I want to write an trigger,The condition is" if the parent case records should not be close,when its having a child case are open".It will show an error when i close the parent case,

trigger parentCheck on Case (before update) {
    Set<Id> caseIds = new Set<Id>();
    for (Case c : Trigger.new) {  
        if (c.Status == 'Closed') {
            caseIds.add(c.Id);
        }
    }
    if (!caseIds.isEmpty()) {
        Map<Id, List<Case>> caseToParentMap = new Map<Id, List<Case>>();
        for (Id id : caseIds) {
            caseToParentMap.put(id, new List<Case>());
        }
        for (Case c : [
            select ParentId
            from Case
            where ParentId in :caseIds and
                Status != 'Closed'
        ]) {
            caseToParentMap.get(c.ParentId).add(c);
        }   
        for (Id id : caseIds) {
            if (!caseToParentMap.get(id).isEmpty()) {
                Trigger.newMap.get(id).addError('Case has unclosed children');
            }
        }
    }
}