Program to find last two digits of Nth Fibonacci number

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 ` `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

 ` `

Output:

```1
61
13
53
```

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