Day 27 – ECET 2026 Evening Section: DS – Linear Search & Binary Search

In ECET 2026 Computer Science, Searching Algorithms are simple yet very scoring topics. Every year, 1–2 direct questions come from Linear Search and Binary Search. If you practice the logic and formulas properly, you can secure easy marks.

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📘 Concept Notes

🔹 Linear Search

• Linear Search is the simplest searching technique.
• We compare the target element with each element in the list sequentially.
• Works on unsorted arrays.
• Time Complexity:
  • Best Case = (if element found at first position)
  • Worst Case = (if element is last or not found)
• Algorithm Steps:
  1. Start from the first element.
  2. Compare it with the target element.
  3. If match found → return index.
  4. If end reached → element not found.

Example:
Array = [2, 5, 7, 9, 11], Target = 9
→ Compare one by one, found at index 3 (0-based indexing).

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🔹 Binary Search

• Binary Search is faster but works only on sorted arrays.
• Process: Divide & Conquer.
• Compare target with middle element:
  • If target = mid → found.
  • If target < mid → search left half.
  • If target > mid → search right half.
• Time Complexity:
  • Best Case =
  • Worst Case =
• Algorithm Steps:
  1. Set low = 0, high = n-1.
  2. Repeat while low ≤ high:
     • mid = (low + high)/2
     • If arr[mid] == target → found.
     • Else if arr[mid] > target → high = mid – 1.
     • Else low = mid + 1.

Example:
Array = [2, 5, 7, 9, 11, 15, 20], Target = 15

• mid = 7 (arr[3] = 9), 15 > 9 → search right half
• New mid = arr[5] = 15 → Found at index 5.

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⚙️ Formulas

• Linear Search Complexity:

Binary Search Complexity:

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🔟 10 Most Expected MCQs – ECET 2026

Q1. Linear Search works on:
A) Sorted arrays only
B) Unsorted arrays only
C) Both sorted & unsorted arrays
D) None

Q2. Worst case time complexity of Linear Search is:
A)
B)
C)
D)

Q3. Binary Search requires:
A) Random access
B) Sorted array
C) Sequential access
D) Unsorted array

Q4. Which is faster for large data?
A) Linear Search
B) Binary Search
C) Both same
D) None

Q5. Best case complexity of Binary Search:
A)
B)
C)
D) None

Q6. If array size is 1024, maximum comparisons in Binary Search = ?
A) 10
B) 11
C) 1024
D) 512

Q7. Which algorithm follows Divide & Conquer?
A) Linear Search
B) Binary Search
C) Both
D) None

Q8. Linear Search in best case requires:
A) 1 comparison
B) comparisons
C) comparisons
D) 2 comparisons

Q9. Binary Search is not suitable for:
A) Large sorted arrays
B) Linked lists
C) Random access memory
D) None

Q10. For array size n, Binary Search maximum comparisons = ?
A)
B)
C)
D) 1

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✅ Answer Key (Table format – WordPress friendly)

Q.No	Answer
Q1	C
Q2	B
Q3	B
Q4	B
Q5	A
Q6	B
Q7	B
Q8	A
Q9	B
Q10	A

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🧠 Explanations

• Q1 → C: Linear search checks one by one, so works on both sorted & unsorted arrays.
• Q2 → B: Worst case → all n elements checked.
• Q3 → B: Binary search requires array to be sorted.
• Q4 → B: Binary search is much faster than linear for large n.
• Q5 → A: If found at mid in first step → O(1).
• Q6 → B: , so max = 11 comparisons.
• Q7 → B: Binary search uses divide & conquer.
• Q8 → A: Best case = first element match → only 1 comparison.
• Q9 → B: Binary search needs random access, linked list doesn’t support.
• Q10 → A: Max comparisons = .

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🎯 Why Practice Matters for ECET 2026

Linear and Binary Search are guaranteed topics in ECET exams.

• Questions are direct, mostly formula or logic-based.
• Helps build strong basics for advanced searching and sorting algorithms.
• Mastering these ensures at least 2–3 marks in Data Structures section.

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