5_01

辽宁师范大学 • 张大为@https://daweizh.github.io/noip/

5 小学奥数 (20)

余数相同问题http://noi.openjudge.cn/math/7647/[+]

#include <iostream>
using namespace std;

int main(){
    int a,b,c;
    cin >> a >> b >> c;
    
    for(int i=2;i<1000000;i++){
        int t = a%i;
        if(b%i==t && c%i==t){
            cout << i << endl;
            break;
        }
    }
    
    return 0;
}

蓄水池水管问题，http://noi.openjudge.cn/math/7648/[+]

#include <iostream>
using namespace std;

int main(){
    long long a,b,c,d;
    double t=0;
    
    cin >> a >> b >> c >> d;
    long long r= a*b*c*d;
    long long a2 = b*c*d;
    long long b2 = a*c*d;
    long long c2 = a*b*d;
    long long d2 = a*b*c;
    while(1){
        if(r>a2){
            r = r-a2;
            t = t +1;
        }else{
            t = t + (double)r/a2;
            break;
        }
        r = r + b2;
        t = t+1;
        if(r>c2){
            r = r-c2;
            t = t + 1;
        }else{
            t = t + (double)r/c2;
            break;
        }
        r = r + d2;
        t = t+1;
    }
    printf("%.2f",t);
    
    return 0;
}

我家的门牌号，http://noi.openjudge.cn/math/7649/[+]

#include <iostream>
using namespace std;

int main(){
    int n,flag = 0,home,my;
    
    cin >> n;
    for(int i=1;i<=n;i++){
        for(int j=1;j<=i;j++){
            if((1+i)*i/2-2*j==n){
                home = i;
                my = j;
                flag = 1;
                break;
            }
        }
        if(flag)
            break;
    }
    cout << my << " " << home << endl;
      
    return 0;
}

不定方程求解http://noi.openjudge.cn/math/7650/[+]

#include <iostream>
using namespace std;

int main(){
    int a ,b ,c ,ans=0;

    cin >> a >> b >> c;
    for(int i=0;i<=c/a;i++)
        for(int j=0;j<=c/b;j++)
            if(a*i+b*j==c)
                ans = ans + 1;
    cout << ans << endl;
    
    return 0;
}

自来水供给，http://noi.openjudge.cn/math/7651/[+]

#include <iostream>
using namespace std;

//                      ----
// a ======b ==== c ===d----e ----f---g
//                      ---   ----
const int maxn = ~((unsigned int)0)>>1;
const int N = 100;
int s[N+1],t[N+1];

int main(){
    int n,ans;

    cin >> n;
    s[0] = 0;
    t[0] = 0;
    for(int i=1;i<=n;i++){
        cin >> s[i];
        s[i] = s[i] + s[i-1]; 
        t[i] = t[i-1] + s[i];
    }		
    
    ans = maxn;
    for(int i=1;i<=n;i++)
        ans = min(ans,s[i]*8000+(t[n]-t[i]-(n-i)*s[i])*2000);
      
    cout << ans << endl;
      
    return 0;
}

乘积最大的拆分，http://noi.openjudge.cn/math/7652/[+]

#include <iostream>
using namespace std;

int n,ans[1005],p=0;

int main(){
    cin >> n;
    if(n==1){
        cout << 1 << endl;
        return 0;
    }
    for(int i=2;i<=n;i++){
        ans[p] = i;
        n = n - i;
        p++;
    }
    for(int i=p-1;i>=0 && n>0;i--){
        ans[i]++;
        n--;
    }
    if(n){
        ans[p-1]++;
    }
    for(int i=0;i<p;i++)
        cout << ans[i] << " ";
    cout << endl;
    
    return 0;
}

地球人口承载力估计，http://noi.openjudge.cn/math/7653/[+]

#include <iostream>
using namespace std;

int main(){
    double x,a,y,b;
    
    cin >> x >> a >> y >> b;
    printf("%.2f",(b*y-a*x)/(b-a)); 
    
    return 0;
}

等差数列末项计算，http://noi.openjudge.cn/math/7654/[+]

#include <iostream>
using namespace std;
int a1,a2,n;

int main(){
    
    cin >> a1 >> a2 >> n;
    cout << a1+(n-1)*(a2-a1) << endl;

    return 0;
}

回文数个数，http://noi.openjudge.cn/math/7655/[+]

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

int n,sum=0;

int main(){

    cin >> n;
    for(int i=1;i<=n;i++){
        int p = (i-1)/2;
        sum = sum + 9*pow(10,p);
    }
    cout << sum << endl;
    
    return 0;
}

李白的酒，http://noi.openjudge.cn/math/7656/[+]

#include <iostream>
using namespace std;

double d,h=1.0;
int n;

int main(){
    
    cin >> n;
    for(int i=n;i>=1;i--){
        h = h / 2 + 1.0;
    }
    printf("%.5lf\n",h-1);

    return 0;
}

连乘积末尾0的个数，http://noi.openjudge.cn/math/7657/[+]

#include <iostream>
using namespace std;

int a,b,ans2=0,ans5=0;

int count(int a,int mod){
    int cnt = 0;
    while(a%mod==0){
        cnt ++;
        a=a/mod;
    }
    return cnt;
}

int main(){

    cin >> a >> b;
    for(int i=a;i<=b;i++ ){
        ans2 = ans2 + count(i,2);
        ans5 = ans5 + count(i,5);
    }
    int ans = ans2<ans5?ans2:ans5;
    cout << ans << endl;
    
    return 0;
}

分苹果http://noi.openjudge.cn/math/7826/[+]

#include <iostream>
using namespace std;

int main(){
    int n,sum=0;
    
    cin >> n;
    for(int i=1;i<=n;i++){
        sum = sum + i;
    }
    cout << sum << endl;
    
    return 0;
}

质数的和与积，http://noi.openjudge.cn/math/7827/[+]

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

int s;
bool prime(int a){
    int r = sqrt(a);
    for(int i=2;i<=r;i++){
        if(a%i==0){
            return false;
        }
    }
    return true;
}

int main(){
  cin >> s;
  int t = s/2;
  for(int i=t;i<s;i++){
      if(prime(i) && prime(s-i)){
          cout << i * (s-i) << endl;
          break;
      }		
  }
  
  return 0;
}

最大公约数与最小公倍数，http://noi.openjudge.cn/math/7828/[+]

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

int g,l,x,y;

int gcd(int n,int m){
    int r=n%m;
    while(r){
        r = n%m;
        n=m;
        m=r;
    }
    return n;
}

int main(){
    cin >> g >> l;
      
    int m=g*l;
    int r=sqrt(m);
    int ans = m;
    for(int i=1;i<=r;i++){
        if(m%i==0){
            x = i;
            y = m/i;
            int t = x + y;
            if(t<ans && gcd(x,y)==g)
                ans = t;
        }
    }	
    
    cout << ans << endl;
    
    return 0;
}

神奇序列求和，http://noi.openjudge.cn/math/7829/[+]

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

int a[2][1000],n,x,y;

int main(){
    int len=2,src,dst,p,ans=0;

    cin >> x >> y >> n;

    a[0][0]=x;
    a[0][1]=y;	
    for(int i=0;i<n;i++){
        src = i%2;
        dst = (i+1)%2;
        p=0;
        for(int j=0;j<len-1;j++){
            a[dst][p++] = a[src][j];
            a[dst][p++] = a[src][j]+a[src][j+1];
        }
        a[dst][p++] = a[src][len-1];
        len = p;
    }	
    for(int j=0;j<len;j++)
        ans = ans + a[dst][j];
      
    cout << ans << endl;
    
    return 0;
}

求小数的某一位http://noi.openjudge.cn/math/7830/[+]

#include <iostream>
using namespace std;

int main(){
    int a,b,n;
    
    cin >> a >> b >> n;
    for(int i=1;i<=n;i++){
        a = a%b;
        a = a*10;
    }
    cout << a/b << endl;
    
    return 0;
}

计算星期几http://noi.openjudge.cn/math/7831/[+]

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

string wk[7]={"Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"};

int main(){
    int a,b,t=1;
    
    cin >> a >> b;
    for(int i=1;i<=b;i++){
        t = t * a ;
        t = t % 7;
    } 
    cout << wk[t] << endl;
    
    return 0;
}

最接近的分数，http://noi.openjudge.cn/math/7832/[+]

#include <iostream>
using namespace std;

int n,x,y;
double a,b,mx=-0.1;

int main(){
    cin >> n >> a >> b;
    
    double t = a/b;
    for( int i=1;i<=n;i++){
        for(int j=1;j<=n;j++){
            double z = double(i)/double(j);
            if(z<t && z > mx ){
                mx = z;
                x = i;
                y = j;
            }	
        }
    }
    cout << x << " " << y << endl;
    
    return 0;
}

幂的末尾http://noi.openjudge.cn/math/7833/[+]

#include <iostream>
using namespace std;

int main(){
    int a,b,t=1;
    
    cin >> a >> b;
    for(int i=1;i<=b;i++){
        t = t * a;
        t = t % 1000;
    }
    if(t<10)
        cout << "00" << t << endl;
    else if(t<100)
        cout << "0" << t << endl;
    else
        cout << t << endl;
    
    return 0;
}

分成互质组，http://noi.openjudge.cn/math/7834/[+]

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

vector< vector<int> > g;
int n,a[100];

int gcd(int x,int y){
    int r=x%y;
    while(r){
        x = y;
        y = r;
        r = x % y;
    }
    return y;
}

int main(){
    cin >> n;
    for(int i=1;i<=n;i++)
      cin >> a[i];
      
    vector<int > v;
    v.push_back(a[1]);
    g.push_back(v);
    
    for(int p=2;p<=n;p++){
        int flag1 = 1;
        for(int i=0;i<g.size();i++){
            int flag2 = 1;
            for(int j=0;j<g[i].size();j++){
                if(gcd(a[p],g[i][j])!=1){
                    flag2 = 0;
                    break;
                }
            }
            if(flag2){
                g[i].push_back(a[p]);
                flag1 = 0;
                break;
            }
        }
        if(flag1){
            vector<int> t;
            t.push_back(a[p]);
            g.push_back(t);
        }			
    }
    cout << g.size() << endl;
    
  //	for(int i=0;i<g.size();i++){
  //		v = g[i];
  //		for( int j=0;j<v.size();j++){
  //			cout << v[j] << " ";
  //		}
  //		cout << endl; 
  //	}

    return 0;
}

参考网址

http://noi.openjudge.cn