Trigger to update account

Question

This should update the account once a case with the Customer Save record type is saved. The trigger does not work, but there is no error.

    Trigger UpdateLEStatus on Case (after insert) { 
    Set UpdatedAccountIds = new Set();
    Id recordTypeId = Schema.SObjectType.Case.RecordTypeInfosByName.get('Customer Save').RecordTypeId;

    for (Case c: Trigger.new) {
        if (c.RecordTypeId == recordTypeId) {
            UpdatedAccountIds.add(c.accountid);
        }    
    }
    List<Account> AccountForUpdating = [SELECT LE_Status__c
                                                       FROM Account
                                                       WHERE Account.Id IN: UpdatedAccountIds];
    for (Account item: AccountForUpdating) {
        item.LE_Status__c = 'Red';
    }
    update AccountForUpdating;
    }

Answer 1

@Vignex provided this answer

Trigger UpdateLEStatus on Case (after insert) { Set<id> UpdatedAccountIds =    new Set<id>();

    Id recordTypeId =Schema.SObjectType.Case.RecordTypeInfosByName.get('Customer Save').RecordTypeId;

for (Case c: Trigger.new) {
    if (c.RecordTypeId == recordTypeId) {
        UpdatedAccountIds.add(c.accountid);
    }    
}
List<Account> AccountForUpdating = [SELECT LE_Status__c FROM Account WHERE Id IN: UpdatedAccountIds];
for (Account item: AccountForUpdating) {
    item.LE_Status__c = 'Red';
    item.LE_Status_Notes__c = 'Customer Save Case';
}
update AccountForUpdating;
}