Batch add column to layers and add layer prefix in PyQGIS

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I have a number of layers each with a prefix like A_ B_ and so forth.

I'd like to:

1. Add a column (text) called DENSITY to each shp
2. Add the prefix letter from the layer name to each row in the DENSITY column for each shp file.

Can it be done?

I'm using QGIS 2.8.1

Update:

I think there was a typo here with a missing +

print "- layer: " child.layerName() + " ID: " + child.layerId()and I ran this:

# Iterate through the Legend to find all groups and layersroot = QgsProject.instance().layerTreeRoot()for child in root.children(): if isinstance(child, QgsLayerTreeGroup): print "- group: " + child.name()# If we find a group, save the prefix name prefix = group.name().split('_')[0] elif isinstance(child, QgsLayerTreeLayer): print "- layer: " + child.layerName() + " ID: " + child.layerId() layer = child.layer()# Add code to add a field named density to the layer.######## Add code to iterate through each feature in the layer and populate the field with prefix value#######but got these errors:

line 4, in root = QgsProject.instance().layerTreeRoot() AttributeError: 'QgsProject' object has no attribute 'layerTreeRoot'

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