Lexicographically smallest numeric string having odd digit counts

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:

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 <bits/stdc++.h>
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

<script>
        // JavaScript Program to implement
        // the above approach

        // Function to construct lexicographically
        // smallest numeric string having an odd
        // count of each characters
        function genString(N)
        {

            // Stores the resultant string
            let ans = "";

            // If N is even
            if (N % 2 == 0) {
                ans = '1'.repeat(N - 1) + '2';
            }

            // Otherwise
            else {
                ans = '1'.repeat(N);
            }

            return ans;
        }

        // Driver code
        let N = 5;
        document.write(genString(N));

     // This code is contributed by Potta Lokesh
    </script>

Output:

11111

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