Consider the algorithm:procedure GT(n : positive integer)F:=1for i:= 1 to n doF: = F * iPrint(F)Give the best big-O complexity for the algorithm above.

Step 1: Break Down the Problem

We need to analyze the given algorithm to determine its time complexity in big-O notation. The algorithm calculates the factorial of a positive integer $n$.

Step 2: Relevant Concepts

1. Understanding the Loop: The loop runs from 1 to $n$, which means it executes $n$ times.
2. Operations Inside the Loop: The main operation inside the loop is the multiplication $F := F * i$, which is a constant time operation, $O(1)$.

Step 3: Analysis and Detail

1. Loop Execution: Since the loop runs $n$ times, we accumulate a total cost given by:

   • Each iteration of the loop takes constant time: $O(1)$.
   • Total time for the loop becomes $O(n)$.

2. Overall Complexity: After considering the operations inside the loop, we conclude that the complexity of the algorithm is dominated by the loop.

Step 4: Verify and Summarize

• The multiplication operation does not introduce any additional complexity beyond $O(1)$ for each iteration.
• Thus, the overall time complexity of the algorithm is $O(n)$.

Final Answer

The best big-O complexity for the algorithm is $O(n)$.