Binary search works by repeatedly dividing the search interval in half. This process only works correctly if the list is sorted, allowing the algorithm to eliminate half of the remaining elements in each step.

The initial list is {10, 8, 4, 6}. The first pass inserts 8, resulting in {8, 10, 4, 6}. The second pass takes the next element, 4, and inserts it into the sorted portion {8, 10}. This results in {4, 8, 10, 6}.

For an already sorted array, insertion sort is highly efficient. In each pass, it compares the current element only with the one before it and finds it is in the correct place, requiring no shifts. This is its best-case scenario.

While selection sort's comparison count is predictable, its overall runtime complexity is O($$n^2$$). Insertion sort's worst-case is also O($$n^2$$). Merge sort has a worst-case runtime of O(n log n), which is much more efficient for large datasets than O($$n^2$$), making it the best choice for predictable, efficient performance.

In the first pass (j=0), the smallest element (2) is found and swapped with the element at index 0. The array becomes {2, 4, 8, 6, 5}. In the second pass (j=1), the smallest element in the rest of the array (4) is already at index 1, so it is swapped with itself. The array remains {2, 4, 8, 6, 5}.

The merge process compares the first elements of each subarray and adds the smaller one to the result. It repeats this until all elements from both subarrays are in the result. The correct merged sequence is {2, 4, 8, 9, 12, 15}.

Comparison 1: 4 vs 7 → add 4, advance first pointer. Comparison 2: 8 vs 7 → add 7, advance second pointer. Comparison 3: 8 vs 12 → add 8, advance first pointer. Comparison 4: 15 vs 12 → add 12, advance second pointer. Result: [4, 7, 8, 12] with pointers at 15 and 18. Choice B incorrectly adds 15 instead of 12 in the 4th step. Choice C shows correct result but wrong pointer position for first array. Choice D stops one comparison early.

This description accurately defines insertion sort. Selection sort finds the minimum and swaps. Merge sort divides and conquers. Binary search (not a sort) finds an element in a sorted list.

Selection sort performs exactly one swap at the end of each pass of its outer loop, even if an element is swapped with itself. Since there are n - 1 passes, there are n - 1 swaps.

Insertion sort's performance improves as the array becomes more sorted. For a nearly sorted array, it performs very few shifts and comparisons, making it more efficient than selection sort, whose number of comparisons is always the same regardless of the initial order.