中位数性质（环形均分纸牌）

#include <iostream>
#include <cstring>
#include <string>
#include <algorithm>
using namespace std;
const int N = 1e5+10;
typedef long long ll;
//中位数性质:每个点到中位数距离之和一定是到任意点的距离之和的最小值
ll row[N],col[N];
ll srow[N],scol[N];
int main(){
    int n,m,t;
    cin>>n>>m>>t;
    int sum=t;
    for(int i=0;i<t;i++){
        int x,y;
        cin>>x>>y;
        row[x]++;
        col[y]++;
    }
    // cout<<t<<endl;
    if(sum%n!=0&&sum%m!=0){
        cout<<"impossible"<<endl;
        return 0;
    }
    if(sum%n==0&&sum%m!=0){
        srow[0]=0;
        int avg=sum/n;
        for(int i=1;i<=n;i++){
            srow[i]=srow[i-1]+row[i]-avg;
        }
        sort(srow+1,srow+n+1);
        int mid=(1+n)>>1;
        ll cnt=0;
        for(int i=1;i<=n;i++){
            cnt+=abs(srow[i]-srow[mid]);
        }
        cout<<"row ";
        cout<<cnt<<endl;
        return 0;
    }
    if(sum%n!=0&&sum%m==0){
        scol[0]=0;
        int avg=sum/m;
        for(int i=1;i<=m;i++){
            scol[i]=scol[i-1]+col[i]-avg;
        }
        sort(scol+1,scol+m+1);
        int mid=(1+m)>>1;
        ll cnt=0;
        for(int i=1;i<=m;i++){
            cnt+=abs(scol[i]-scol[mid]);
        }
        cout<<"column ";
        cout<<cnt<<endl;
        return 0;
    }
    int avg1=sum/n,avg2=sum/m;
    srow[0]=0;
    for(int i=1;i<=n;i++){
        srow[i]=srow[i-1]+row[i]-avg1;
    }
    sort(srow+1,srow+n+1);
    int mid=(1+n)>>1;
    ll cnt1=0;
    for(int i=1;i<=n;i++){
        cnt1+=abs(srow[i]-srow[mid]);
    }
    scol[0]=0;
    for(int i=1;i<=m;i++){
        scol[i]=scol[i-1]+col[i]-avg2;
    }
    sort(scol+1,scol+m+1);
    mid=(1+m)>>1;
    ll cnt2=0;
    for(int i=1;i<=m;i++){
        cnt2+=abs(scol[i]-scol[mid]);
    }
    cout<<"both ";
    cout<<cnt1+cnt2<<endl;
    return 0;
}