2785_Himiya za 96

#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<string>
#include<vector>
#include<stack>
#include<queue>
#include<deque>
#include<cstdio>
#include<fstream>
#include<map>
#include<set>
using namespace std;
const int maxe=(1<<14),maxel=64,maxn=(1<<12),inf=(1<<30);
struct edge
{
    int to,cap,next;
    edge(){}
    edge(int _to,int _cap,int _next)
    {
        to=_to;
        cap=_cap;
        next=_next;
    }
};
edge e[maxe];int bre;
int sum_of_a;
int n,m,allv,a[maxel][maxel],S,T,F,p;
int head[maxn],ptr[maxn],path[maxn],sz=0;
int lvl[maxn];
void read()
{
    cin>>n>>m;
    string s;
    for(int i=1;i<=n;i++)
    {
        cin>>s;
        for(int j=0;j<m;++j)
        {
            switch(s[j])
            {
                case 'H':a[i][j+1]=1;
                         sum_of_a+=a[i][j+1];
                         break;
                case 'O':a[i][j+1]=2;
                         sum_of_a+=a[i][j+1];
                         break;
                case 'N':a[i][j+1]=3;
                         sum_of_a+=a[i][j+1];
                         break;
                case 'C':a[i][j+1]=4;
                         sum_of_a+=a[i][j+1];
                         break;
            }
        }
    }
}
void add_edge(int from,int to,int cap)
{
    e[bre]=edge(to,cap,head[from]);
    head[from]=bre;bre++;
}
void init_graph()
{
    memset(head,-1,sizeof(head));
    S=0;T=n*m+1;
    int cur,cur1;
    for(int i=1;i<=n;++i)
        for(int j=1;j<=m;++j)
        {
            if(a[i][j])
            {
                cur=(i-1)*m+j;
                //if((i%2==1&&j%2==1)||(i%2==0&&j%2==0))
                if(i%2==j%2)
                {
                    add_edge(S,cur,a[i][j]);
                    add_edge(cur,S,0);
                    if(1<i)
                    {
                        if(a[i-1][j])
                        {
                            cur1=(i-2)*m+j;
                            add_edge(cur,cur1,1);
                            add_edge(cur1,cur,0);
                        }
                    }
                    if(i<n)
                    {
                        if(a[i+1][j])
                        {
                            cur1=(i)*m+j;
                            add_edge(cur,cur1,1);
                            add_edge(cur1,cur,0);
                        }
                    }
                    if(1<j)
                    {
                        if(a[i][j-1])
                        {
                            cur1=(i-1)*m+j-1;
                            add_edge(cur,cur1,1);
                            add_edge(cur1,cur,0);
                        }
                    }
                    if(j<m)
                    {
                        if(a[i][j+1])
                        {
                            cur1=(i-1)*m+j+1;
                            add_edge(cur,cur1,1);
                            add_edge(cur1,cur,0);
                        }
                    }
                }
                else
                {
                    add_edge(cur,T,a[i][j]);
                    add_edge(T,cur,0);
                }
            }
        }
}
bool BFS()
{
    memset(lvl,0,sizeof(lvl));
    lvl[T]=1;
    queue<int>q;
    q.push(T);
    int w;
    while(!q.empty())
    {
        w=q.front();
        q.pop();
        for(int i=head[w];i!=-1;i=e[i].next)
            if(lvl[e[i].to]==0&&e[i^1].cap>0)
        {
            lvl[e[i].to]=lvl[w]+1;
            q.push(e[i].to);
        }
    }
    return lvl[S];
}
bool DFS(int ver)
{
    if(ver==T)return true;
    for(int i=ptr[ver];i!=-1;i=ptr[ver]=e[i].next)
        if(lvl[e[i].to]+1==lvl[ver]&&e[i].cap>0)
        {
            if(DFS(e[i].to))
            {
                if(p>e[i].cap)
                    p=e[i].cap;
                path[sz]=i;
                sz++;
                return true;
            }
        }
    return false;
}
void inline update()
{
    int x;
    for(int i=0;i<sz;++i)
    {
        x=path[i];
        e[x].cap-=p;
        e[x^1].cap+=p;
    }
}
void Dinitz()
{
    while(BFS())
    {
        for(int i=0;i<=n*m+1;++i)
            ptr[i]=head[i];
        sz=0;
        p=inf;
        while(DFS(S))
        {
            F+=p;
            update();
            sz=0;
            p=inf;
        }
    }
    if(sum_of_a%2)
        cout<<"Invalid\n";
    else if(F*2==sum_of_a)
        cout<<"Valid\n";
    else cout<<"Invalid\n";
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    read();
    init_graph();
    /*cout<<"Initializated graph\n";
    for(int i=0;i<=n*m+1;i++)
    {
        cout<<"i=="<<i<<endl;
        for(int j=head[i];j!=-1;j=e[j].next)
            cout<<e[j].to<<' '<<e[j].cap<<endl;
        cout<<endl;
    }
    cout<<endl;*/
    Dinitz();
return 0;
}
/*
3 4
HOH.
NCOH
OO..
*/