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Question4Max. score: 100.00Fibonacci Series - Dynamic ProgrammingFind the nth fibonacci numberThe Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …The next number is found by adding up the two preceding numbers.Let F[i] be the ith fibonacci numberF[0]=0F[1]=1F[i]=F[i-1]+F[i-2]This problem can be solved very easily by using recursion. But this is not an efficient solution. Using DP, we can solve this problem in O. You are required to solve this in a bottom up manner and keep caching all the values to avoid recomputation.Sample Input:3     Sample Output: 2Constraints:1 ≤ N ≤ 10000

Question

Question4Max. score: 100.00Fibonacci Series - Dynamic ProgrammingFind the nth fibonacci numberThe Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …The next number is found by adding up the two preceding numbers.Let F[i] be the ith fibonacci numberF[0]=0F[1]=1F[i]=F[i-1]+F[i-2]This problem can be solved very easily by using recursion. But this is not an efficient solution. Using DP, we can solve this problem in O. You are required to solve this in a bottom up manner and keep caching all the values to avoid recomputation.Sample Input:3     Sample Output: 2Constraints:1 ≤ N ≤ 10000

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Solution

To solve this problem, we will use a bottom-up approach of dynamic programming. Here are the steps:

  1. Initialize an array F of size n+1.
  2. Set F[0] to 0 and F[1] to 1. These are the base cases.
  3. For i from 2 to n, set F[i] to F[i-1] + F[i-2]. This is the recurrence relation given in the problem.
  4. Return F[n].

Here is a Python solution:

def fibonacci(n):
    F = [0, 1] + [0]*(n-1)
    for i in range(2, n+1):
        F[i] = F[i-1] + F[i-2]
    return F[n]

This function takes an integer n as input and returns the nth Fibonacci number. The time complexity is O(n), which is much more efficient than the recursive solution.

This problem has been solved

Similar Questions

Find the nth fibonacci numberThe Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …The next number is found by adding up the two preceding numbers.Let F[i] be the ith fibonacci numberF[0]=0F[1]=1F[i]=F[i-1]+F[i-2]This problem can be solved very easily by using recursion. But this is not an efficient solution. Using DP, we can solve this problem in O. You are required to solve this in a bottom up manner and keep caching all the values to avoid recomputation.Sample Input:3     Sample Output: 2

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Problem StatementCreate a program that generates and prints the Fibonacci series up to a specified number 'N'. The Fibonacci series is a sequence of numbers in which each number is the sum of the two preceding numbers, starting with 0 and 1. Your program should take an integer input 'N' and display the Fibonacci series up to the Nth term using a while loop.Fibonacci series: 0, 1, 1, 2, 3, 5, 8,... Note: This question is one of the most asked questions in placements.Input format :The input consists of a positive integer N.Output format :The output displays the Fibonacci series up to the Nth term separated by space.Refer to the sample output for the formatting specifications.Code constraints :In this scenario, the test cases fall under the following constraints:1 ≤ N ≤ 20The Fibonacci series starts from 0.Sample test cases :Input 1 :7Output 1 :0 1 1 2 3 5 8 Input 2 :1Output 2 :0 Input 3 :20Output 3 :0 1 1 2 3 5 8 13 21 34 55

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