How to use trigger to count number of contacts associated with an account without violating the governor limits in Salesforce?

trigger ContactTrigger on Contact (after insert, after update, after delete, after undelete) {
//—> above handling all states which could see a contact added to or removed from an account

//—> on delete we use Trigger.Old, all else, Trigger.new
List<Contact> contacts = Trigger.isDelete ? Trigger.old : Trigger.new;

//—> the Set class rocks for finding the unique values in a list
Set<Id> acctIds = new Set<Id>();

for (Contact c : contacts) {
//yes, you can have a contact without an account
if (c.AccountId != null) {
acctIds.add(c.AccountId);
}
}

List<Account> acctsToRollup = new List<Account>();

//****** Here is the Aggregate query…don’t count in loops, let the DB do it for you*****
for (AggregateResult ar : [SELECT AccountId AcctId, Count(id) ContactCount
FROM Contact
WHERE AccountId in: acctIds
GROUP BY AccountId]){
Account a = new Account();
a.Id = (Id) ar.get(‘AcctId’); //—> handy trick for updates, set the id and update
a.Contact_Count__c = (Integer) ar.get(‘ContactCount’);
acctsToRollup.add(a);
}

//—-> probably you’ll want to do a little more error handling than this…but this should work.
update acctsToRollup;

}