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A research student is given a singly-linked list. Each node
of the list has a color, which is either “Black”
or “White”. He must find if there are more black nodes than
white nodes, or vice versa. His advisor
gives him 5,000Rs to buy a computer to do the work. He goes
to the computer store and finds a
slightly defective computer which costs a mere 3,000Rs. This
computer has the small problem of not
being able to do arithmetic. This means that he cannot use a
counter to count the nodes in the list to
determine the majority color. The computer is otherwise
fully functional. He has the evil idea that he
could buy the defective computer and somehow use it to do
his work, so that he can use the rest of
the money on enjoyment. Show how he can accomplish this
amazing task. Write code for an algorithm
called ‘findMajorityColor’ which takes a singly-linked list,
L, with n nodes and returns the majority color
among nodes of L. This algorithm should have the same
asymptotic running time as counting the
nodes (O(n)). Note: No arithmetic is allowed.
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Answer / tayyab nasir
The best way to do this is to create a new linked list and insert Black nodes at head and White nodes at tail from the previous to the new list. Then find the middle point of the new list. If middle point is Black then Black nodes are more in number else the White nodes.
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