Given a range, count Fibonacci numbers in given range. First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 141, ..
Input: low = 10, high = 100 Output: 5 There are five Fibonacci numbers in given range, the numbers are 13, 21, 34, 55 and 89. Input: low = 10, high = 20 Output: 1 There is only one Fibonacci Number, 13. Input: low = 0, high = 1 Output: 3 Fibonacci numbers are 0, 1 and 1
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A Brute Force Solution is to one by one find all Fibonacci Numbers and count all Fibonacci numbers in given range
An Efficient Solution is to use previous Fibonacci Number to generate next using simple Fibonacci formula that fn = fn-1 + fn-2.
Count of Fibonacci Numbers is 5
Time Complexity Analysis:
Consider the that Fibonacci Numbers can be written as below
So the value of Fibonacci numbers grow exponentially. It means that the while loop grows exponentially till it reaches ‘high’. So the loop runs O(Log (high)) times.
One solution could be directly use above formula to find count of Fibonacci Numbers, but that is not practically feasible (See this for details).
Auxiliary Space: O(1)
This article is contributed by Sudhanshu Gupta. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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