Alice implements Merge Sort so, on a particular machine, it requires exactly ⌈8n log n⌉ steps to sort n elements. Bob implements Heap Sort so it requires exactly ⌈5n log n⌉ steps to sort n elements....

Alice implements Merge Sort so, on a particular machine, it requires exactly ⌈8n log n⌉ steps to sort n elements. Bob implements Heap Sort so it requires exactly ⌈5n log n⌉ steps to sort n elements. Charlie implements Selection Sort so it requires exactly 2n 2 steps to sort n elements. Suppose that Alice can sort 1000 elements in 1 minut

1. How many elements can Bob sort in a minute? How many can Charlie sort in a minute?

2. What is the largest value of n that Charlie can sort faster than Alice?

3. Charlie, devastated by the news from the last exercise, buys a computer that’s twice the speed of