Welcome to this comprehensive guide on Fibonacci Search! We're excited to help you explore this powerful algorithmic technique that can significantly improve search efficiency.
Fibonacci Search is an advanced search algorithm, designed to find an element in a sorted list more efficiently than linear search. It uses Fibonacci numbers to determine the search intervals, which is the key to its efficiency.
Fibonacci Search is useful when dealing with large, sorted datasets, as it reduces the number of comparisons required to find an element. This can lead to a significant speedup, making it valuable in real-world applications.
Fibonacci numbers are a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. They play a crucial role in Fibonacci Search.
Fibonacci Series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
The Fibonacci Search algorithm works by recursively dividing the search space using Fibonacci numbers, focusing the search on the most likely position.
Let's dive into some code! Here's a simple implementation of Fibonacci Search in Python:
def fibonacci_search(arr, target):
fibonacci = [0, 1]
while len(fibonacci) < len(arr):
fibonacci.append(fibonacci[-1] + fibonacci[-2])
# Calculate the index for each Fibonacci number
offset = [-1] * len(fibonacci)
for i in range(len(arr)):
fibonacci.append(arr[-1] + i)
# Initialize pointers for each Fibonacci number
left, mid, right = 0, 0, len(fibonacci) - 1
while left < right:
# Find the Fibonacci number that determines the search interval
k = (right + left) // 2
l, r = mid - offset[k], mid + 1
if arr[l] < target <= arr[r]:
mid = r
elif arr[r] < target:
left = r + 1
right = min(right, r + fibonacci[k] - fibonacci[k - 1])
elif arr[l] > target:
mid = l
right = min(right, r + fibonacci[k] - fibonacci[k - 1])
else:
return mid
if mid == len(arr) and arr[mid] == target:
return mid
return -1Fibonacci Search can be useful in various scenarios, such as database management, text search engines, and more. It's all about finding a needle in a haystack efficiently!
Which of the following is the third Fibonacci number?
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