Question 48

Comparison Cost for Merging Two Lists:
Merging two sorted lists of lengths $m$ and $n$ requires at most $m + n - 1$ comparisons in the worst case.

Optimal Merge Pattern (Greedy Selection):
Always merge the two shortest available lists at each step.
Initial list sizes: $\{20, 24, 30, 35, 50\}$.

• Step 1: Merge 20 and 24:

  $$\text{New size} = 20 + 24 = 44.$$
  $$\text{Comparisons} = 20 + 24 - 1 = 43.$$

  Available sizes: $\{30, 35, 44, 50\}$.

• Step 2: Merge 30 and 35:

  $$\text{New size} = 30 + 35 = 65.$$
  $$\text{Comparisons} = 30 + 35 - 1 = 64.$$

  Available sizes: $\{44, 50, 65\}$.

• Step 3: Merge 44 and 50:

  $$\text{New size} = 44 + 50 = 94.$$
  $$\text{Comparisons} = 44 + 50 - 1 = 93.$$

  Available sizes: $\{65, 94\}$.

• Step 4: Merge 65 and 94:

  $$\text{New size} = 65 + 94 = 159.$$
  $$\text{Comparisons} = 65 + 94 - 1 = 158.$$

Total Worst-Case Comparisons: