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++ 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;
} |
// Java program to count Fibonacci numbers in given range import 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 Code low, high = 10 , 100
print ( "Count of Fibonacci Numbers is" ,
countFibs(low, high))
# This code is contributed # by mohit kumar |
// 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. |
<?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)