Set Algorithm Complexity and Control Structure

• n₁ = size of range 1, n₂ = size of range 2; n = n₁ + n₂, m = MIN(n₁,n₂)
• Unsorted input ranges - For each element in range 1, iterate through range 2:
  Runtime = Θ(n₁ x n₂)
• Sorted input ranges - Iterate through each range one time only:
  Runtime = Θ(n₁ + n₂) = Θ(n)
• Sorted range control structure
• compare current elements from each input range
• perform action based on comparison
• increment past elements used for action
• continue until an input range is exhausted
• deal with tail of remaining range
• runtime O(n)
• Some algorithms (union, merge) must iterate through tail, resulting in runtime Θ (n)
• Others (intersection, difference) may deal with tail by ignoring it, resulting in data-dependent "early bailout" and runtime Ω (m)