Merge Sort

1. Which of the following is an array that does NOT have all elements of the same type?

a: [1, 4, 3, 10] Explanation

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b: ["A", true, "Yes", "Hello world"] Explanation

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c: ["Test", "False", "x", "hi"] Explanation

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d: [true, false, false, true] Explanation

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2. Which of the following arrays is sorted in descending order?

a: [-17, -14, -8, -19] Explanation

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b: [-17, 20, 20, 100] Explanation

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c: [900, 14, -100, -1] Explanation

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d: [100, 100, 10, 0] Explanation

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3. Consider the following arrays: A = [5, -5, 10, 1] and B = [0, 100, 1, 0]. Which of the following arrays shows all elements from both arrays combined and sorted in ascending order?

a: [5, -5, 10, 1, 0, 100, 1, 0] Explanation

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b: [0, 100, 1, 0, 5, -5, 10, 1] Explanation

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c: [0, 0, 1, 1, -5, 5, 10, 100] Explanation

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d: [-5, 0, 0, 1, 1, 5, 10, 100] Explanation

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4. If you repeatedly split an array into a fixed number of smaller parts at each step, how does increasing the number of parts you split into at each step affect the total number of splitting rounds needed to break the array down? (Assume you always split into the same number of parts at each round.)

a: The number of rounds does not change; it is independent of the number of parts per step. Explanation

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b: It depends on the situation. Explanation

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c: The number of rounds decreases as you increase the number of parts per step. Explanation

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d: The number of rounds increases as you increase the number of parts per step. Explanation

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5. In merge sort, why are the elements repeatedly divided until the subarrays contain only one element?

a: A one-element subarray is already sorted and can be used as a base case. Explanation

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b: One-element subarrays always contain the smallest elements. Explanation

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c: One-element subarrays require no memory. Explanation

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d: Dividing into one-element subarrays makes the algorithm run in constant time. Explanation

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6. For an array containing

N

elements, approximately how many splitting levels are required in merge sort to reach subarrays containing one element?

N

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\log_2 N

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N-1

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2N

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7. Which statement describes the base case of the recursive division process in merge sort?

a: The process stops when every subarray contains two elements. Explanation

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b: The process stops when the original array is already sorted. Explanation

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c: The process stops when every subarray contains one element or is empty. Explanation

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d: The process stops after exactly two splitting levels. Explanation

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8. When merging two sorted subarrays in ascending order, which operation is repeatedly performed?

a: Compare the first remaining elements of both subarrays and copy the smaller one. Explanation

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b: Reverse both subarrays before combining them. Explanation

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c: Randomly select an element from either subarray. Explanation

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d: Sort both subarrays again before combining them. Explanation

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9. Which expression best represents the worst-case time complexity of merge sort for an array containing

N

elements?

O(N)

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O(N^2)

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O(\log N)

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O(N\log N)

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