What is the time complexity of inserting at the end in dynamic arrays?OptionsEither O(1) or O(n)O(n)O(1)O(log n)

Break Down the Problem

1. Identify the operation being analyzed: insertion at the end of a dynamic array.
2. Evaluate the average case and worst-case scenarios for the insertion operation.

Relevant Concepts

1. Dynamic Arrays: A dynamic array can resize itself when it runs out of space.
2. Time Complexity:
   • Inserting an element at the end can generally be O(1) if there is space available.
   • If the dynamic array needs to resize (generally doubling in size), the time complexity for that operation becomes O(n) as each existing element must be copied to the new array.

Analysis and Detail

1. Average Case:
   • When there is enough space in the dynamic array, inserting an element at the end takes constant time, O(1).
2. Worst Case:
   • If the array is full, resizing it requires copying all elements to a new larger array, leading to a time complexity of O(n) during that operation.

Verify and Summarize

• In general, for a dynamic array:
  • Insertion at the end is O(1) on average due to amortization, but O(n) when resizing is needed.
• Thus, the best answer considering average behavior is O(1), but it can reach O(n) under specific conditions.

Final Answer

O(1) (amortized time complexity for insertion at the end of a dynamic array, but it can be O(n) if resizing is necessary).