# Count Fibonacci numbers in given range in O(Log n) time and O(1) space

• Difficulty Level : Medium
• Last Updated : 28 Jun, 2021

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, ..
Example :

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.

## C++

 // C++ program to count Fibonacci numbers in given range#include using namespace std; // Returns count of fibonacci numbers in [low, high]int countFibs(int low, int high){    // Initialize first three Fibonacci Numbers    int f1 = 0, f2 = 1, f3 = 1;     // Count fibonacci numbers in given range    int result = 0;     while (f1 <= high)    {        if (f1 >= low)        result++;        f1 = f2;        f2 = f3;        f3 = f1 + f2;    }     return result;} // Driver programint main(){int low = 10, high = 100;cout << "Count of Fibonacci Numbers is "        << countFibs(low, high);return 0;}

## Java

 // Java program to count Fibonacci numbers in given rangeimport java.io.*; class GFG {     // Returns count of fibonacci numbers in [low, high]    public static int countFibs(int low, int high)    {        // Initialize first three Fibonacci Numbers        int f1 = 0, f2 = 1, f3 = 1;         // Count fibonacci numbers in given range        int result = 0;         while (f1 <= high) {            if (f1 >= low)                result++;            f1 = f2;            f2 = f3;            f3 = f1 + f2;        }         return result;    }     // Driver program    public static void main(String[] args)    {        int low = 10, high = 100;        System.out.println("Count of Fibonacci Numbers is "                           + countFibs(low, high));    }} // This code is contributed by RohitOberoi.

## Python3

 # Python3 program to count Fibonacci# numbers in given range # Returns count of fibonacci# numbers in [low, high]def countFibs(low, high):         # Initialize first three    # Fibonacci Numbers    f1, f2, f3 = 0, 1, 1     # Count fibonacci numbers in    # given range    result = 0     while (f1 <= high):        if (f1 >= low):            result += 1        f1 = f2        f2 = f3        f3 = f1 + f2     return result # Driver Codelow, high = 10, 100print("Count of Fibonacci Numbers is",                 countFibs(low, high)) # This code is contributed# by mohit kumar

## C#

 // C# program to count Fibonacci// numbers in given rangeusing System; public class GFG{         // Returns count of fibonacci    // numbers in [low, high]    static int countFibs(int low,                        int high)    {                 // Initialize first three        // Fibonacci Numbers        int f1 = 0, f2 = 1, f3 = 1;             // Count fibonacci numbers        // in given range        int result = 0;             while (f1 <= high)        {            if (f1 >= low)            result++;            f1 = f2;            f2 = f3;            f3 = f1 + f2;        }             return result;    }         // Driver Code    public static void Main(String []args)    {        int low = 10, high = 100;        Console.WriteLine("Count of Fibonacci Numbers is "                        + countFibs(low, high));    }}     // This code is contributed by Sam007.

## PHP

 = $low) $result++;        $f1 = $f2;        $f2 = $f3;        $f3 = $f1 + $f2; }  return $result;} // Driver Code$low = 10; $high = 100;echo "Count of Fibonacci Numbers is ",               countFibs($low, $high); // This code is contributed by nitin mittal.?>

## Javascript

 

Output :

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)