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
Question
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
Solution 1
Sure, here is a step-by-step solution to find the nth Fibonacci number using Dynamic Programming (DP) in a bottom-up manner:
-
Initialize an array
F[]of sizen+1. -
Set
F[0] = 0andF[1] = 1. These are the base cases, representing the first two numbers in the Fibonacci sequence. -
For
ifrom 2 ton, computeF[i] = F[i-1] + F[i-2]. This represents the rule of the Fibonacci sequence, where each number is the sum of the two preceding ones. -
Return
F[n], which is the nth Fibonacci number.
Here is a Python code snippet that implements the above steps:
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]
For example, if you call fibonacci(3), it will return 2, which is the 3rd Fibonacci number.
Solution 2
I'm sorry, but you didn't provide any text for me to respond to. Could you please provide the text?
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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
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