Program to find last two digits of Nth Fibonacci number
Last Updated :
24 Mar, 2023
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;
}
// 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.*/
# 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"
// 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
// 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.
?>
<script>
// Program to find last two digits of n-th
// Fibonacci number
// Fills f[] with first 300 fibonacci numbers
function precomput(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 (let i = 2; i < 300; i++)
f[i] = (f[i-1] + f[i-2])%100;
}
// Returns last two digits of n'th Fibonacci
// Number
function findLastDigit(f, n)
{
return f[n%300];
}
/* Driver program to test above function */
// Precomputing units digit of first 300
// Fibonacci numbers
let f = new Uint8Array(300);
precomput(f);
let n = 1;
document.write(findLastDigit(f, n) + "<br>");
n = 61;
document.write(findLastDigit(f, n) + "<br>");
n = 7;
document.write(findLastDigit(f, n) + "<br>");
n = 67;
document.write(findLastDigit(f, n) + "<br>");
// This code is contributed by Mayank Tyagi
</script>
Output:
1
61
13
53
Time Complexity: O(300), it will run in constant time.
Auxiliary Space: O(300), no extra space is required, so it is a constant.
Approach 2: Iterative Approach:
In this implementation, we simply iterate through the Fibonacci sequence up to the n-th number, keeping track of the last two digits of each number using the modulo operator. This allows us to compute the last two digits of even large Fibonacci numbers without needing to store all of the previous numbers in the sequence.
Here Are steps of this approach:
- We start by initializing the first two terms of the sequence to 0 and 1 respectively. Then, for each i from 2 to n, we calculate the ith Fibonacci number by adding the (i-1)th and (i-2)th Fibonacci numbers.
- In each iteration, we keep track of the previous two Fibonacci numbers using two variables, prev and curr. Initially, prev is set to 0 and curr is set to 1. In each iteration, we update prev to curr and curr to the sum of prev and curr. After n iterations, the value of curr is the nth Fibonacci number.
- This approach has a time complexity of O(n) and a space complexity of O(1) since we only need to store two variables at any given time. This makes it more efficient than the recursive approach, which has a time complexity of O(2^n) and a space complexity of O(n). However, the iterative approach can be harder to understand than the recursive approach for some people, as it involves more explicit manipulation of variables and requires a good understanding of loops and basic arithmetic operations.
C++
#include <bits/stdc++.h>
using namespace std;
// Function to find last two digits of the n-th Fibonacci number
int findLastTwoDigits(int n) {
int a = 0, b = 1;
if (n == 0)
return a;
if (n == 1)
return b;
for (int i = 2; i <= n; i++) {
int c = (a + b) % 100;
a = b;
b = c;
}
return b;
}
int main() {
int n = 1;
cout << findLastTwoDigits(n) << endl;
n = 61;
cout << findLastTwoDigits(n) << endl;
n = 7;
cout << findLastTwoDigits(n) << endl;
n = 67;
cout << findLastTwoDigits(n) << endl;
return 0;
}
import java.util.*;
public class LastTwoDigitsFibonacci {
// Function to find last two digits of n-th Fibonacci number
public static int findLastDigit(int n) {
int f1 = 0, f2 = 1, f3;
// Iterate till n-1
for (int i = 1; i < n; i++) {
f3 = (f1 + f2) % 100;
f1 = f2;
f2 = f3;
}
// Return last two digits of n-th Fibonacci number
return f2;
}
// Driver code
public static void main(String[] args) {
int n = 1;
System.out.println(findLastDigit(n));
n = 61;
System.out.println(findLastDigit(n));
n = 7;
System.out.println(findLastDigit(n));
n = 67;
System.out.println(findLastDigit(n));
}
}
# Program to find last two digits of n-th
# Fibonacci number
import math
# Returns last two digits of n'th Fibonacci
# Number
def findLastDigit(n):
a = 0
b = 1
if (n <= 1):
return n
else:
for i in range(2, n + 1):
c = (a + b) % 100
a = b
b = c
return b
# Driver program to test above function
n = 1
print(findLastDigit(n))
n = 61
print(findLastDigit(n))
n = 7
print(findLastDigit(n))
n = 67
print(findLastDigit(n))
using System;
class Program
{
static int FindLastDigit(int n)
{
int a = 0, b = 1, c;
for (int i = 2; i <= n; i++)
{
c = (a + b) % 100;
a = b;
b = c;
}
return b;
}
static void Main(string[] args)
{
int n = 1;
Console.WriteLine(FindLastDigit(n));
n = 61;
Console.WriteLine(FindLastDigit(n));
n = 7;
Console.WriteLine(FindLastDigit(n));
n = 67;
Console.WriteLine(FindLastDigit(n));
}
}
function findLastTwoDigits(n) {
let a = 0, b = 1;
if (n === 0)
return a;
if (n === 1)
return b;
for (let i = 2; i <= n; i++) {
let c = (a + b) % 100;
a = b;
b = c;
}
return b;
}
console.log(findLastTwoDigits(1));
console.log(findLastTwoDigits(61));
console.log(findLastTwoDigits(7));
console.log(findLastTwoDigits(67));
Time Complexity: O(N).
Auxiliary Space: O(1), no extra space is required, so it is a constant.
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem