# Lexicographically smallest numeric string having odd digit counts

• Last Updated : 18 Oct, 2021

Given a positive integer N, the task is to generate a lexicographically smallest numeric string of size N having an odd count of each digit.

Examples:

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Input: N = 4
Output: 1112
Explanation:
Digit 1 and 2 both have an even count and is the lexicographically smallest string possible.

Input: N = 5
Output: 11111
Explanation:
Digit 1 has an odd count and is the lexicographically smallest string possible.

Approach: The given problem can be solved based on the observation that if the value of N is even, then the resulting string contains 1s, (N – 1) number of times followed by a single 2 is the smallest lexicographic string possible. Otherwise, the resulting string contains 1s, N number of times is the smallest lexicographic string possible.

Below is the implementation of the above approach:

## C++14

 `// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Function to construct lexicographically``// smallest numeric string having an odd``// count of each characters``string genString(``int` `N)``{``    ``// Stores the resultant string``    ``string ans = ``""``;` `    ``// If N is even``    ``if` `(N % 2 == 0) {``        ``ans = string(N - 1, ``'1'``) + ``'2'``;``    ``}` `    ``// Otherwise``    ``else` `{``        ``ans = string(N, ``'1'``);``    ``}` `    ``return` `ans;``}` `// Driver code``int` `main()``{``    ``int` `N = 5;``    ``cout << genString(N);` `    ``return` `0;``}`

## Python3

 `# python program for the above approach``# Function to construct lexicographically``# smallest numeric string having an odd``# count of each characters``def` `genString(N):``  ` `    ``# Stores the resultant string``    ``ans ``=` `""` `    ``# If N is even``    ``if` `(N ``%` `2` `=``=` `0``) :``        ``ans ``=` `"``".join("``1``" ``for` `i ``in` `range``(N``-``1``))``        ``ans ``=` `ans ``+` `"2"``    ` `    ``# Otherwise``    ``else` `:``        ``ans ``=` `"``".join("``1``" ``for` `i ``in` `range``(N))``    ` `    ``return` `ans``  ` `# Driver code``if` `__name__ ``=``=` `"__main__"``:``    ``N ``=` `5``    ``print``(genString(N))`  `# This code is contributed by anudeep23042002`

## C#

 `// C# program for the above approach``using` `System;``class` `GFG {` `    ``// Function to construct lexicographically``    ``// smallest numeric string having an odd``    ``// count of each characters``    ``static` `string` `genString(``int` `N)``    ``{``      ` `        ``// Stores the resultant string``        ``string` `ans = ``""``;` `        ``// If N is even``        ``if` `(N % 2 == 0) {``            ``for` `(``int` `i = 0; i < N - 1; i++)``                ``ans += ``'1'``;``            ``ans += ``'2'``;``        ``}` `        ``// Otherwise``        ``else` `{``            ``for` `(``int` `i = 0; i < N; i++)``                ``ans += ``'1'``;``        ``}` `        ``return` `ans;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `N = 5;``        ``Console.WriteLine(genString(N));``    ``}``}` `// This code is contributed by ukasp.`

## Javascript

 ``
Output:
`11111`

Time Complexity: O(N)
Auxiliary Space: O(N)

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