[NOIP2013] 普及组

计数问题

纯模拟

 #include<cstdio>
 #include<iostream>
 using namespace std;
 int main(){
     int n,x;
     cin>>n>>x;
     int i,c=;
     for(i=;i<=n;i++){
         int a=i;
         while(a!=){
             if(a%==x)c++;
             a/=;
         }
     }
     cout<<c;
     return ;
 }

计数问题

表达式求值

模拟计算，扫一遍出解

 /*NOIP2013普及组t2 洛谷P1981 表达式求值*/
 /**/
 #include<algorithm>
 #include<iostream>
 #include<cstring>
 #include<cstdio>
 #include<cmath>
 using namespace std;
 char last;
 char c;
 int x=;
 int a=,b=;
 int sum=;
 int main(){
     int i,j;
     bool flag=;
     do{
         if(cin>>c);
         else{
             flag=;
             c='+';
         }
         if(c>='' && c<='')x=x*+c-'';
         else{
             a=x;
             x=;
         }
         if(c=='*'){
             last=;
             b=(a*b)%;
         }
         if(c=='+'){
             if(last){
                 a=(a*b)%;
                 sum=(sum+a)%;
                 b=;
                 last=;
             }
             else sum+=a;
         }

     }while(flag==);
     printf("%d",sum%);
     return ;
 }

表达式求值

小朋友的数字

线性DP

 #include<iostream>
 #include<cstdio>
 #include<cmath>
 #include<algorithm>
 using namespace std;
 const long long inf=;
 int n,p,a[];

 long long su[]={};//特征值
 long long scoremx=-inf;//前排最大分数
 long long dmx=-inf;
 long long ans=-inf;
 int sum1(){
     int i,j;
     long long s=;
     long long mx=-inf;
     for(i=;i<=n;i++){
         if(s+a[i]>mx)mx=s+a[i];
         su[i]=mx;
         if(s+a[i]>) s+=a[i];
         else s=;
     }
     //
     for(i=;i<=n;i++){
         su[i]%=p<<;
     }
     return ;
 }
 int main(){
     int i,j;
     scanf("%d%d",&n,&p);
     for(i=;i<=n;i++)scanf("%d",&a[i]);
     sum1();
     long long score;
 //
     scoremx=su[];
     score=su[];
     dmx=score+su[];
 //end
     for(i=;i<=n;i++){
         score=dmx;
         if(dmx>scoremx)scoremx=dmx;
         if(su[i]+score>dmx)dmx=su[i]+score;
     }
     printf("%d",scoremx%p);
     return ;
 }

小朋友的数字

车站分级

从已知的低级站向高级站连边，跑拓扑排序得出层级关系

 #include<iostream>
 #include<cstdio>
 #include<cmath>
 #include<cstring>
 #include<algorithm>
 using namespace std;
 int n,m;
 int a;//[第i趟车次的停靠站数]
 int s[];//[第i趟车次停靠的站]
 int mp[][]={};
 int book[];
 int r[],c[];
 int st[];
 int ans=;
 void rd(){
     scanf("%d%d",&n,&m);
     int i,j,k;
     for(i=;i<=m;i++){
         memset(book,,sizeof(book));
         scanf("%d",&a);
         for(j=;j<=a;j++){
             scanf("%d",&s[j]);
             book[s[j]]=;
         }
         for(k=s[];k<=s[a];k++)//遍历从始发站到终点站
         {
             if(!book[k])
                 for(j=;j<=a;j++)
                 if(!mp[k][s[j]])//从低级连到高级可过，从高级连到低级超时
                 {
                  mp[k][s[j]]=;
                  r[s[j]]++;}
         }

     }
 }
 int main(){
 //    freopen("level.in","r",stdin);
 //    freopen("level.out","w",stdout);
     rd();
     int i,j;
     int top=;
     memset(book,,sizeof(book));
     while(){
         ans++;
         top=;
         for(i=;i<=n;i++)
             if(!r[i] && !book[i])
             {
                 top++;
                 st[top]=i;
                 book[i]=;
             }

         if(!top)break;
         for(j=;j<=n;j++)
           for(i=;i<=top;i++){
               if(mp[st[i]][j]){
                   mp[st[i]][j]=;
                   r[j]--;
               }
           }
         if(!top)break;
     }    

     printf("%d",ans-);

     return ;
 }