【思特奇杯·云上蓝桥-算法集训营】第1周

**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;
}