四川省赛

frog has  n  integers  a1,a2,…,an , and she wants to add them pairwise.

 

Unfortunately, frog is somehow afraid of carries (进位). She defines \emph{hardness}  h(x,y)  for adding  x  and  y  the number of carries involved in the calculation. For example,  h(1,9)=1,h(1,99)=2 .

 

Find the total hardness adding  n  integers pairwise. In another word, find

∑1≤i<j≤nh(ai,aj)

.

//B  统计进位  就是说n个数  如果他们相加需要进位的话就加1   求所有俩俩之间的进位和
/*
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<vector>
using namespace std;
typedef long long ll;
#define inf 0x3f3f3f3f
#define eps 1e-10
#define maxl 100010
#define mem(i,j) memset(i,j,sizeof(i))
int a[maxl],d[maxl][15];
int main()
{
    freopen("in.txt", "r", stdin);
    int n;
    while(scanf("%d",&n)!=EOF){
        memset(d,0,sizeof(d));
        for(int i=0;i<n;i++) {
            scanf("%d",&a[i]);
            int temp=a[i];
            int cnt=0;
            while(temp){
                d[i][cnt++]=temp%10;
                temp/=10;
            }
        }
        ll ans=0;
        vector<int> v;
        for(int i=0;i<=10;i++){
            v.clear();
            for(int j=0;j<n;j++){
                int res=0;
                for(int k=i;k>=0;k--){
                    res=res*10+d[j][k];
                }
                v.push_back(res);
            }
            ll sum=1;
            for(int j=0;j<=i;j++) sum*=10;
            sort(v.begin(),v.end());
            for(int j=0;j<v.size();j++){
                ans+=v.size()-(lower_bound(v.begin()+j+1,v.end(),sum-v[j])-v.begin());
            }
        }
        printf("%lld\n",ans);
    }
}
*/

frog has a graph with \(n\) vertices \(v(1), v(2), \dots, v(n)\) and \(m\) edges \((v(a_1), v(b_1)), (v(a_2), v(b_2)), \dots, (v(a_m), v(b_m))\).

 

She would like to color some vertices so that each edge has at least one colored vertex.

 

Find the minimum number of colored vertices.

//D   就是一个图  不一定是联通的  让你给点染色  保证所有的边都有至少一个点被染色了
/*
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<vector>
using namespace std;
typedef long long ll;
#define inf 0x3f3f3f3f
#define eps 1e-10
#define maxl 510
#define mem(i,j) memset(i,j,sizeof(i))
int d[maxl][maxl];
int res[maxl],vis[maxl];
int n,m,ans;
bool solve(int u){
    for(int v=1;v<=n;v++){
        if(vis[v]||!d[u][v]) continue;
        vis[v]=1;
        if(res[v]==0||solve(res[v])){//二分图
            res[v]=u;
            return true;
        }
    }
    return false;
}
int main()
{
    freopen("in.txt", "r", stdin);
    while(scanf("%d%d",&n,&m)!=EOF){
        memset(d,0,sizeof(d));
        memset(res,0,sizeof(res));
        ans=0;
        int u,v;
        for(int i=0;i<m;i++){
            scanf("%d%d",&u,&v);
            if(d[u][v]) continue;
            d[u][v]=1;d[v][u]=1;
        }
        for(int i=1;i<=n;i++){
            memset(vis,0,sizeof(vis));
            if(solve(i)) ans++;
        }
        printf("%d\n",ans/2);
    }
}
*/