GATE DA 2025 Set 1 — Question 29
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Programming, Data Structures & Algorithms → Searching & Sorting → Insertion Sort
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Question
Suppose that insertion sort is applied to the array and it takes exactly two swaps to sort the array. Select all possible values of .
Correct answer
(A) 10; (C) 14
Solution
The array is initially sorted up to index 5: .
We insert the remaining elements , , and sequentially.Case 1:
We insert the remaining elements , , and sequentially.Case 1:
1.Insert 10: Compare with 11. , swap. Compare with 9. , stop. (1 swap). Array: .
2.Insert 15: , no swap. (0 swaps). Array: .
3.Insert 13: Compare with 15. , swap. Compare with 11. , stop. (1 swap). Total swaps = . Correct.
Case 2: 1.Insert 12: , no swap. (0 swaps). Array: .
2.Insert 15: , no swap. (0 swaps). Array: .
3.Insert 13: Compare with 15. , swap. Compare with 12. , stop. (1 swap). Total swaps = . Incorrect.
Case 3: 1.Insert 14: , no swap. (0 swaps). Array: .
2.Insert 15: , no swap. (0 swaps). Array: .
3.Insert 13: Compare with 15. , swap. Compare with 14. , swap. Compare with 11. , stop. (2 swaps). Total swaps = . Correct.
Case 4: 1.Insert 16: , no swap. (0 swaps). Array: .
2.Insert 15: Compare with 16. , swap. (1 swap). Array: .
3.Insert 13: Compare with 16 (swap), compare with 15 (swap). (2 swaps). Total swaps = . Incorrect.
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