This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
const int MAXN=1e6+6;
int a[MAXN][2];
int n;
int dpmin[MAXN][2];
int dpmax[MAXN][2];
string ans="";
int main()
{
cin>>n;
for(int i=1;i<=2*n;i++)cin>>a[i][0];
for(int i=1;i<=2*n;i++)cin>>a[i][1];
dpmin[1][1]=1;
dpmin[1][0]=0;
dpmax[1][1]=1;
dpmax[1][0]=0;
for(int i=2;i<=2*n;i++)
{
dpmin[i][0]=MAXN;
dpmin[i][1]=MAXN;
if(a[i][0]>=a[i-1][0])
{
dpmin[i][0]=min(dpmin[i][0],dpmin[i-1][0]);
dpmax[i][0]=max(dpmax[i][0],dpmax[i-1][0]);
}
if(a[i][0]>=a[i-1][1])
{
dpmin[i][0]=min(dpmin[i][1],dpmin[i-1][1]);
dpmax[i][0]=max(dpmax[i][1],dpmax[i-1][1]);
}
if(a[i][1]>=a[i-1][0])
{
dpmin[i][1]=min(dpmin[i][0],dpmin[i-1][0]+1);
dpmax[i][1]=max(dpmax[i][0],dpmax[i-1][0]+1);
}
if(a[i][1]>=a[i-1][1])
{
dpmin[i][1]=min(dpmin[i][1],dpmin[i-1][1]+1);
dpmax[i][1]=max(dpmax[i][1],dpmax[i-1][1]+1);
}
//cout<<dpmax[i][1]<<" "<<dpmax[i][0]<<" "<<dpmin[i][1]<<" "<<dpmin[i][0]<<endl;
}
int t,cnt;
if(dpmax[2*n][0]>=n&&dpmin[2*n][0]<=n)
{
ans+='A';
t=0;
cnt=0;
}
else if(dpmax[2*n][1]>=n&&dpmin[2*n][1]<=n)
{
ans+='B';
t=1;
cnt=1;
}
else
{
cout<<"-1\n";
return 0;
}
for(int i=2*n-1;i>=1;i--)
{
if(a[i+1][t]>=a[i][0]&&dpmin[i][0]<=n-cnt&&dpmax[i][0]>=n-cnt)
{
t=0;
ans+='A';
}
else
{
t=1;
ans+='B';
cnt++;
}
}
reverse(ans.begin(),ans.end());
cout<<ans<<endl;
return 0;
}
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