UVA 1391 Astronauts 2-sat

//#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<iostream>
#include<sstream>
#include<cmath>
#include<climits>
#include<string>
#include<map>
#include<queue>
#include<vector>
#include<stack>
#include<set>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
#define pb(a) push(a)
#define INF 0x1f1f1f1f
#define lson idx<<1,l,mid
#define rson idx<<1|1,mid+1,r
#define PI  3.1415926535898
template<class T> T min(const T& a,const T& b,const T& c) {
    return min(min(a,b),min(a,c));
}
template<class T> T max(const T& a,const T& b,const T& c) {
    return max(max(a,b),max(a,c));
}
void debug() {
#ifdef ONLINE_JUDGE
#else

    freopen("d:\\in1.txt","r",stdin);
    freopen("d:\\out1.txt","w",stdout);
#endif
}
int getch() {
    int ch;
    while((ch=getchar())!=EOF) {
        if(ch!=' '&&ch!='\n')return ch;
    }
    return EOF;
}

struct Edge
{
    int u,v;
};
const double eps=10e-6;
const int maxn=100005;
double x;

int age[maxn];

struct TwoSat
{
    int n;
    int mark[maxn*2];
    vector<int> g[maxn*2];
    int s[maxn],c;

    void init(int n)
    {
        this->n=n;
        for(int i=0;i<n*2;i++)
            g[i].clear();
        memset(mark,0,sizeof(mark));
    }
    void add_clause(int u,int v)
    {
        g[u].push_back(v);
    }

    bool dfs(int u)
    {
        if(mark[u^1])return false;
        if(mark[u])return true;
        mark[u]=1;
        s[c++]=u;

        for(int i=0;i<g[u].size();i++)
        {
            if(!dfs(g[u][i]))return false;
        }
        return true;
    }

    bool solve()
    {
        for(int i=0;i<n*2;i+=2)
        {
            if(!mark[i]&&!mark[i+1])
            {
                c=0;
                if(!dfs(i))
                {
                    while(c)mark[s[--c]]=0;
                    if(!dfs(i+1))return false;
                }
            }
        }
        return true;
    }
};

int n,m;
TwoSat solver;


bool same(int a,int b)
{
    if(age[a]>=x&&age[b]>=x)return true;
    if(age[a]<x&&age[b]<x)return true;
    return false;
}
int main()
{
    while(scanf("%d%d",&n,&m)!=EOF&&(n||m))
    {
        x=0;
        solver.init(n);
        for(int i=0;i<n;i++)
        {
            scanf("%d",&age[i]);
            x+=age[i];
        }
        x/=n;

        for(int i=0;i<m;i++)
        {
            int u,v;
            scanf("%d%d",&u,&v);
            u--;v--;
            if(same(u,v))
            {
                solver.add_clause(u*2,v*2+1);
                solver.add_clause(u*2+1,v*2);
                solver.add_clause(v*2,u*2+1);
                solver.add_clause(v*2+1,u*2);
            }else
            {
                solver.add_clause(u*2,v*2+1);
                solver.add_clause(v*2,u*2+1);
            }
        }
        bool res=solver.solve();
        if(!res)
            printf("No solution.\n");
        else
        {
            for(int i=0;i<n;i++)
            {
                if(solver.mark[i*2])
                {
                    printf("C\n");
                }else
                {
                    printf("%c\n",age[i]>=x?'A':'B');
                }
            }
        }
    }
    return 0;
}