Exam CS502 / Online-Overseas
2:00 (PKST) – 13-Dec-2025

Question was a equation given had to give right ans according to it.
theta ( 4n³ + 15n² + 11n / 6 ) ,theta ( 4n³ + 15n³ + 11n ) ,theta 15n²

in random access machine instructions are executed. Choices are five at a time, infinite instructions at a time, one by one parallel.

The sieve technique is a special case of divide and conquer strategy where at each iteration the number of sub problems is just choices 0 1 2 3

In three dimensional space a point P has dash coordinates choices are X00 Y X Y X Y Z

Asymptotic growth of the function f ( n )equals to 8 n square log n plus 5 n square plus n is choices theta n square theta n square log n theta n log n theta n square log n square

The time complexity of the given recurrent relation will be __.
dn = t ( n / 4 )+ t ( n / 2 plus cn square)
Choices zero and log n zero
θ n³ θ n² θ n

Incomplete binary tree access to the dash involves simple arithmetic operations choices root nodes level links

In added distance calculation if characters are same then no substitutional is needed and E ( i J ) close is equal to choices capital E (I J – J ),E I – I J ,E I – 1 , J – 1 , E I – 1 J

Merge sort requires choices extra storage, no need for of extra storage, sometimes requires as extra storage, extra time than other some sorting algorithms.

To analyze the average running time, let T bracket N bracket close denote the average running time of quick sort on a list of size dash. Choices 0, 10, 100, N.

Asymptotic growth of plane sweep algorithm in (finding maximal points ) is __. choices theta ( n ),theta (log n ), theta ( n log n ), theta (n ^ 2)

theta n log n represents the dash time complexity of merge sort choices best case case average case worst case all cases

In which way an algorithm can be measured or analyzed? Choices, running time and memory to check if it will run on machine or not, to check either it is a correct algorithm or not, operating system and compiler.

For n greater than one, __ divides into two halves, sorts the two and then combine them together. Choices, insertion sort, heap sort, merge sort, bubble sort.

Short:

express the geometric series in summation form and also with capital theta notation.

list down the steps which are required in bucket sort algorithm.

Long:

Given the array A equals to [ 9 3 7 1 6 4 8 2 ] apply the sieve technique for selection using four as the pivot and write the sub arrays containing elements less than equal to and greater than the pivot.

Given below are some Asymptotic running times. You are required to correctly write each Asymptotic running time against its correct description in the table below. Asmptotic running times theta n square , theta log n , theta 1 , theta n log n , theta n Asymptotic time description the table.

1, constant time does not change with input size. Time increases.
2, time increases linearly with input size.
3, time grows logarithmically. Logarithmically increases slowly as input grows.
4, time grows faster than linear but slower than quadratic, common in efficient sorting algorithms.
5, time grows quadratically, often found in simple nested loops. I have to write for all these five asymptotic running time.