Sorting Algorithms

In the best case of linear search, the target element is found at the first position of the list, requiring the search to check only one element.

- Statement A is true as the collision in hash tables is handled by hashing methods.
- Statement B is false since linear search doesn't require a sorted list and doesn't divide it in the middle.
- Statement C is true as the modulo division method is often used in hash functions.
- Statement D is true, traversal involves checking whether the key exists in the list or not.
- Statement E is true as binary search works on sorted lists and divides them in the middle.
Thus, the correct statements are A, B, and C.

In the first pass of insertion sort:
- 9 and 8 swap, resulting in: 8, 9, 14, 2, -8, 5.
- 14 is already in the correct place.
- 2 and 14 swap, followed by 2 and 9 swapping.
Thus, 2 swaps are made in pass 1.

In the first pass of Bubble sort, the largest element (13) "bubbles" to the end. After the second pass:
- The 7 and 8 are swapped.
- Then 1 and 7 are swapped, followed by 1 and -9.
- The result after pass 2 is 7, 1, -9, 4, 8, 13.

In the selection sort algorithm, the number of passes required is because in each pass the algorithm selects the smallest (or largest) element from the unsorted portion of the list and places it in its correct position. Therefore, passes are needed to sort the list.

Bubble Sort works by repeatedly comparing adjacent elements in a list and swapping them if they are in the wrong order. This process continues until no more swaps are required, indicating that the list is sorted. Therefore, the correct answer is "Bubble Sort."

Step 1: Bubble sort principle.
In bubble sort, the largest element bubbles to the last position after each pass by successive swaps.
Step 2: Trace passes.
- Start (A):
- Pass 1: Swap 4 and -9 → (B):
- Next swaps move 2 and 6 before 30 → (D):
- Then bubble sort continues and swaps 2 with 12 → (C): (intermediate).
Step 3: Correct sequence.
Hence correct ordering is: (A) → (B) → (D) → (C).
Final Answer:

Step 1: Definition.
Time complexity refers to the computational complexity that describes the amount of time it takes to run an algorithm as a function of the size of the input.
Step 2: Differentiate from other terms.
- Process time: Generic term, not a formal measure.
- Time period: Refers to cycles in physics/electronics, not algorithms.
- Time bound: Relates to deadlines, not algorithm analysis.

Step 3: Correct terminology.
The correct term is Time Complexity.
Final Answer:

Step 1: Recall binary search mechanism.
In binary search, the array is divided into two halves at each iteration using mid index.
Step 2: Progress of search.
At each pass, either the left half or the right half is discarded, reducing the search space by 50%.
Step 3: Efficiency.
This logarithmic halving of search space makes binary search efficient with time complexity .
Step 4: Eliminate wrong options.
- Option 1: Wrong, size never increases.
- Option 3: Wrong, search space reduces each step.
- Option 4: Wrong, reduction is by half not one third.

Final Answer:

Step 1: Understanding queue operations.
- isEmpty: Needed to check if the queue is empty before performing dequeue.
- peek: Allows viewing the front element without removing it. Useful for efficiency.
- isFull: Required to check if the queue is full before performing enqueue (important in circular queues).
- update: Not a standard queue operation.
Step 2: Eliminate wrong choices.
Since isEmpty, peek, and isFull are required, correct set is (A), (B), (C).
Final Answer: