1题 跑步训练

$10000/300=33...100$

$10000-32*300=400$

$600/60=10$

$400/10+32*2*60=3880s$

2题 阶乘约数

#include <iostream>
using namespace std;

int p[100];

int main()
{
    for (int i = 2; i <= 100; ++i)
    {
        int n = i;
        for (int j = 2; j*j <= n; ++j)
            while(n % j == 0)
            {
                ++p[j];
                n /= j;
            }
        if(n > 1) ++p[n];    
    }
    
    long long ans = 1;
    for (int i = 2; i <= 100; ++i)
        if(p[i]) ans *= (p[i] + 1);

    cout << ans << endl;
    return 0;    
}

39001250856960000

3题 出栈次序

#include <iostream>
using namespace std;
int f(int n,int m)
{
    if(n == 0)
        return 1;
    if(m == 0)
        return f(n - 1,1);
    return f(n - 1,m + 1) + f(n,m - 1); 
} 
int main()
{
    cout<<f(16,0);
    return 0;
}

35357670

4题 哥德巴赫分解

#include <iostream>

using namespace std;

bool is_prime(int num) {
    for (int i = 2; i*i <=num; ++i)
        if (num % i == 0) return false;
    return true;
}

int main() {
    int m = 0;
    for (int i = 10000; i > 3; i -= 2) {
        for (int j = 2; j <= i/2; ++j) {
            if (is_prime(j) && is_prime(i - j)) {
                m = max(m, j);
                break;
            }
        }
    }
    cout << m << endl;
    return 0;
}

173

5题 图书排列

#include <iostream>
using namespace std;
int a[]={1,2,3,4,5,6,7,8,9,10};
int main()
{
    int ans=0;
    do
    {
        if(abs(a[0]-a[1])==1) continue;
        if(abs(a[1]-a[2])==1) continue;
        if(abs(a[2]-a[3])==1) continue;
        if(abs(a[3]-a[4])==1) continue;
        if(abs(a[4]-a[5])==1) continue;
        if(abs(a[5]-a[6])==1) continue;
        if(abs(a[6]-a[7])==1) continue;
        if(abs(a[7]-a[8])==1) continue;
        if(abs(a[8]-a[9])==1) continue;
        ans++;

    }while(next_permutation(a,a+10));
    cout<<ans<<endl;
    return 0;
}
//479306

6题 猴子分香蕉

#include <iostream>
using namespace std;
int main()
{
    int i=6;
    while(true)
    {
        if(i%5==1)
        {
            int x1=i-(i-1)/5;
            x1=x1-1;
            if(x1%5==2)
            {
                int x2=x1-(x1-2)/5;
                x2=x2-2;
                if(x2%5==3)
                {
                    int x3=x2-(x2-3)/5;
                    x3=x3-3;
                    if(x3%5==4)
                    {
                        int x4=x3-(x3-4)/5;
                        x4=x4-4;
                        if(x4%5==0 && x4!=0)
                        {
                            cout<<i<<endl;
                            break;
                        }
                    }
                }
            }
        }
        i++;
    }
    return 0;
}

3141

7题 稍小分数

int gcd(int a, int b) {
    if(b==0) return a;
    return gcd(b,a%b);
}
int main() {
    int a = 7;
    int b = 13;
    int m,n;
    int max_a = 0;
    int max_b = 1;
    for(n=100; n>1; --n) {
        for(m=n-1; m>=1; --m) {
            if(m*b<a*n && gcd(m,n)==1) {
                if( max_b*m>(max_a*n) ) {
                    max_a = m;
                    max_b = n;
                    break;
                }
            }
        }
    }
    printf("%d/%d\n", max_a, max_b);
    return 0;
}

8题 excel地址

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

int ans[100];

int main()
{
    long n;
    cin>>n;
    int cnt=0;
    while(n)
    {
        if(n%26==0)
        {
            ans[cnt++]=26;//特殊处理，能除尽的情况下，把26作为余数 
            n=n/26-1;//商减少1，作为被除数 
        }
        else
        {
            ans[cnt++]=n%26;//正常情况，记录余数 
            n/=26;//商作为被除数 
        } 
    }
    for(int i=cnt-1;i>=0;i--)
    {
        cout<<(char)('A'+(ans[i]-1));
    } 
    return 0;
}

9题 日期问题

#include<cstdio>
#include<vector>
using namespace std;
int a[3];
const int month[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
struct Date{
    int a,b,c;
}d[3];
bool com(Date x,Date y){
    if(x.a!=y.a)return x.a<y.a;
    if(x.b!=y.b)return x.b<y.b;
    return x.c<y.c;
}
int main(){
    scanf("%d/%d/%d",&a[0],&a[1],&a[2]);
    d[0].a=a[0]+(a[0]<60?2000:1900),d[0].b=a[1],d[0].c=a[2];
    d[1].a=a[2]+(a[2]<60?2000:1900),d[1].b=a[0],d[1].c=a[1];
    d[2].a=a[2]+(a[2]<60?2000:1900),d[2].b=a[1],d[2].c=a[0];
    for(int i=0;i<3;i++){
        for(int j=i+1;j<3;j++){
            if(!com(d[i],d[j])){
                Date t=d[i];
                d[i]=d[j];
                d[j]=t;
            }
        }
    }
    for(int i=0;i<3;i++){
        printf("%d-%02d-%02d\n",d[i].a,d[i].b,d[i].c);
    }
    return 0;
}

10题 整数划分

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;

const int N = 55;

int n;
int f[N][N]={0};

int main()
{
    while(cin >> n)
    {
        f[0][0] = 1;
    
        for(int i = 1; i <= n; i++)
        {
            for(int j = 0; j <= n; j++)
            {
                for(int k = 0; k * i <= j; k++)
                {
                    f[i][j] += f[i - 1][j - k * i];
                }
            }
        }
        
        cout << f[n][n] << endl;
    }

    return 0;
}

11题 一步之遥

#include <iostream>

using namespace std;
const int maxn = 1000;
int main(){
    for(int i = 0; i < maxn; ++i){
        for(int j = 0; j < maxn; ++j){
            if(97 * i - 127 * j == 1){
                cout << i <<" "<< j <<endl;
                return 0;
            }
        }
    }   
    return 0;
}

12题 机器人塔

13题 七星填空

//全排列
do
{
    
}while(next_permutation(a,a+10))

#include<iostream>
#include<algorithm>
using namespace std;
int a[20]={1,2,3,4,5,7,8,9,10,12,13};
int main()
{
    do
    {
        int x1=a[0]+a[1]+a[2]+a[3];
        int x2=a[0]+a[4]+a[6]+a[9];
        int x3=6+a[1]+a[4]+14;
        int x4=6+a[2]+a[5]+11;
        int x5=a[3]+a[5]+a[7]+a[10];
        int x6=14+a[6]+a[8]+a[10];
        int x7=a[9]+a[8]+a[7]+11;
        if(x1==x2 && x1==x3 && x1==x4 && x1==x5 && x1==x6 && x1==x7)
        {
            for(int i=0;i<11;i++)
                cout<<a[i]<<" ";
            cout<<endl;
        }
    }while(next_permutation(a,a+10));
    return 0;
}