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a) (15pts) Describe an NTM M = (Q, 2, 6, qo, F) that computes CLIQUE in 0(n2) time. Define the ,5 components without ambiguity.

Work these out to best of your ability. Please explain steps so I can understandScreen Shot 2018-04-24 at 5.37.57 PM.pngScreen Shot 2018-04-24 at 5.38.04 PM.png

Screen Shot 2018-04-24 at 5.37.57 PM.png

a) (15pts) Describe an NTM M = (Q, 2, 6, qo, F) that computes CLIQUE
in 0(n2) time. Define the ,5 components without ambiguity.

Screen Shot 2018-04-24 at 5.38.04 PM.png

b) (20pts) Prove that the following problem is NP-complete.
HAM-CYCLE
Input: graph GflV, E)
Output: True if and only if there is a simple cycle
including every node in V.
In addition to the reduction, explain your basic method in 5-15 lines.

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