Reduce number to a single digit by subtracting adjacent digits repeatedly

Given a number N, the task is to reduce it to a single-digit number by repeatedly subtracting the adjacent digits. That is, in the first iteration, subtract all of the adjacent digits to generate a new number, if this number contains more than one digit, repeat the same process until it becomes a single-digit number.

Examples:

Input: N = 6972
Output: 2
| 6 – 9 | = 3
| 9 – 7 | = 2
| 7 – 2 | = 5



After first step we get 325 but 325 is not a single-digit number so we’ll further reduce it until we do not get single digit number.

| 3 – 2 | = 1
| 2 – 5 | = 3

And now the number will become 13, we’ll reduce it furthur
| 1 – 3 | = 2

Input: N = 123456
Output: 0

Approach: Here we are using Array to represent the inital number N for simplicity.

  1. Count the number of digits in N and store the value in l.
  2. Create an array a[] of size l.
  3. Copy the given number into the array a[].
  4. Calculate the RSF by subtracting the consecutive digits of array a.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the resultant digit
// after performing the given operations
int RSF(int n)
{
    while (n >= 10) {
  
        // Creating an extra copy of n
        int x = n;
        int l = 0;
  
        // Counting the number of digits in n
        while (n > 0) {
            n = n / 10;
            l++;
        }
  
        // Now n is 0
        // Creating an array of length l
        int a[l];
  
        // Initializing i with the last index of array
        int i = l - 1;
        while (x > 0) {
  
            // Filling array from right to left
            a[i] = x % 10;
            x = x / 10;
            i--;
        }
  
        // Calculating the absolute consecutive difference
        for (int j = 0; j < l - 1; j++) {
  
            // Updating the value of n in every loop
            n = n * 10 + abs(a[j] - a[j + 1]);
        }
    }
  
    // While loop ends here and we have found
    // the RSF value of N
    return n;
}
  
// Driver code
int main()
{
    int n = 614;
  
    // Passing n to RSF function and getting answer
    int ans = RSF(n);
  
    // Printing the value stored in ans
    cout << ans;
  
    return 0;
}

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Java

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// Java implementation of the approach
class GFG {
  
    // Function to return the resultant digit
    // after performing the given operations
    static int RSF(int n)
    {
        while (n >= 10) {
  
            // Creating an extra copy of n
            int x = n;
            int l = 0;
  
            // Counting the number of digits in n
            while (n > 0) {
                n = n / 10;
                l++;
            }
  
            // Now n is 0
            // Creating an array of length l
            int a[] = new int[l];
  
            // Initializing i with the last index of array
            int i = l - 1;
  
            while (x > 0) {
  
                // Filling array from right to left
                a[i] = x % 10;
                x = x / 10;
                i--;
            }
  
            // Calculating the absolute consecutive difference
            for (int j = 0; j < l - 1; j++) {
  
                // Updating the value of n in every loop
                n = n * 10 + Math.abs(a[j] - a[j + 1]);
            }
        }
  
        // While loop ends here and we have found
        // the RSF value of N
        return n;
    }
  
    // Driver code
    public static void main(String[] arg)
    {
        int n = 6972;
  
        // Passing n to RSF function and getting answer
        int ans = RSF(n);
  
        // Printing the value stored in ans
        System.out.println(ans);
    }
}

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Python3

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# Python3 implementation of the approach
  
# Function to return the resultant digit
# after performing the given operations
def RSF(n):
    while (n >= 10):
  
        # Creating an extra copy of n
        x = n;
        l = 0;
  
        # Counting the number of digits in n
        while (n > 0):
            n = n // 10;
            l += 1;
  
        # Now n is 0
        # Creating an array of length l
        a = [0] * l;
  
        # Initializing i with the last index of array
        i = l - 1;
        while (x > 0):
  
            # Filling array from right to left
            a[i] = x % 10;
            x = x // 10;
            i -= 1;
  
        # Calculating the absolute 
        # consecutive difference
        for j in range(0, l - 1):
  
            # Updating the value of n in every loop
            n = n * 10 + abs(a[j] - a[j + 1]);
              
    # While loop ends here and we have found
    # the RSF value of N
    return n;
  
# Driver code
if __name__ == '__main__':
    n = 614;
  
    # Passing n to RSF function 
    # and getting answer
    ans = RSF(n);
  
    # Printing the value stored in ans
    print(ans);
  
# This code is contributed by Rajput-Ji

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C#

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// C# implementation of the approach
using System;
class GFG 
{
  
// Function to return the resultant digit
// after performing the given operations
static int RSF(int n)
{
    while (n >= 10) 
    {
  
        // Creating an extra copy of n
        int x = n;
        int l = 0;
  
        // Counting the number of digits in n
        while (n > 0) 
        {
            n = n / 10;
            l++;
        }
  
        // Now n is 0
        // Creating an array of length l
        int []a = new int[l];
  
        // Initializing i with the last index of array
        int i = l - 1;
  
        while (x > 0) 
        {
  
            // Filling array from right to left
            a[i] = x % 10;
            x = x / 10;
            i--;
        }
  
        // Calculating the absolute
        // consecutive difference
        for (int j = 0; j < l - 1; j++)
        {
  
            // Updating the value of n in every loop
            n = n * 10 + Math.Abs(a[j] - a[j + 1]);
        }
    }
  
    // While loop ends here and we have found
    // the RSF value of N
    return n;
}
  
// Driver code
public static void Main(String[] arg)
{
    int n = 6972;
  
    // Passing n to RSF function and getting answer
    int ans = RSF(n);
  
    // Printing the value stored in ans
    Console.WriteLine(ans);
}
}
  
// This code is contributed by Princi Singh

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Output:

2


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