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

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
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 rangeAn Efficient Solution is to use previous Fibonacci Number to generate next using simple Fibonacci formula that fn = fn-1 + fn-2. 
 
C++
Java
Python3
C#
PHP
Javascript
// C++ program to count Fibonacci numbers in given range#include <bits/stdc++.h>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 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 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# 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// PHP program to count// Fibonacci numbers in// given range // Returns count of fibonacci// numbers in [low, high]function countFibs($low, $high){    // Initialize first    // three Fibonacci Numbers    $f1 = 0; $f2 = 1; $f3 = 1;     // Count fibonacci    // numbers in given range    $result = 0;     while ($f1 <= $high)    {        if ($f1 >= $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.?>
<script> // JavaScript program to count Fibonacci// numbers in given range     // Returns count of fibonacci    // numbers in [low, high]    function countFibs(low, high)    {                   // Initialize first three        // Fibonacci Numbers        let f1 = 0, f2 = 1, f3 = 1;               // Count fibonacci numbers        // in given range        let result = 0;               while (f1 <= high)        {            if (f1 >= low)            result++;            f1 = f2;            f2 = f3;            f3 = f1 + f2;        }               return result;    } // Driver program         let low = 10, high = 100;        document.write("Count of Fibonacci Numbers is "                           + countFibs(low, high)); // This code is contributed by susmitakundugoaldanga.</script>
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)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 
Sam007
nitin mittal
mohit kumar 29
susmitakundugoaldanga
RohitOberoi
Fibonacci
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