Given a number ‘n’, write a function that prints the last two digits of n-th (‘n’ can also be a large number) Fibonacci number.

Examples:

Input : n = 65
Output : 65

Input : n = 365
Output : 65

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

A simple solution is to find n-th Fibonacci number and print its last two digit. But N can be very large, so it wouldn’t work.

A better solution is to use the fact that after 300-th Fibonacci number last two digits starts repeating.
1) Find m = n % 300.
2) Return m-th Fibonacci number.

C++

// Program to find last two digits of n-th 
// Fibonacci number 
#include<bits/stdc++.h> 
using namespace std; 
typedef long long int ll; 
   
// Fills f[] with first 300 fibonacci numbers 
void precomput(ll f[]) 
{ 
    /* 0th and 1st number of the series are 0 and 1*/
    f[0] = 0; 
    f[1] = 1; 
   
    /* Add the previous 2 numbers in the series 
       and store last two digits of result */
    for (ll i = 2; i < 300; i++) 
        f[i] = (f[i-1] + f[i-2])%100; 
} 
   
// Returns last two digits of n'th Fibonacci  
// Number 
int findLastDigit(ll f[], int n) 
{ 
    return f[n%300]; 
} 
   
/* Driver program to test above function */
int main () 
{ 
    // Precomputing units digit of first 300 
    // Fibonacci numbers 
    ll f[300] = {0}; 
    precomput(f); 
  
    ll n = 1; 
    cout << findLastDigit(f, n) << endl; 
    n = 61; 
    cout << findLastDigit(f, n) << endl; 
    n = 7; 
    cout << findLastDigit(f, n) << endl; 
    n = 67; 
    cout << findLastDigit(f, n) << endl; 
    return 0; 
} 

Java

// Program to find last two digits of  
// n-th Fibonacci number 
import java.util.Arrays; 
class GFG { 
      
    // Fills f[] with first 300  
    // fibonacci numbers 
    static void precomput(long f[]) 
    { 
        /* 0th and 1st number of the 
        series are 0 and 1*/
        f[0] = 0; 
        f[1] = 1; 
        
        /* Add the previous 2 numbers in  
        the series and store last two  
        digits of result */
        for (int i = 2; i < 300; i++) 
            f[i] = (f[i-1] + f[i-2]) % 100; 
    } 
        
    // Returns last two digits of n'th 
    // Fibonacci Number 
    static long findLastDigit(long f[], int n) 
    { 
        return (f[(n%300)]); 
    } 
        
    /* Driver program to test above function */
    public static void main (String args[]) 
    { 
        // Precomputing units digit of  
        // first 300 Fibonacci numbers 
        long f[] = new long[300]; 
        Arrays.fill(f,0); 
        precomput(f); 
       
        int n = 1; 
        System.out.println(findLastDigit(f, n)); 
        n = 61; 
        System.out.println(findLastDigit(f, n)); 
        n = 7; 
        System.out.println(findLastDigit(f, n)); 
        n = 67; 
        System.out.println(findLastDigit(f, n)); 
    } 
} 
  
/*This code is contributed by Nikita Tiwari.*/

Python3

# Python code to find last two  
# digits of n-th Fibonacci number 
  
def precomput(f): 
      
    # 0th and 1st number of the series  
    # are 0 and 1 
    f.append(0) 
    f.append(1) 
      
    # Add the previous 2 numbers in the series 
    # and store last two digits of result 
    for i in range(2,300): 
        f.append((f[i-1] + f[i-2]) % 100) 
  
# Returns last two digits of  
# n'th Fibonacci Number      
def findLastDigit(f,n): 
    return f[n%300] 
      
# driver code 
f = list() 
precomput(f) 
n = 1
print(findLastDigit(f, n)) 
n = 61
print(findLastDigit(f, n)) 
n = 7
print(findLastDigit(f, n)) 
n = 67
print(findLastDigit(f, n)) 
  
# This code is contributed by "Abhishek Sharma 44" 

C#

// Program to find last two digits of  
// n-th Fibonacci number 
using System; 
  
class GFG { 
      
    // Fills f[] with first 300  
    // fibonacci numbers 
    static void precomput(long []f) 
    { 
          
        /* 0th and 1st number of the 
        series are 0 and 1*/
        f[0] = 0; 
        f[1] = 1; 
      
        /* Add the previous 2 numbers in  
        the series and store last two  
        digits of result */
        for (int i = 2; i < 300; i++) 
            f[i] = (f[i-1] + f[i-2]) % 100; 
    } 
      
    // Returns last two digits of n'th 
    // Fibonacci Number 
    static long findLastDigit(long []f, int n) 
    { 
        return (f[(n % 300)]); 
    } 
      
    /* Driver program to test above function */
    public static void Main () 
    { 
          
        // Precomputing units digit of  
        // first 300 Fibonacci numbers 
        long []f = new long[300]; 
        precomput(f); 
      
        int n = 1; 
        Console.WriteLine(findLastDigit(f, n)); 
          
        n = 61; 
        Console.WriteLine(findLastDigit(f, n)); 
          
        n = 7; 
        Console.WriteLine(findLastDigit(f, n)); 
          
        n = 67; 
        Console.WriteLine(findLastDigit(f, n)); 
    } 
} 
  
// This code is contributed by anuj_67. 

PHP

<?php 
// Program to find last two  
// digits of n-th Fibonacci  
// number 
  
// Fills f[] with first  
// 300 fibonacci numbers 
function precomput() 
{ 
    /* 0th and 1st number of 
    the series are 0 and 1*/
    $f[0] = 0; 
    $f[1] = 1; 
  
    /* Add the previous 2 numbers  
    in the series and store last  
    two digits of result */
    for ($i = 2; $i < 300; $i++) 
        $f[$i] = ($f[$i - 1] +  
                  $f[$i - 2]) % 100; 
      
    return $f; 
} 
  
// Returns last two digits  
// of n'th Fibonacci Number 
function findLastDigit($f, $n) 
{ 
    return $f[$n % 300]; 
} 
  
// Driver code 
  
// Precomputing units digit  
// of first 300 Fibonacci numbers 
$f = precomput(); 
  
$n = 1; 
echo findLastDigit($f, $n) . "\n"; 
$n = 61; 
echo findLastDigit($f, $n) . "\n"; 
$n = 7; 
echo findLastDigit($f, $n) . "\n"; 
$n = 67; 
echo findLastDigit($f, $n) . "\n"; 
  
// This code is contributed by mits. 
?> 

Output:

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My Personal Notes

Program to find last two digits of Nth Fibonacci number

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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