Answer:
Explanation:
( n cards are there initially )
we pick out the first card in random it takes n-1 comparisons to figure out
its Equivalence card - n-1 steps
Two cards have been eliminated ( this leaves us with 2 and n-2 cards)
we pick out the 2nd card in random it takes n-3 comparisons to figure out
its Equivalence card - n-3 steps
we continue to do this.. till all cards are exhausted ( leaves us with 2
and n-4 cards again)
the last comparison will
have
- n-(n-3)
the sum of all these steps - (n-1) + (n-3) + (n-5) + .........+
(n-(n-3))
if you draw this in the form of a tree.
n - n
2
n-2 - n
2
n-4 - n-2
2
n-6 - n-4
2
n-8 - n- 6
the height of the tree will be log n , sum @ each level is at most n
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