UITableView Checkmark ONLY ONE Row at a Time

The best way is to set the accessory type in cellForRowAtIndexPath.

Use didSelectRowAtIndexPath to only record which path should be selected and then call reloadData.

Objective-C:

- (void)tableView:(UITableView *)tableView didSelectRowAtIndexPath:(NSIndexPath   *)indexPath
{
     [tableView cellForRowAtIndexPath:indexPath].accessoryType = UITableViewCellAccessoryCheckmark;
}

-(void)tableView:(UITableView *)tableView didDeselectRowAtIndexPath:(NSIndexPath *)indexPath 
{
    [tableView cellForRowAtIndexPath:indexPath].accessoryType = UITableViewCellAccessoryNone;
}

Swift:

func tableView(_ tableView: UITableView, didSelectRowAt indexPath: IndexPath) {
    tableView.cellForRow(at: indexPath)?.accessoryType = .checkmark
}

func tableView(_ tableView: UITableView, didDeselectRowAt indexPath: IndexPath) {
    tableView.cellForRow(at: indexPath)?.accessoryType = .none
}

You can create a new variable to track the index selected at didSelectRowAtIndex.

int selectedIndex;

in your cellForRowAtIndexPath

if(indexPath.row == selectedIndex)
{
   cell.accessoryType = UITableViewCellAccessoryCheckmark;
}
else
{
   cell.accessoryType = UITableViewCellAccessoryNone;
}

and in your didSelectRowAtIndex

selectedIndex = indexPath.row;
[tableView reloadData];