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Largest Even and Odd N-digit numbers of base B

• Last Updated : 22 Jul, 2021

Given an integer N and base B, the task is to find the largest Even and Odd N-digit numbers of Base B in decimal form.

Examples:

Input: N = 2, B = 5
Output:
Even = 24
Odd = 23
Explanation:
Largest Even Number of 2 digits in base 5 = 44 which is 24 in decimal form.
Largest Odd Number of 2 digits in base 5 = 43 which is 23 in decimal form.

Input: N = 2, B = 10
Output:
Even = 98
Odd = 99

Approach:
To get the largest Even and Odd N-digits number of base B in decimal form is given by:

1. If Base B is Even, then:
• Largest N-digit even number is (BN – 2).
• Largest N-digit odd number is (BN – 1).
2. If Base B is Odd, then:
• Largest N-digit Even number is (BN – 1).
• Largest N-digit Odd number is (BN – 2).

Below is the implementation of the above approach:

C++

 `// C++ implementation of the``// above approach``#include ``using` `namespace` `std;` `// Function to print the largest``// N-digit even and odd numbers``// of base B``void` `findNumbers(``int` `n, ``int` `b)``{``    ``// Initialise the Number``    ``int` `even = 0, odd = 0;` `    ``// If Base B is even, then``    ``// B^n will give largest``    ``// Even number of N+1 digit``    ``if` `(b % 2 == 0) {` `        ``// To get even number of``        ``// N digit subtract 2 from``        ``// B^n``        ``even = ``pow``(b, n) - 2;` `        ``// To get odd number of``        ``// N digit subtract 1 from``        ``// B^n``        ``odd = ``pow``(b, n) - 1;``    ``}` `    ``// If Base B is odd, then``    ``// B^n will give largest``    ``// Odd number of N+1 digit``    ``else` `{` `        ``// To get even number of``        ``// N digit subtract 1 from``        ``// B^n``        ``even = ``pow``(b, n) - 1;` `        ``// To get odd number of``        ``// N digit subtract 2 from``        ``// B^n``        ``odd = ``pow``(b, n) - 2;``    ``}``    ``cout << ``"Even Number = "` `<< even << ``'\n'``;``    ``cout << ``"Odd Number = "` `<< odd;``}` `// Driver's Code``int` `main()``{``    ``int` `N = 2, B = 5;` `    ``// Function to find the``    ``// numbers``    ``findNumbers(N, B);``    ``return` `0;``}`

Java

 `// Java implementation of the``// above approach``import` `java.util.*;` `class` `GFG{`` ` `// Function to print the largest``// N-digit even and odd numbers``// of base B``static` `void` `findNumbers(``int` `n, ``int` `b)``{``    ``// Initialise the Number``    ``double` `even = ``0``, odd = ``0``;`` ` `    ``// If Base B is even, then``    ``// B^n will give largest``    ``// Even number of N+1 digit``    ``if` `(b % ``2` `== ``0``) {`` ` `        ``// To get even number of``        ``// N digit subtract 2 from``        ``// B^n``        ``even = Math.pow(b, n) - ``2``;`` ` `        ``// To get odd number of``        ``// N digit subtract 1 from``        ``// B^n``        ``odd = Math.pow(b, n) - ``1``;``    ``}`` ` `    ``// If Base B is odd, then``    ``// B^n will give largest``    ``// Odd number of N+1 digit``    ``else` `{`` ` `        ``// To get even number of``        ``// N digit subtract 1 from``        ``// B^n``        ``even = Math.pow(b, n) - ``1``;`` ` `        ``// To get odd number of``        ``// N digit subtract 2 from``        ``// B^n``        ``odd = Math.pow(b, n) - ``2``;``    ``}``    ``System.out.println(``"Even Number = "` `+  (``int``)even );``    ``System.out.print(``"Odd Number = "` `+  (``int``)odd);``}`` ` `// Driver's Code``public` `static` `void` `main(String[] args)``{``    ``int` `N = ``2``, B = ``5``;`` ` `    ``// Function to find the``    ``// numbers``    ``findNumbers(N, B);``}``}` `// This code is contributed by Rajput-Ji`

Python3

 `# Python implementation of the``# above approach` `# Function to print the largest``# N-digit even and odd numbers``# of base B``def` `findNumbers(n, b):``    ``# Initialise the Number``    ``even ``=` `0``;``    ``odd ``=` `0``;` `    ``# If Base B is even, then``    ``# B^n will give largest``    ``# Even number of N+1 digit``    ``if` `(b ``%` `2` `=``=` `0``):` `        ``# To get even number of``        ``# N digit subtract 2 from``        ``# B^n``        ``even ``=` `pow``(b, n) ``-` `2``;` `        ``# To get odd number of``        ``# N digit subtract 1 from``        ``# B^n``        ``odd ``=` `pow``(b, n) ``-` `1``;``    `  `    ``# If Base B is odd, then``    ``# B^n will give largest``    ``# Odd number of N+1 digit``    ``else``:` `        ``# To get even number of``        ``# N digit subtract 1 from``        ``# B^n``        ``even ``=` `pow``(b, n) ``-` `1``;` `        ``# To get odd number of``        ``# N digit subtract 2 from``        ``# B^n``        ``odd ``=` `pow``(b, n) ``-` `2``;``    ` `    ``print``(``"Even Number = "``,``int``(even));``    ``print``(``"Odd Number = "``, ``int``(odd));` `# Driver's Code``if` `__name__ ``=``=` `'__main__'``:``    ``N ``=` `2``;``    ``B ``=` `5``;` `    ``# Function to find the``    ``# numbers``    ``findNumbers(N, B);``    ` `# This code is contributed by 29AjayKumar`

C#

 `// C# implementation of the``// above approach``using` `System;` `class` `GFG{``  ` `// Function to print the largest``// N-digit even and odd numbers``// of base B``static` `void` `findNumbers(``int` `n, ``int` `b)``{``    ``// Initialise the Number``    ``double` `even = 0, odd = 0;``  ` `    ``// If Base B is even, then``    ``// B^n will give largest``    ``// Even number of N+1 digit``    ``if` `(b % 2 == 0) {``  ` `        ``// To get even number of``        ``// N digit subtract 2 from``        ``// B^n``        ``even = Math.Pow(b, n) - 2;``  ` `        ``// To get odd number of``        ``// N digit subtract 1 from``        ``// B^n``        ``odd = Math.Pow(b, n) - 1;``    ``}``  ` `    ``// If Base B is odd, then``    ``// B^n will give largest``    ``// Odd number of N+1 digit``    ``else` `{``  ` `        ``// To get even number of``        ``// N digit subtract 1 from``        ``// B^n``        ``even = Math.Pow(b, n) - 1;``  ` `        ``// To get odd number of``        ``// N digit subtract 2 from``        ``// B^n``        ``odd = Math.Pow(b, n) - 2;``    ``}``    ``Console.WriteLine(``"Even Number = "` `+  (``int``)even );``    ``Console.Write(``"Odd Number = "` `+  (``int``)odd);``}``  ` `// Driver's Code``public` `static` `void` `Main(String[] args)``{``    ``int` `N = 2, B = 5;``  ` `    ``// Function to find the``    ``// numbers``    ``findNumbers(N, B);``}``}` `// This code is contributed by 29AjayKumar`

Javascript

 ``
Output:
```Even Number = 24
Odd Number = 23```

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