Find the next number by adding natural numbers in order on alternating indices from last

Given a numeric string S of size N, the task is to find the number formed by adding numbers 1, 2, 3, … up to infinity to every alternative digit of the given numeric string S(starting from the last position). At any point, if the addition result is not a single digit, perform the repeated addition of digits until the result is a single digit.

Examples:

Input: S = “1345”
Output: 1546
Explanation:
Adding 1 to the last digit i.e., 5 will become 6 which modifies the string to “1346”.
Adding 2 to the second last digit i.e., 3 will become 5 which modifies the string to “1546”.
After the above steps, the resultant string formed is “1546”.

Input: S = “789”
Output: 981

Approach: The idea to solve this problem lies over the part of repeated addition. There is actually no need to perform addition repeatedly until there is one digit. Instead, perform number % 9. If the number % 9 is equal to 9, then the sum of the digits will be equal to 9, else the sum of the digits will be equal to the number % 9. Follow the steps below to solve the problem:

• Initialize the variables temp and adding_number as 0 to store the position to be altered and the number to be added.
• Initialize the string variable result as an empty string to store the result.
• Iterate over the range [len-1, 0] where len is the length of the string, using the variable i and perform the following steps:
  • Initialize the variable digit as the digit at the current position in the string.
  • If temp%2 equals 0 then increase the value of adding_number by 1 and add it to the variable digit.
  • If digit greater than equals to 10 then set the value of digit as digit%9 and if still, digit equals 0 then set its value as 9.
  • Add the variable digit to the variable result in the beginning.
• After performing the above steps, print the value of result as the answer.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to generate the resultant
// number using the given criteria
string generateNumber(string number)
{
    int temp = 0, adding_number = 0;

    // Storing end result
    string result = "";

    // Find the length of numeric string
    int len = number.size();

    // Traverse the string
    for (int i = len - 1; i >= 0; i--) {

        // Storing digit at ith position
        int digit = number[i] - '0';

        // Checking that the number would
        // be added or not
        if (temp % 2 == 0) {

            adding_number += 1;
            digit += adding_number;

            // Logic for summing the digits
            // if the digit is greater than 10
            if (digit >= 10) {
                digit %= 9;
                if (digit == 0)
                    digit = 9;
            }
        }

        // Storing the result
        result = to_string(digit) + result;
        temp += 1;
    }

    // Returning the result
    return result;
}

// Driver Code
int main()
{
    string S = "1345";
    cout << generateNumber(S);

    return 0;
}

Java

// Java program for the above approach
class GFG
{

    // Function to generate the resultant
    // number using the given criteria
    public static String generateNumber(String number) {
        int temp = 0, adding_number = 0;

        // Storing end result
        String result = "";

        // Find the length of numeric string
        int len = number.length();

        // Traverse the string
        for (int i = len - 1; i >= 0; i--) {

            // Storing digit at ith position
            int digit = (int) number.charAt(i) - (int) '0';

            // Checking that the number would
            // be added or not
            if (temp % 2 == 0) {

                adding_number += 1;
                digit += adding_number;

                // Logic for summing the digits
                // if the digit is greater than 10
                if (digit >= 10) {
                    digit %= 9;
                    if (digit == 0)
                        digit = 9;
                }
            }

            // Storing the result
            result = digit + result;
            temp += 1;
        }

        // Returning the result
        return result;
    }

    // Driver Code
    public static void main(String args[]) {
        String S = "1345";
        System.out.println(generateNumber(S));
    }

}

// This code is contributed by gfgking.

Python3

# Python3 program for the above approach

# Function to generate the resultant
# number using the given criteria
def generateNumber(number) :

    temp = 0; adding_number = 0;

    # Storing end result
    result = "";

    # Find the length of numeric string
    l = len(number);

    # Traverse the string
    for i in range(l - 1, -1, -1) :

        # Storing digit at ith position
        digit = ord(number[i]) - ord('0');

        # Checking that the number would
        # be added or not
        if (temp % 2 == 0) :

            adding_number += 1;
            digit += adding_number;

            # Logic for summing the digits
            # if the digit is greater than 10
            if (digit >= 10) :
                digit %= 9;
                if (digit == 0) :
                    digit = 9;

        # Storing the result
        result = str(digit) + result;
        temp += 1;

    # Returning the result
    return result;

# Driver Code
if __name__ ==  "__main__" :

    S = "1345";
    print(generateNumber(S));

    # This code is contributed by AnkThon

Javascript

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


        // Function to generate the resultant
        // number using the given criteria
        function generateNumber(number) {
            let temp = 0, adding_number = 0;

            // Storing end result
            let result = "";

            // Find the length of numeric string
            let len = number.length;

            // Traverse the string
            for (let i = len - 1; i >= 0; i--) {

                // Storing digit at ith position
                let digit = parseInt(number[i]);

                // Checking that the number would
                // be added or not
                if (temp % 2 == 0) {

                    adding_number += 1;
                    digit += adding_number;

                    // Logic for summing the digits
                    // if the digit is greater than 10
                    if (digit >= 10) {
                        digit %= 9;
                        if (digit == 0)
                            digit = 9;
                    }
                }

                // Storing the result
                result = (digit).toString() + result;
                temp += 1;
            }

            // Returning the result
            return result;
        }

        // Driver Code

        let S = "1345";
        document.write(generateNumber(S));


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

C#

// C# program for the above approach
using System;
public class GFG
{

    // Function to generate the resultant
    // number using the given criteria
    public static String generateNumber(string number) {
        int temp = 0, adding_number = 0;

        // Storing end result
        string result = "";

        // Find the length of numeric string
        int len = number.Length;

        // Traverse the string
        for (int i = len - 1; i >= 0; i--) {

            // Storing digit at ith position
            int digit = (int)number[i] - (int)'0';

            // Checking that the number would
            // be added or not
            if (temp % 2 == 0) {

                adding_number += 1;
                digit += adding_number;

                // Logic for summing the digits
                // if the digit is greater than 10
                if (digit >= 10) {
                    digit %= 9;
                    if (digit == 0)
                        digit = 9;
                }
            }

            // Storing the result
            result = digit + result;
            temp += 1;
        }

        // Returning the result
        return result;
    }

    // Driver Code
    public static void Main(string []args) {
        string S = "1345";
        Console.WriteLine(generateNumber(S));
    }

}

// This code is contributed by AnkThon

Output:

1546

Time Complexity: O(N)
Auxiliary Space: O(1)