Answer: O(log n)

Explanation: The binary search algorithm has a time complexity of O(log n), which is considered efficient. It involves repeatedly dividing the search space in half until the target value is found or determined to not exist.

Answer: Solving a problem by breaking it down into smaller subproblems

Explanation: The divide and conquer approach involves breaking a problem down into smaller subproblems and solving each subproblem independently. The solutions to the subproblems are then combined to solve the original problem.

Answer: It only works on sorted lists

Explanation: The binary search algorithm requires that the list be sorted, which can be a disadvantage if the list is not already sorted or if sorting it is expensive.

Answer: It requires a lot of memory

Explanation: The divide and conquer approach often involves breaking a problem down into smaller subproblems, which may require creating new data structures in memory. This can lead to high memory usage, which is a disadvantage of the approach.

Answer: Searching for a solution by gradually eliminating possibilities

Explanation: The binary search algorithm involves searching for a target value in a sorted list by repeatedly dividing the list in half and eliminating one half of the remaining possibilities at each step.

Answer: O(n log n)

Explanation: The merge sort algorithm has a time complexity of O(n log n), which is considered efficient. It involves dividing the list into smaller sublists, sorting them independently, and then merging them together.

Answer: Computing the greatest common divisor of two numbers

Explanation: The binary search approach can be used to efficiently compute the greatest common divisor of two numbers by repeatedly dividing the larger number by the smaller number until the remainder is 0.

Answer: It can be parallelized to run on multiple processors

Explanation: The divide and conquer approach can be parallelized to run on multiple processors, which can result in faster execution times. This is an advantage of the approach for some problems, especially those with large input sizes.

Answer: Sorting a list of integers

Explanation: Sorting a list of integers can be done using the divide and conquer approach, such as merge sort or quicksort. The list is divided into smaller sublists, sorted independently, and then merged together.

Answer: Finding the shortest path between two nodes in a graph

Explanation: While some graph problems can be solved using the divide and conquer approach, finding the shortest path between two nodes typically requires a different algorithm, such as Dijkstra's algorithm or Bellman-Ford algorithm.