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You are given an integer n, representing the size of a board with numbers ranging from 1 to n. The task is to count the number of distinct numbers on this board.

Write a function countDistinctNumbers(n: int) -> int that returns the count of distinct numbers on the board.

Clarifying Questions

1. Are all the numbers on the board distinct inherently?
   • Yes, since the board contains numbers ranging from 1 to n.
2. What is the expected input range for n?
   • Typically, n will be a positive integer. For edge cases, we should consider boundary values.
3. Are there any constraints on the execution time or space complexity?
   • Given that we need to simply count the numbers from 1 to n, the complexity should be optimal.

Strategy

Since the numbers on the board range from 1 to n, and each number appears exactly once, the task is straightforward:

1. Identify the Range: The numbers are inherently distinct from 1 to n.
2. Count the Numbers: The number of distinct elements is equal to the count of numbers within that range, which is n.

Code

Here is the Python function to achieve this:

def countDistinctNumbers(n: int) -> int:
    return n

Time Complexity

• Time Complexity: (O(1))
  • The function performs a single operation, directly returning the input value.
• Space Complexity: (O(1))
  • No additional space is required other than the input itself.

This solution is optimal as the number of distinct numbers in the given range from 1 to n is inherently equal to n.

Example

countDistinctNumbers(5)  # Output: 5
countDistinctNumbers(10) # Output: 10
countDistinctNumbers(1)  # Output: 1

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