Sage Or Python Algorithm to find no. of colours

#TRY NO. 1  (GOOD FOR SMALL NO. OF COLOURS BUT EXTREMLY INEFFICIENT FOR REST)

Screenshot from 2015-06-26 21:21:16

#TRY NO. 2  (CONSTANT LEVEL OF EFFICIENY FOR FOR ALL TYPES BUT OVERALL VERY  INEFFICIENT )

Screenshot from 2015-06-26 21:19:01

#TRY NO. 3  ( FINAL AND BEST ONE)

Screenshot from 2015-06-26 21:25:15

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