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1

### GATE CSE 1997

The concatenation of two lists is to be performed on 0(1) time. Which of the following implementations of a list should be used?
A
B
C
D
Array implementation of list

## Explanation

For Circular Doubly linked list there will be no traversal for concatenation.

Except for circular linked lists for all other lists we need to reach till end to attach the second list.
2

### GATE CSE 1996

Which of the following is false?
A
$$100\,n\,\log n = O\left( {{{n\,\log \,n} \over {100}}} \right)$$
B
$$\sqrt {\log \,n} = O(\log \,\log \,n)$$
C
if 0 < x < y then n x = O(ny)
D
$${2^n} \ne O({n^k})$$

## Explanation

Option (a):
100nlogn = O(nlogn) = O($${{n\log n} \over {100}}$$)(As 100 is a constant so multiplication or division does not change the order).
This is True.

Option (b):
$$\sqrt {\log n}$$ = log1/2n = 1/2(logn) = O(logn)
Which is not O(loglogn).So,this is False.

Option (c):
0 < x < y
Let x = 3, y = 5
n3 = O(n5) = lower = O(higher)
This is True.

Option (d):
2n != O(nk)
Here,2n is higher growth rate function than nk.So,This option is True.

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