In Merge Sort, the recurrence is T(n)=2T(n2)+O(n)T(n)=2T(n2)+O(n). This recurrence falls into Case 2, with a time complexity of Θ(n log n). In Binary Search, the recurrence T(n)=T(n2)+O(1)T(n)=T(n2)+O(1) falls under Case 1, with a complexity of Θ(log n)...