public map<Id,List<Contact>> accountmap= new map<id,List<Contact>>();
  List<Account> lstAccount = [SELECT Id, name, (SELECT Id, Name FROM Contacts) FROM Account];//you can filter here
 for(Account acc : lstAccount)
 {
  accountmap.put(acc.Id,acc.contacts.size());
  }
 for(Account ac:lstAccount){
     if(accountmap.containskey(ac.id){
       system.debug('contact size for each account-->'+accountmap.get(ac.id).size());
   }