2017 济南精英班 Day1

Posted 2020-10-05 日拱一卒 功不唐捐

不管怎么掰都是n*m-1

#include<cstdio>
using namespace std;
int main()
{
    freopen("bpmp.in","r",stdin);
    freopen("bpmp.out","w",stdout);
    int n,m;
    scanf("%d%d",&n,&m);
    int ans=(1ll*n*m-1)%998244353;
    printf("%d",ans);
}

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将行状态压缩，枚举哪些行被折成了一条

枚举时，上一次选取的行 与 这一次选取的行 奇偶性不同，这两行才能折到一起

选取列也要求 上一个选的列与这一个选的列奇偶性不同

dp计算这一条上选哪些列

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int n,m,ans;
int a[21][501],c[501];
int dp(int s)
{
    bool f=false;
    memset(c,0,sizeof(c));
    for(int i=0;i<n;i++)
        if(s&(1<<i))
            for(int j=0;j<m;j++)
                c[j]+=a[i][j];
    for(int j=0;j<m;j++)
        if(c[j]>0) { f=true; break; }
    if(!f) return -2e9;
    int c0=0,c1=0,x;
    for(int i=0;i<m;i++)
        if(i&1) c1=max(c[i]+c0,c1);
        else c0=max(c[i]+c1,c0);
    return max(c1,c0);
}
void dfs(int now,int last,int state)
{
    if(now==n)
    {
        ans=max(ans,dp(state));
        return;
    } 
    if(last==-1 || ((now-last)&1)) dfs(now+1,now,state|(1<<now));
    dfs(now+1,last,state);
}
int main()
{
    freopen("cfyw.in","r",stdin);
    freopen("cfyw.out","w",stdout); 
    scanf("%d%d",&n,&m);
    ans=-2e9;
    for(int i=0;i<n;i++)
        for(int j=0;j<m;j++)
            scanf("%d",&a[i][j]),ans=max(ans,a[i][j]);
    if(ans>0) dfs(0,-1,0);
    printf("%d",ans);
}

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   推公式+除法分块

http://www.cnblogs.com/TheRoadToTheGold/p/6696450.html

#include<cstdio>
#include<algorithm>
#define N 10000001
#define mod 998244353
using namespace std;
int p[1000001],phi[N],cnt;
long long sum[N];
bool vis[N];
void pre(int n)
{
    phi[1]=1;
    for(int i=2;i<=n;i++)
    {
        if(!vis[i])
        {
            vis[i]=true;
            phi[i]=i-1;
            p[++cnt]=i;
        }
        for(int j=1;j<=cnt;j++)
        {
            if(i*p[j]>n) break;
            vis[i*p[j]]=true;
            if(i%p[j]==0)
            {
                phi[i*p[j]]=phi[i]*p[j];
                break;
            }
            else phi[i*p[j]]=phi[i]*(p[j]-1);
        }
    }
    for(int i=1;i<=n;i++) sum[i]=sum[i-1]+phi[i];
}
int main()
{
    freopen("hoip.in","r",stdin);
    freopen("hoip.out","w",stdout);
    int n,m;
    scanf("%d%d",&n,&m);
    pre(min(n,m));
    long long ans=0;
    long long j;
    for(long long i=1;i<=min(n,m);i=j+1) 
    {
        j=min(n/(n/i),m/(m/i));
        ans=(ans+(sum[j]-sum[i-1])*(n/i)%mod*(m/i)%mod)%mod; 
    }
    printf("%I64d",ans);
}

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