小课堂

【小课堂】参考答案

1.1

C++: 

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#include<iostream>
using namespace std;
int main(){
    cout<<"#\n##\n###\n####\n#####"<<endl;
    return 0;
}

C: 

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#include<stdio.h>
int main(){
    printf("#\n##\n###\n####\n#####");
    return 0;
}

1.2

C++: 

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#include<iostream>
using namespace std;
int main(){
    cout<<1024*512<<endl;
    return 0;
}

C: 

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#include<stdio.h>
int main(){
    printf("%d\n",1024*512);
    return 0;
}

2.1

C++: 

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#include<iostream>
using namespace std;
int main(){
    int a,b;
    cin>>a>>b;
    cout<<a+b<<endl;
    return 0;
}

C: 

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#include<stdio.h>
int main(){
    int a,b;
    scanf("%d%d",&a,&b);
    printf("%d",a+b);
    return 0;
}

2.2

C++: 

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#include<iostream>
using namespace std;
int main(){
    double r,pi=3.14159265;
    cin>>r;
    cout<<"s="<<pi*r*r<<",c="<<2*pi*r<<endl;
    return 0;
}

C: 

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#include<stdio.h>
int main(){
    double r,pi=3.14159265;
    scanf("%lf",&r);
    printf("s=%.2lf,c=%.2lf",pi*r*r,2*pi*r);
    return 0;
}

2.3

C++: 

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#include<iostream>
#include<cmath>
using namespace std;
int main(){
    double a,b,c,d,x1,x2;
    cin>>a>>b>>c;
    d=b*b-4*a*c;
    x1=(-b+sqrt(d))/(2*a);
    x2=(-b-sqrt(d))/(2*a);
    cout<<"x1="<<x1<<",x2="<<x2<<endl;
    return 0;
}

C: 

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#include<stdio.h>
#include<math.h>

int main(){
    double a,b,c,d;
    scanf("%lf%lf%lf",&a,&b,&c);
    d=b*b-4*a*c;
    printf("x1=%lf,x2=%lf",(-b+sqrt(d))/(2*a),(-b-sqrt(d))/(2*a));
    return 0;
}

3.1

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#include<stdio.h>
int main(){
    int n;
    scanf("%d",&n);
    if(n%3==0)printf("YES");
    else printf("NO");
    return 0;
}

3.2

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#include<stdio.h>
int main(){
    int n,a,b,c,d;
    scanf("%d",&n);
    a=n/100;
    b=n/10%10;
    c=n%10;
    d=a*a*a+b*b*b+c*c*c;
    if(n<1000&&d==n)printf("YES");
    else printf("NO");
    return 0;
}

3.3

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#include<stdio.h>
int main(){
    int a,b,c,t;
    scanf("%d%d%d",&a,&b,&c);
    if(a<b){
        t=a;
        a=b;
        b=t;
    }
    if(b<c){
        t=b;
        b=c;
        c=t;
    }
    if(a<b){
        t=a;
        a=b;
        b=t;
    }
    printf("%d %d %d",a,b,c);
    return 0;
}

3.4

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#include<stdio.h>
int main(){
    int m,n,d=1;
    scanf("%d%d",&m,&n);
    if(m>1)d+=31;
    if(m>2)d+=28;
    if(m>3)d+=31;
    if(m>4)d+=30;
    if(m>5)d+=31;
    if(m>6)d+=30;
    if(m>7)d+=31;
    if(m>8)d+=31;
    if(m>9)d+=30;
    if(m>10)d+=31;
    if(m>11)d+=30;
    d+=n;
    d%=7;
    printf("%d",d);
    return 0;
}

3.5

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#include<stdio.h>
int main(){
    int n;
    float f=0;
    scanf("%d",&n);
    if(n<=150)f=n*0.4463;
    else if(n<=400)f=150*0.4463+(n-150)*0.4663;
    else f=150*0.4463+250*0.4663+(n-400)*0.5663;
    printf("%.1f",f);
    return 0;
}

4.1.1

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#include<stdio.h>
int main(){
    int i,j,m,n;
    scanf("%d%d",&n,&m);
    for(i=1;i<=n;i++){
        for(j=1;j<=m;j++)
            printf("*");
        printf("\n");
    }
    return 0;
}

4.1.2

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#include<stdio.h> 
int main(){
    int n,a,b,t,i=1;
    scanf("%d",&n);
    a=1;
    b=1;
    i=2;
    while(i<n){
        t=a+b;
        a=b;
        b=t;
        i++;
    }
    printf("%d",b);
    return 0;
}

4.1.3

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#include<stdio.h>
#include<math.h>
int main(){
    int x,i,flag=1;
    scanf("%d",&x);
    for(i=2;i<=sqrt(x);i++)
        if(x%i==0)flag=0;
    if(flag&&x!=1) printf("yes");
    else printf("no");
    return 0;
}

4.1.4

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#include<stdio.h> 
int main(){
    float a,b,c,s,i=0;
    scanf("%f",&a);
    c=a;
    while(a!=-1){
        s=s+a;
        if(a>b)b=a;
        if(a<c)c=a; 
        i++;
        scanf("%f",&a);   
    }
    printf("%f %f %f",s/i,b,c);
    return 0;
}

4.1.5

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#include<stdio.h>
#include<stdlib.h>
int main(){
    int n,i,j;
    scanf("%d",&n);
    for(i=1;i<=2*n-1;i++){ 
        for(j=1;j<=abs(n-i);j++)
            printf(" ");
            
        for(j=1;j<=2*(n-abs(n-i))-1;j++)
            printf("%c",n-abs(n-i)-abs(n-abs(n-i)-j)+64);//对称中心n-abs(n-i) 
            
        printf("\n");
    }
    return 0;
}

4.2.1

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#include<iostream>
using namespace std;

int main(){
    int n,a[200];
    cin>>n;
    for(int i=1;i<=n;i++)
        cin>>a[i];
    
    for(int i=n;i>=1;i--)
        cout<<a[i]<<" ";
    
    return 0;
}

4.2.2

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#include<iostream>
using namespace std;

int main(){
    int n,m,k,a[200];
    cin>>n;
    for(int i=1;i<=n;i++)
        cin>>a[i];
    cin>>m>>k;
    
    for(int i=n;i>=m;i--)
        a[i+1]=a[i];
    a[m]=k;
    
    for(int i=1;i<=n+1;i++)
        cout<<a[i]<<" ";
    
    return 0;
}

4.2.3

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#include<iostream>
using namespace std;

int main(){
    int n,a[200],t;
    cin>>n;
    for(int i=1;i<=n;i++)
        cin>>a[i];
    
    for(int i=1;i<=n;i++)
        for(int j=n;j>i;j--)
            if(a[j]<a[j-1]){
                t=a[j];
                a[j]=a[j-1];
                a[j-1]=t;
            }
    
    for(int i=1;i<=n;i++)
        cout<<a[i]<<" ";
    
    return 0;
}

4.2.4

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#include<iostream>
using namespace std;

int main(){
    int n,m,a[100][100];
    cin>>n>>m;
    for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++)
            cin>>a[j][i];
        
    for(int i=1;i<=m;i++){
        for(int j=1;j<=n;j++)
            cout<<a[i][j]<<" ";
        cout<<"\n";
    }
    
    return 0;
}

4.2.5

普通版：

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#include<cstdio.h>

int main(){
    int n,a[100][100]={0},b,c,i=0,j=0;
    bool flag=false;
    scanf("%d",&n);
    for(int s=1;s<=n*n;s++){
        a[i][j]=s;
        if(flag){j--;i++;}
        else{j++;i--;}
        
        if(i<0){
            i++;
            flag=true;
        }
        if(j<0){
            j++;
            flag=false;
        }
        if(j>=n && i<=0 && flag)i--;
        if(i>=n && j<=0 && !flag)j--;
        if(j>=n){i+=2;j--;flag=true;}
        if(i>=n){j+=2;i--;flag=false;}
    }
    
    for(i=0;i<n;i++){
        for(j=0;j<n;j++)
            printf("%5d",a[i][j]);
        printf("\n");
    }
    return 0;
}

状态机版（供参考）：

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#include<iostream>
#include<cstdio>
using namespace std;

int main(){
    int n,a[100][100];
    int sx[5]={0,0, 1,1,-1},
        sy[5]={0,1,-1,0, 1};//状态机状态
    int x=1,y=1,dx=sx[1],dy=sy[1];//起始状态
    bool switchflag=false;
    scanf("%d",&n);
    
    for(int now=1;now<=n*n;now++){
        a[x][y]=now;
        x+=dx;
        y+=dy;
        if(n%2==0 && x==n)switchflag=true;
        if(n%2==1 && y==n)switchflag=true;//切换
        if(!switchflag){//状态机1 
            if(dx==sx[1]&&dy==sy[1]){//状态1
                dx=sx[2];dy=sy[2];//转到状态2 
            }
            else if(dx==sx[2]&&dy==sy[2]){//状态2
                if(y==1){dx=sx[3];dy=sy[3];}//转到状态3 
            }
            else if(dx==sx[3]&&dy==sy[3]){//状态3
                dx=sx[4];dy=sy[4];//转到状态4
            }
            else{//状态4
                if(x==1){dx=sx[1];dy=sy[1];}//转到状态1
            }
        } 
        else{//状态机2 
            if(dx==sx[1]&&dy==sy[1]){//状态1
                dx=sx[4];dy=sy[4];//转到状态4
            }
            else if(dx==sx[2]&&dy==sy[2]){//状态2
                if(x==n){dx=sx[1];dy=sy[1];}//转到状态1
                
            }
            else if(dx==sx[3]&&dy==sy[3]){//状态3
                dx=sx[2];dy=sy[2];//转到状态2
            }
            else{//状态4
                if(y==n){dx=sx[3];dy=sy[3];}//转到状态3
            }
        }
    }
    
    for(int i=1;i<=n;i++){
        for(int j=1;j<=n;j++)
            printf("%5d",a[i][j]);
        printf("\n");
    }
    return 0;
}

5.1.1

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#include<iostream>
#include<cmath>
using namespace std;
bool isprime(int n){
    for(int i=2;i<=sqrt(n);i++)
        if(n%i==0)return false;
    return true;
}

int main(){
    int n;
    cin>>n;
    for(int i=2;i<=n;i++)
        if(isprime(i))cout<<i<<" ";
    
    return 0;
}

5.1.2

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#include<iostream>
#include<cmath>
using namespace std;
bool isprime(int n){
    for(int i=2;i<=sqrt(n);i++)
        if(n%i==0)return false;
    return true;
}

bool ispalindrome(int n){
    int x=n,y=0;
    while(x>0){
        y=y*10+x%10;
        x/=10;
    }
    return y==n;
}

int main(){
    int n;
    cin>>n;
    for(int i=2;i<=n;i++)
        if(isprime(i)&&ispalindrome(i))
            cout<<i<<" ";
    
    return 0;
}

5.1.3

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#include<iostream>
using namespace std;
int factorial(int x){
    int s = 1;
    for(int i=2;i<=x;i++)
        s *= i;
    return s;
}

int combinatorial(int n,int m){
    return factorial(n)/(factorial(m)*factorial(n-m));
}

int main(){
    int n,m;
    cin>>n>>m;
    cout<<combinatorial(n,m);
    return 0;
}

5.1.4

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#include<iostream>
using namespace std;
int a[1000];

void sortxy(int x,int y){
    int t;
    for(int i=x;i<=y;i++)
        for(int j=y;j>i;j--)
            if(a[j]<a[j-1]){
                t=a[j];
                a[j]=a[j-1];
                a[j-1]=t;
            }
}

int main(){
    int n,x,y;
    cin>>n;
    for(int i=1;i<=n;i++)
        cin>>a[i];
    cin>>x>>y;
    
    sortxy(x,y);
    
    for(int i=1;i<=n;i++)
        cout<<a[i]<<" ";
    
    return 0;
}

5.1.5

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#include<iostream>
using namespace std;

int a[100],len;

void change(int x){
    len = 1;
    while(x>1){
        a[len]=x%2;
        x/=2;
        len++;
    }
    a[len]=x;
}

void printb(int x){
    for(int i=x;i>=1;i--)
        cout<<a[i];
}

int main(){
    int n;
    cin>>n;
    change(n);
    printb(len);
    return 0;
}

5.2.1

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func(1) = 1
func(2) = 2
func(3) = func(1) - func(2) = -1
func(4) = func(2) - func(3) = 3
func(5) = func(3) - func(4) = -4
func(6) = func(4) - func(5) = 7
func(7) = func(5) - func(6) = -11

5.2.2

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r1 = 1
r2 = 2
r3 = 3
r4 = 4
r5 = 5
r6 = -1  //循环内r1到r5均大于0，故返回-1
r7 = 1   //循环执行到i=1，即r6<0成立，故返回1，下同理
r8 = 2
r9 = 3
r10 = 4
r11 = 5
r12 = -1
r13 = 1
r14 = 2
r15 = 3
r16 = 4

5.2.3

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int Ackermann(int m,int n){
    if(m==0)return n+1;
    if(n==0)return Ackermann(m-1,n+1);
    return Ackermann(m-1,Ackermann(m,n-1));
}

5.2.4

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int sum(int n){
    if(n==1)return 3;
    return 2*n+1+sum(n-1);
}

5.2.5

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void func(int n){
    if(n==0)return;
    cout<<n%10;
    func(n/10);
}

5.2.6

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void func(int n){
    if(n==0)return;
    func(n/2);
    cout<<n%2;
}

6.1

C：

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#include<stdio.h>
#include<string.h>
int main(){
    int n,i,l;
    char t[100];
    scanf("%d",&n);
    scanf("%s",t);
    l=strlen(t);
    for(i=0;i<l;i++){
        printf("%c",(t[i]-'a'+n)%26+'a');
    }
    return 0;
}

C++：

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#include<iostream>
#include<string>
using namespace std;

int main(){
    int n,l;
    string t;
    cin>>n>>t;
    l=t.length();
    for(int i=0;i<l;i++)
        t[i]=(t[i]-'a'+n)%26+'a';
    
    cout<<t;
    return 0;
}

6.2

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#include<cstdio>
#include<cstring>
using namespace std;
int main(){
    int l=0,r=0,i,len,f=1;
    char s[300];
    scanf("%s",s);
    len=strlen(s);
    for(i=0;i<len;i++){
        if(s[i]=='(')l++;
        if(s[i]==')')r++;
        if(r>l){f=0;break;}
    }
    if(l!=r)f=0;
    if(f)printf("YES");
    else printf("NO");
    return 0;
}

6.3

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#include<iostream>
#include<string>
using namespace std;

int main(){
    string s;
    cin>>s;
    int l=s.length();
    int ans=0,num;
    for(int i=l-1;i>=0;i--){
        if(s[i]>='0'&&s[i]<='9'){
            num=s[i]-'0';
        }
        else if(s[i]=='+'){
            ans+=num;
        }
        else if(s[i]=='-'){
            ans-=num;
        }
    }
    ans+=num;
    cout<<ans;
    return 0;
}

6.4

* 此法为逆波兰表达式（后缀表达式）求值，仅供参考

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#include<iostream>
#include<string>
using namespace std;
string s;
int l;

int st[1000],head=0;
void push(int t){
    st[head]=t;
    head++;
}

int top(){
    return st[head-1];
}

bool empty(){
    if(head>0)return false;
    return true;
}

void pop(){
    head--;
}

void MidToPost(){
    string t(s);
    int p=0;
    for(int i=0;i<l;i++){
        switch(s[i]){
            case '*':
            case '/':
                push(s[i]);
                break;
            case '+':
            case '-':
                while(!empty()){
                    t[p]=top();
                    p++;
                    pop();
                }
                push(s[i]);
                break;
            default:
                t[p]=s[i];
                p++;
        }
    }
    while(!empty()){
        t[p]=top();
        p++;
        pop();
    }
    
    s=t;
}

int oper(int a,int b,char o){
    switch(o){
        case '+':
            return a+b;
        case '-':
            return a-b;
        case '*':
            return a*b;
        case '/':
            return a/b;
    }
}

int calculate(){
    int left,right;
    for(int i=0;i<l;i++){
        switch(s[i]){
            case '+':
            case '-':
            case '*':
            case '/':
                right=top();
                pop();
                left=top();
                pop();
                push(oper(left,right,s[i]));
                break;
            default:
                push(s[i]-'0');
        }
    }
    return top();
}

int main(){
    cin>>s;
    l=s.length();
    MidToPost();
    cout<<calculate();
    return 0;
}

6.5

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#include<iostream>
#include<string>
#include<stack>
using namespace std;

string s;
int l;

int postExpr[1000];
bool isOper[1000];
int vlen=0;

int st[1000],head=0;
void push(int t){
    st[head]=t;
    head++;
}

int top(){
    return st[head-1];
}

bool empty(){
    if(head>0)return false;
    return true;
}

void pop(){
    head--;
}

void MidToPost(){
    int t,j;
    for(int i=0;i<l;i++){
        switch(s[i]){
            case '*':
            case '/':
                push(s[i]);
                break;
            case '+':
            case '-':
                while(!empty()){
                    postExpr[vlen]=top();
                    isOper[vlen]=true;
                    vlen++;
                    pop();
                }
                push(s[i]);
                break;
            default:
                
                t=0;
                for(j=i;j<l;j++){
                    if(s[j]<'0'||s[j]>'9'){
                        i=j-1;
                        break;
                    }
                    t=10*t+s[j]-'0';
                }
                if(j==l)i=j;
                
                postExpr[vlen]=t;
                isOper[vlen]=false;
                vlen++;
        }
    }
    while(!empty()){
        postExpr[vlen]=top();
        isOper[vlen]=true;
        vlen++;
        pop();
    }
    
}

int oper(int a,int b,char o){
    switch(o){
        case '+':
            return a+b;
        case '-':
            return a-b;
        case '*':
            return a*b;
        case '/':
            return a/b;
    }
}

int calculate(){
    int left,right;
    for(int i=0;i<vlen;i++){
        if(isOper[i]){
            right=top();
            pop();
            left=top();
            pop();
            push(oper(left,right,postExpr[i]));
        }
        else push(postExpr[i]);
    }
    return top();
}

int main(){
    cin>>s;
    l=s.length();
    MidToPost();
    cout<<calculate();
    return 0;
}

8.1

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#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
char a[1000],b[1000],c[1000];

int numcmp(char s1[],char s2[]){//a>b 1 a=b 0 a<b -1
    if(strcmp(a,b)==0)return 0;
    int al=strlen(s1),bl=strlen(s2);
    if(al>bl)return 1;
    if(al<bl)return -1;
    //al==bl:
    for(int i=0;i<al;i++)
        if(s1[i]>s2[i])return 1;
        else if(s1[i]<s2[i])return -1;
    return 0;
}

void sub(char s1[],char s2[],char ans[]){
    int cmp=numcmp(s1,s2);
    bool nega=0;
    if(cmp==0){
        strcpy(ans,"0");
        return;
    }
    if(cmp<0){
        char t[1000];
        strcpy(t,s1);
        strcpy(s1,s2);
        strcpy(s2,t);
        nega=1;
    }
    
    int al=strlen(s1),bl=strlen(s2),pa=al-1,pb=bl-1;
    short a[1000]={0},b[1000]={0};
    int i,j,jw=0,t1,t2=0;

    for(i=0;i<al;i++)
        a[i]=s1[al-1-i]-'0';

    for(i=0;i<bl;i++)
        b[i]=s2[bl-1-i]-'0';
    
    t1=max(al,bl);
    for(i=0;i<t1;i++){
        a[i]-=jw;
        jw=0;
        if(a[i]<b[i]){
            a[i]+=10;
            jw++;
        }
        a[i]=a[i]-b[i];
    }
    
    while(a[i]==0)i--;
    if(nega){
        ans[t2]='-';
        t2++;
        
    }
    for(;i>=0;i--){
        ans[t2]=a[i]+'0';
        t2++;
    }
    ans[t2]='\0';
}

int main(){
    scanf("%s%s",a,b);
    sub(a,b,c);
    puts(c);
    return 0;
}

8.2

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#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
char a[1000],b[1000],c[1000];

void add(char s1[],char s2[],char ans[]){
    if(s1[0]=='0'&&s2[0]=='0'){
        strcpy(ans,"0");
        return;
    }
    int al=strlen(s1),bl=strlen(s2),pa=al-1,pb=bl-1;
    short a[1000]={0},b[1000]={0};
    int i,j,jw=0,t1,t2=0;

    for(i=0;i<al;i++)
        a[i]=s1[al-1-i]-'0';

    for(i=0;i<bl;i++)
        b[i]=s2[bl-1-i]-'0';

    t1=max(al,bl);
    for(i=0;i<t1;i++){
        a[i]=a[i]+b[i]+jw;
        jw=a[i]/10;
        a[i]%=10;
    }

    a[i]=jw;
    while(a[i]==0)i--;
    for(;i>=0;i--){
        ans[t2]=a[i]+'0';
        t2++;
    }
    ans[t2]='\0';
}

void mul(char s1[],char s2[],char ans[]){
    if(s1[0]=='0'||s2[0]=='0'){
        strcpy(ans,"0");
        return;
    }
    
    int al=strlen(s1),bl=strlen(s2),pa=al-1,pb=bl-1;
    if(al<bl){
        swap(s1,s2);
        swap(al,bl);
    }
    
    short a[1000]={0},b[1000]={0},c[1000]={0};
    char tans[1000]={0};
    int i,j,k,jw=0,t1=0,t2=0;

    for(i=0;i<al;i++)
        a[i]=s1[al-1-i]-'0';

    for(i=0;i<bl;i++)
        b[i]=s2[bl-1-i]-'0';
    
    strcpy(ans,"0");
    for(i=0;i<bl;i++){
        jw=0;
        for(j=0;j<al;j++){
            c[i+j]=a[j]*b[i]+jw;
            jw=c[i+j]/10;
            c[i+j]%=10;
        }
        c[i+j]=jw;
        while(c[i+j]==0)j--;
        t2=0;
        for(j=i+j;j>=0;j--){
            tans[t2]=c[j]+'0';
            c[j]=0;
            t2++;
        }
        tans[t2]='\0';
        add(ans,tans,ans);
    }
    
}

int main(){
    scanf("%s%s",a,b);
    mul(a,b,c);
    puts(c);
    return 0;
}

8.3

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#include<iostream>
#include<cstdio>
using namespace std;
int a[200000]={0};

void QuickSort(int l,int r){
    int i,j,mid,t;
    i=l;
    j=r;
    mid=a[(i+j)/2];
    do{
        while(a[i]<mid)i++;
        while(a[j]>mid)j--;
        if(i<=j){
            t=a[i];
            a[i]=a[j];
            a[j]=t;
            i++;
            j--;
        }
        
    }while(i<=j);
    if(i<r)QuickSort(i,r);
    if(j>l)QuickSort(l,j);
}

int main(){
    int i,n;
    scanf("%d",&n);
    for(i=1;i<=n;i++)
      scanf("%d",&a[i]);
      
    QuickSort(1,n);
    for(i=1;i<=n;i++)
      printf("%d ",a[i]);
    
    return 0;
}

8.4

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#include<iostream>
using namespace std;

int ans=0,a[9]={0},b[9]={0},c[9]={0},d[9]={0};

void eq(int i){
    int j;
    for(j=1;j<=8;j++)
        if(!b[j] && !c[i-j] && !d[i+j]){
            a[i]=j; b[j]=1; c[i-j]=1; d[i+j]=1;
            if(i==8)ans++;
            else eq(i+1);
            b[j]=0;
            c[i-j]=0;
            d[i+j]=0;
        }
}

int main(){
  eq(1);
  cout<<ans;
  return 0;
}