,and2ofthemarethesame,e.g.100,121,144,225,400,441,484,676,900.include<iostream>#include<cmath>usingnamespacestd;intmain()(inti,n,a,b,c;for(i=10;i<=sqrt(1000);i+)(;/(1)a=n100;/(2)c=n%10;if(a=bHa=cb=c)cout<<n<<"")cout<<endl;return0;)9 .三重回文数ThisprogramistofindthePalindromeNumbers,whosesquareandcubicarealsoPalindromeNumbers.include<iostream>usingnamespacestd;boolisPalindrome(intn)(intx,y=0;x=n;while(x!=0)(;/(1);/(2)returny=n;)intmain()(intm;for(m=11;m<1000;m+)(if(isPalindrome(m)&&isPalindrome(m*m)&&isPalindrome(m*m*m)cout<<m<<""<<m*m<<"M«m*m*m«endl;)returnO;10 .SIXandNINEThisprogramistofindthenumbersofSIXandNINE,whichsatisfytheformulaSIX+SIX+SIX=NINE+NINE,whereS,I,X,N,Estandfordigitsbetween0and9.#include<iostream>usingnamespacestd;intmain()inti,x,a,b,c,d;for(i=668;i<=999;)/(1)(x=3*i2;a=i10%10;b=x100%10;c=x1000;d=x%10010;if()/(2)(cout<<i<<""<<x<<endl;)return0;)或include<iostream>usingnamespacestd;intmain()(ints,i,x,n,e,six,nine;for(s=1;s<10;s+)for(i=0;i<10;i+)for(x=0;x<10;x+)for(n=1;n<10;n+)for(e=0;e<10;e+)(six=;/(3)nine=;/(4)if()/(5)cout<<six<<",<<nine<<endl;)return0;)11 .马克思手稿中的数学题ThisprogramistosolveaninterestingmathquestioninKarlMarx'smanuscript.TheProblemisasfollows:30personsspent50yuaninarestaurant,amonythem,eachmanspent3yuan,eachwomanspent2yuan,andeachchildspent1yuan.Thequestionishowmanymen,womenandchildrenarethere?#include<iostream>usingnamespacestd;intmain()(intx,y,z;cout<<"MentWomentChildren',<<endl;for(x=0;x<=10;x+)(;/(1);/(2)if()
