126 lines
3.4 KiB
Markdown
126 lines
3.4 KiB
Markdown
### Q2. 25%, Checking mathematical series number
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Fibonacci Sequence
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Write a Python function named `check_mathematical_series` that takes a positive integer n as input and checks whether the given number belongs to any of the following important mathematical series: `Fibonacci sequence`, `Triangular sequence`, `Square sequence`.
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The function should determine the series type and return a string indicating the result.
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The possible return values are:
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- "Fibonacci" if the number belongs to the Fibonacci sequence.
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- "Triangular" if the number belongs to the Triangular sequence.
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- "Square" if the number belongs to the Square sequence.
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- "None" if the number does not belong to any of the above sequences.
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For this question, consider the following definitions for the series:
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1. Fibonacci sequence: A series of numbers in which each number (after the first two) is the sum of the two preceding ones. The sequence starts with 0 and 1. For example, the Fibonacci sequence begins as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, …
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```python
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def fibonacci_sequence(n):
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# Check if the input is valid
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if n <= 0:
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return []
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elif n == 1:
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return [0]
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elif n == 2:
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return [0, 1]
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# Initialize the sequence with the first two numbers
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sequence = [0, 1]
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# Generate the Fibonacci sequence
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for i in range(2, n):
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next_num = sequence[-1] + sequence[-2]
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sequence.append(next_num)
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return sequence
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```
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2. Triangular sequence: A sequence of numbers in which each term represents the
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total number of dots required to form a triangle with that many dots on each side.
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The nth term of the triangular sequence is given by the formula (n * (n + 1)) / 2.
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For example, the triangular sequence begins as follows: 1, 3, 6, 10, 15, …
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```python
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def triangular_sequence(n):
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# Check if the input is valid
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if n <= 0:
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return []
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# Initialize the sequence with the first number
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sequence = [1]
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# Generate the Triangular sequence
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for i in range(2, n+1):
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next_num = sequence[-1] + i
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sequence.append(next_num)
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return sequence
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```
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Square number sequence: A sequence of numbers that are the squares of
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consecutive integers. For example, the square number sequence begins as follows:
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1, 4, 9, 16, 25, 36, ...
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Write the check_mathematical_series function and test it with the following values
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of n:
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- 21
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- 9
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- 17
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- 10
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```python
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def square_number_sequence(n):
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# Check if the input is valid
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if n <= 0:
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return []
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# Initialize the sequence with the first number
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sequence = [1]
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# Generate the Triangular sequence
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for i in range(2, n+1):
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next_num = sequence[-1] + i
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sequence.append(next_num)
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return sequence
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```
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Print the result for each value of n, indicating the series types to which it belongs.
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Using commas (,) if it belongs to more than 1 series.
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"None" if it doesn't belong to any of the series.
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Your function should have the following signature:
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```python
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def check_mathematical_series(n: int) -> str:
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```
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# Your code here
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Example output:
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```python
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n = 21: Fibonacci, Triangular
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n = 9: Square
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n = 17: None
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n = 10: Triangular
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```
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Note: You can assume that the given n will be a positive integer
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Q:
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有冇話係邊到學python最好？
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我睇完data camp都唔識 🙃🙃
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覺得自己好蠢。
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A:
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你方唔方便比份 notes 我望一望？
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同埋你係咪理科生？
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