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
We strongly recommend you to minimize your browser and try this yourself first.
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
- Sum of Fibonacci Numbers in a range
- Count of Numbers in Range where the number does not contain more than K non zero digits
- Count of Numbers in a Range where digit d occurs exactly K times
- Count of Numbers in a Range divisible by m and having digit d in even positions
- Count Numbers in Range with difference between Sum of digits at even and odd positions as Prime
- Count numbers in a range having GCD of powers of prime factors equal to 1
- Space efficient iterative method to Fibonacci number
- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Count of Numbers in Range where first digit is equal to last digit of the number
- Time complexity of recursive Fibonacci program
- Find Index of given fibonacci number in constant time
- Find maximum in a stack in O(1) time and O(1) extra space
- Count of cells in a matrix which give a Fibonacci number when the count of adjacent cells is added
- Sum of Fibonacci Numbers
- Non Fibonacci Numbers