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Let A be an a...
Question

Let A be an array of integers. A Fixed point of 'A' is an integer 'i' for which A[i] = i. The time complexity of an efficient algorithm to find any fixed point in a sorted array of n is

A
O(log log n)
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B
O(n2)
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C
O(n)
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D
O(log n)
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Solution

The correct option is D O(log n)
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Q. The minimum required number of comparison required to determined if an integer appears more than n/2 times in a sorted array of n integers is
Q. Let P be an array containing n integers. Let t be the lowest upper bound on the number of comparisons of the array elements, required to find the minimun and maximum values in an arbitrary array of n elements. Which one of the following choices is correct?
Q. Consider a new sorting algorithm similar to the bubble sort algorithm, called Rumble Sort. Given an array as input, Rumble Sort attempts to sort the array and produces a sorted array as output. Here' s the pseudocode for RumbleSort (L).

Rumblesort(L):
let sorted = false
while not sorted:
sorted = true
for i = 0; i < len (L) - 2; i + + ;
if L(i) > L [i + 2];
sorted = false
reverse the given list from L(i) to L [i + 2] (unclusive).

Consider running RumblesSort on the following inputs.
(i) [5 6 8 4 3]
(ii) [5 6 4 8 3]
(iii) [3 4 8 6 5]
(iv) [5 4 8 6 3 ]

For how many of the inputs, does RumbleSort produce the correct sorted array?
Q. Let 'a' be an array containing n integers in increasing order. The following algorithm determines whether there are two distinct numbers in the array whose difference is a specified number S > 0

i = 0; j = 1;
while (j < n)
{
if (E)
j++;
else if (a[j] — a[i] = = S)
break;
else
i++;
}
if (j < n)
printf("yes");
else
printf ("no");

Choose the correct expression for E.
Q. If A is a nilpotent matrix of index 2, then for any positive integer n, A(I+A)n is equal to
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