How to count number of child records in lookup relationship using trigger in Salesforce?

For Example Contact in my Child object and Account In my Parent Object.

trigger countTotalContactInAccount on Contact(after insert,after update,after delete){
set<Id> accountIDSet = new set<Id>();
list<Account> accountUpdateList = new list<Account>();
if(trigger.isInsert ){
for(Contact c:trigger.new){
      accountIDSet.add(c.AccountID);
}
if(trigger.isDelete || trigger.isUpdate){
for(Contact c:trigger.old){
     accountIDSet.add(c.AccountID);
}
}
list<Account> accountList = [SELECT id,name,(SELECT id from Contacts) from Account where ID IN : accountIDSet];
for(Account a:accountList){
a.Total_contacts__c = a.contacts.size();
accountUpdateList.add(a);
}
update accountUpdateList;

}


NOTE:- Total_contacts__c is a field(DataType - Number) in Account object which store total number of Contacts in a Account.