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Implement Fibonacci sequence with dynamic programming.

Description​

The code calculates the Fibonacci sequence up to a given number n and returns the sequence as a list. It uses a for loop to generate the Fibonacci numbers and appends them to a list. The function is then called with different values of n to print the corresponding Fibonacci sequences.

Code​

program4c.py
def fib(n):
    a = [0, 1]
    for i in range(2, n+1):
        a.append(a[i-1] + a[i-2])
    return a

print(fib(2))
print(fib(3))
print(fib(5))
print(fib(6))s
print(fib(7))
print(fib(8))

Explanation of above code​

Function Definition:​

  • The code defines a function called fib that calculates the Fibonacci sequence up to the given input n.
  • The function takes a single parameter n, which represents the number of Fibonacci sequence elements to generate.
  • The function will return a list containing the Fibonacci sequence up to the nth element.
  • Fibonacci Sequence Initialization:
  • Inside the function, a list named a is initialized with the first two elements of the Fibonacci sequence: [0, 1].
  • a[0] represents the 0th Fibonacci number (0) and a[1] represents the 1st Fibonacci number (1).
  • Fibonacci Sequence Calculation:
  • A for loop is used to calculate the remaining Fibonacci numbers up to the nth element.
  • The loop starts from 2 and goes up to n+1 (inclusive).
  • In each iteration, the next Fibonacci number is calculated by summing the previous two numbers in the sequence (a[i-1] and a[i-2]).
  • The newly calculated Fibonacci number is then appended to the a list using the append method.
  • Return the Fibonacci Sequence:
  • Once the loop completes, the function returns the a list, which contains the Fibonacci sequence up to the nth element.

Testing the Function:​

  • The print statements at the end of the code call the fib function with different values of n to test its functionality.
  • The function is called with n equal to 2, 3, 5, 6, 7, and 8.
  • The returned Fibonacci sequences are printed, and the output will be:
Output
[0, 1, 1]
[0, 1, 1, 2]
[0, 1, 1, 2, 3, 5]
[0, 1, 1, 2, 3, 5, 8]
[0, 1, 1, 2, 3, 5, 8, 13]
[0, 1, 1, 2, 3, 5, 8, 13, 21]
  • In summary, the code defines a function fib that generates the Fibonacci sequence up to a given number n.
  • The Fibonacci sequence is calculated using a for loop and stored in a list, which is then returned by the function.
  • The code demonstrates the functionality of the fib function by printing Fibonacci sequences for different values of n.

Learn more​

Reference​