Probability Engine · CSC206

Data Structures and Algorithms (BSc CSIT, CSC206): the questions likely to come

20 analyzed questions from 7 past papers (2074-2081), grouped by syllabus unit — each with its probability, how often it's been asked, and where to study the answer.

Papers analyzed

2074-2081

Analyzed questions

across 7 syllabus units

Very likely units

high-probability topics

Units = 80% of marks

study these first

Model answers for this subject are being written. Every question links to its original paper so you can study from the source meanwhile.

Pick a unit

U5 · Q1/4 · 208110 marks

Sorting

Explain merge sort with its algorithm. Sort the list 38, 27, 43, 3, 9, 82, 10 using merge sort showing all the intermediate steps and analyze its complexity.

61%

Likely to appearAppeared in 4 of the last 4 board papers

Seen in

How well do you know this?rating moves you on

MODEL ANSWERU5 · 10 marks

Merge Sort

Merge sort is a divide-and-conquer sorting algorithm. It recursively divides the list into two halves, sorts each half, and then merges the two sorted halves into a single sorted list.

Algorithm

MERGE-SORT(A, low, high)
  if low < high
     mid = (low + high) / 2
     MERGE-SORT(A, low, mid)        // sort left half
     MERGE-SORT(A, mid+1, high)     // sort right half
     MERGE(A, low, mid, high)       // merge the two halves

MERGE(A, low, mid, high)
  copy A[low..mid] into L and A[mid+1..high] into R
  i = 0, j = 0, k = low
  while i < |L| and j < |R|
     if L[i] <= R[j]: A[k++] = L[i++]
     else:            A[k++] = R[j++]
  copy any remaining elements of L and R into A

Sorting 38, 27, 43, 3, 9, 82, 10

Divide (split until single elements):

[38, 27, 43, 3, 9, 82, 10]
[38, 27, 43, 3]            [9, 82, 10]
[38, 27]   [43, 3]        [9, 82]   [10]
[38] [27]  [43] [3]       [9] [82]  [10]

Conquer (merge back, sorted):

[38] + [27]  -> [27, 38]
[43] + [3]   -> [3, 43]
[27,38] + [3,43] -> [3, 27, 38, 43]

[9] + [82]   -> [9, 82]
[9,82] + [10] -> [9, 10, 82]

[3,27,38,43] + [9,10,82] -> [3, 9, 10, 27, 38, 43, 82]

Sorted output: $3, 9, 10, 27, 38, 43, 82$

Complexity Analysis

The recurrence is:

T(n) = 2T(n/2) + \Theta(n)

By the Master Theorem ( $a=2, b=2, f(n)=\Theta(n)$ , so $n^{\log_b a} = n$ ):

T(n) = \Theta(n \log n)

Case	Time
Best	$O(n \log n)$
Average	$O(n \log n)$
Worst	$O(n \log n)$

Space complexity: $O(n)$ for the auxiliary arrays. Merge sort is stable but not in-place.

AI-generated answer · unverifiedView in 2081 paper →

U5 · Question 1 of 4

Question Priority · U5ranked by appearance likelihood — study top-down

Sorting

Analyzed next71%

★ TOP PICK

Explain merge sort with its algorithm. Sort the list 38, 27, 43, 3, 9, 82, 10 using merge sort showing all the intermediate steps and analyze its complexity.

10 marksSEEN IN

61%

What is sorting? Explain the working mechanism of quick sort algorithm with a suitable example. Analyze its best-case and worst-case time complexity.

10 marksSEEN IN

45%

Explain heap sort algorithm with an example and analyze its time complexity.

5 marksSEEN IN

71%

Differentiate between bubble sort and selection sort with examples.

5 marksSEEN IN

64%

03The mock

Sit a probable paper

A full mock exam built from the most likely questions, mirroring the real paper's structure. Every slot is a real past question.

Most Probable Paper

Mirrors the real structure · 60 marks · based on 7 past papers

Section A: Long Answer QuestionsAttempt any TWO questions.

1.
Explain merge sort with its algorithm. Sort the list 38, 27, 43, 3, 9, 82, 10 using merge sort showing all the intermediate steps and analyze its complexity.
[10 marks]
SortingVery likelyfrom 2081 paper →
This question has recurred in 4 of 7 years; so far only in internal assessments, not the board; and its topic (Sorting) appears in 100% of years.
2.
What is a graph? Explain Breadth First Search (BFS) and Depth First Search (DFS) traversal techniques with suitable examples and their applications.
[10 marks]
GraphsVery likelyfrom 2080 paper →
This question has recurred in 4 of 7 years; so far only in internal assessments, not the board; and its topic (Graphs) appears in 100% of years.
3.
What is sorting? Explain the working mechanism of quick sort algorithm with a suitable example. Analyze its best-case and worst-case time complexity.
[10 marks]
SortingVery likelyfrom 2079 paper →
This question has recurred in 3 of 7 years; so far only in internal assessments, not the board; and its topic (Sorting) appears in 100% of years.

Section B: Short Answer QuestionsAttempt any EIGHT questions.

1.
Explain different representations of a graph (adjacency matrix and adjacency list) with examples.
[5 marks]
GraphsVery likelyfrom 2081 paper →
This question has recurred in 6 of 7 years; so far only in internal assessments, not the board; and its topic (Graphs) appears in 100% of years.
2.
What is a heap? Explain the heapify operation and construct a max-heap from 4, 10, 3, 5, 1.
[5 marks]
TreesVery likelyfrom 2081 paper →
This question has recurred in 6 of 7 years; so far only in internal assessments, not the board; and its topic (Trees) appears in 100% of years.
3.
Compare linear search and binary search. Write an algorithm for binary search and analyze its complexity.
[5 marks]
SearchingVery likelyfrom 2081 paper →
This question has recurred in 6 of 7 years; so far only in internal assessments, not the board; and its topic (Searching) appears in 100% of years.
4.
Explain heap sort algorithm with an example and analyze its time complexity.
[5 marks]
SortingVery likelyfrom 2081 paper →
This question has recurred in 5 of 7 years; so far only in internal assessments, not the board; and its topic (Sorting) appears in 100% of years.
5.
Differentiate between bubble sort and selection sort with examples.
[5 marks]
SortingVery likelyfrom 2080 paper →
This question has recurred in 5 of 7 years; so far only in internal assessments, not the board; and its topic (Sorting) appears in 100% of years.
6.
What are the applications of stack? Explain how a stack is used in function calls.
[5 marks]
The Stack and QueueVery likelyfrom 2081 paper →
This question has recurred in 5 of 7 years; so far only in internal assessments, not the board; and its topic (The Stack and Queue) appears in 100% of years.
7.
Define a queue. Explain circular queue and write an algorithm for its enqueue and dequeue operations.
[5 marks]
The Stack and QueueVery likelyfrom 2081 paper →
This question has recurred in 5 of 7 years; so far only in internal assessments, not the board; and its topic (The Stack and Queue) appears in 100% of years.
8.
What is recursion? Write a recursive algorithm to compute the factorial of a number and explain the role of the stack in recursion.
[5 marks]
The Stack and QueueVery likelyfrom 2080 paper →
This question has recurred in 5 of 7 years; so far only in internal assessments, not the board; and its topic (The Stack and Queue) appears in 100% of years.
9.
Explain inorder, preorder and postorder tree traversals with an example binary tree.
[5 marks]
TreesVery likelyfrom 2080 paper →
This question has recurred in 5 of 7 years; so far only in internal assessments, not the board; and its topic (Trees) appears in 100% of years.

04The receipts

Behind the numbers

The raw evidence the predictions are computed from: marks per unit per year, syllabus weights, trends, and coverage.

Show the heatmap, topic table and coverage analysis

The receipt: marks per unit, per year

Each row is a syllabus unit, each column an exam year, each cell the marks that unit earned that year. Click any cell to see the actual questions behind it.

Marks:nonefew → many

2074

2075

2077

2078

2079

2080

2081

Total

U5Sorting

120

U7Graphs

100

U2The Stack and Queue

U4Trees

U1Concept of Data Structure

U6Searching

U3The List

#	Syllabus unit	Probability	Appeared	Avg marks	Syllabus weight	Exam vs syllabus	Trend	Questions
1	U5Sorting	Very likely100%	2074 2075 2077 2078 2079 2080 2081	17.1	13%6 lecture hrs	Over-examinedexam 23% · syllabus 13%	Steady	4 recurring4 total
2	U7Graphs	Very likely100%	2074 2075 2077 2078 2079 2080 2081	14.3	13%6 lecture hrs	Over-examinedexam 19% · syllabus 13%	Steady	3 recurring3 total
3	U2The Stack and Queue	Very likely100%	2074 2075 2077 2078 2079 2080 2081	13.6	18%8 lecture hrs	Balancedexam 18% · syllabus 18%	Steady	4 recurring4 total
4	U4Trees	Very likely100%	2074 2075 2077 2078 2079 2080 2081	13.6	20%9 lecture hrs	Balancedexam 18% · syllabus 20%	Steady	4 recurring4 total
5	U1Concept of Data Structure	Very likely100%	2074 2075 2077 2078 2079 2080 2081	7.1	9%4 lecture hrs	Balancedexam 10% · syllabus 9%	Steady	2 recurring2 total
6	U6Searching	Very likely100%	2074 2075 2077 2078 2079 2080 2081	5.7	9%4 lecture hrs	Balancedexam 8% · syllabus 9%	Steady	1 recurring2 total
7	U3The List	Likely71%	2074 2077 2078 2079 2081	5	18%8 lecture hrs	Under-examinedexam 5% · syllabus 18%	Steady	1 recurring1 total

Study smart, not hard

Drag the slider: studying the top 5 units in priority order covers ~88% of all observed marks.

Units to study5/7

~80% line

Lecture time vs exam marks

Where the exam pays more than the curriculum spends: ● lectures vs ● exam marks, as a share of the whole course. A long teal-leading bar = high-yield unit.

U5Sorting

13% of lectures → 23% of markshigh yield

U7Graphs

13% of lectures → 19% of markshigh yield

U2The Stack and Queue

18% of lectures → 18% of marks

U4Trees

20% of lectures → 18% of marks

U1Concept of Data Structure

9% of lectures → 10% of marks

U6Searching

9% of lectures → 8% of marks

U3The List

18% of lectures → 5% of markslow yield

Data Structures and Algorithms (BSc CSIT, CSC206): the questions likely to come

Merge Sort

Algorithm

Sorting 38, 27, 43, 3, 9, 82, 10

Complexity Analysis

Sorting

Sit a probable paper

Most Probable Paper

Behind the numbers

The receipt: marks per unit, per year

Study smart, not hard

Lecture time vs exam marks

2081 B.S.

Data Structures and Algorithms (BSc CSIT, CSC206)

2080 B.S.

Data Structures and Algorithms (BSc CSIT, CSC206)

2079 B.S.

Data Structures and Algorithms (BSc CSIT, CSC206)

2078 B.S.

Data Structures and Algorithms (BSc CSIT, CSC206)

2077 B.S.

Data Structures and Algorithms (BSc CSIT, CSC206)

2075 B.S.

Data Structures and Algorithms (BSc CSIT, CSC206)

2074 B.S.

Data Structures and Algorithms (BSc CSIT, CSC206)