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

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 f_{n} = f_{n-1} + f_{n-2}.

## C++

`// 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 program ` `int` `main() ` `{ ` ` ` `int` `low = 10, high = 100; ` ` ` `cout << ` `"Count of Fibonacci Numbers is "` ` ` `<< countFibs(low, high); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to count Fibonacci ` `// numbers in given range ` `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` `; ` ` ` `System.out.println(` `"Count of Fibonacci Numbers is "` ` ` `+ countFibs(low, high)); ` ` ` `} ` `} ` ` ` `// This code is contributed by Sam007. ` |

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## 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 Code ` `low, high ` `=` `10` `, ` `100` `print` `(` `"Count of Fibonacci Numbers is"` `, ` ` ` `countFibs(low, high)) ` ` ` `# This code is contributed ` `# by mohit kumar ` |

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## C#

`// C# program to count Fibonacci ` `// numbers in given range ` `using` `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. ` |

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## PHP

`<?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. ` `?> ` |

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**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

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