Print all n-digit numbers with absolute difference between sum of even and odd digits is 1

Given number of digits n, print all n-digit numbers whose absolute difference between sum of digits at even and odd positions is 1. Solution should not consider leading 0’s as digits.

Examples:

Input:  n = 2
Output:  
10 12 21 23 32 34 43 45 54 56 65 67 76 78 87 89 98

Input:  n = 3
Output:  
100 111 120 122 131 133 142 144 153 155 164 166 175 177 186 
188 197 199 210 221 230 232 241 243 252 254 263 265 274 276 
285 287 296 298 320 331 340 342 351 353 362 364 373 375 384 
386 395 397 430 441 450 452 461 463 472 474 483 485 494 496 
540 551 560 562 571 573 582 584 593 595 650 661 670 672 681 
683 692 694 760 771 780 782 791 793 870 881 890 892 980 991 



The idea is to generate all n-digit numbers using recursion and maintain sum of even and odd digits so far in two separate variables. For a given position, we fill it with all digits from 0 to 9 and based on whether current position is even or odd, we increment even or odd sum. We handle leading 0’s case separately as they are not counted as digits.

We have followed Zero-based numbering like array indexes. i.e. leading(leftmost) digit is considered to be present in even position and digit next to it is considered at odd position and so on.

Below is implementation of above idea –

C++

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// A C++ recursive program to print all N-digit numbers with
// absolute difference between sum of even and odd digits is 1
#include <bits/stdc++.h>
using namespace std;
  
// Recursive function to print all N-digit numbers with absolute
// difference between sum of even and odd digits is 1.
// This function considers leading zero as a digit
  
// n --> value of input
// out --> output array
// index --> index of next digit to be filled in output array
// evenSum, oddSum --> sum of even and odd digits so far
void findNDigitNumsUtil(int n, char* out, int index, int evenSum,
                                                     int oddSum)
{
    // Base case
    if (index > n)
        return;
  
    // If number becomes n-digit
    if (index == n)
    {
        // if absolute difference between sum of even and
        // odd digits is 1, print the number
        if (abs(evenSum - oddSum) == 1)
        {
            out[index] = '';
            cout << out << " ";
        }
        return;
    }
  
    // If current index is odd, then add it to odd sum and recurse
    if (index & 1)
    {
        for (int i = 0; i <= 9; i++)
        {
            out[index] = i + '0';
            findNDigitNumsUtil(n, out, index + 1, evenSum, oddSum + i);
        }
    }
    else // else add to even sum and recurse
    {
        for (int i = 0; i <= 9; i++)
        {
            out[index] = i + '0';
            findNDigitNumsUtil(n, out, index + 1, evenSum + i, oddSum);
        }
    }
}
  
// This is mainly a wrapper over findNDigitNumsUtil.
// It explicitly handles leading digit and calls
// findNDigitNumsUtil() for remaining indexes.
int findNDigitNums(int n)
{
    // output array to store n-digit numbers
    char out[n + 1];
  
    // Initialize number index considered so far
    int index = 0;
  
    // Initialize even and odd sums
    int evenSum = 0, oddSum = 0;
  
    // Explicitly handle first digit and call recursive function
    // findNDigitNumsUtil for remaining indexes. Note that the
    // first digit is considered to be present in even position.
    for (int i = 1; i <= 9; i++)
    {
        out[index] = i + '0';
        findNDigitNumsUtil(n, out, index + 1, evenSum + i, oddSum);
    }
}
  
// Driver program
int main()
{
    int n = 3;
  
    findNDigitNums(n);
  
    return 0;
}

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Java

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// Java program to print all n-digit numbers 
// with absolute difference between sum 
// of even and odd digits is 1
  
import java.io.*;
import java.util.*;
  
class GFG 
{
    // Recursive function to print all N-digit numbers 
    // with absolute difference between sum of even 
    // and odd digits is 1. This function considers 
    // leading zero as a digit
   
    // n --> value of input
    // out --> output array
    // index --> index of next digit to be filled in output array
    // evenSum, oddSum --> sum of even and odd digits so far
    static void findNDigitNumsUtil(int n, char out[], int index, 
                                   int evenSum, int oddSum)
    {
        // Base case
        if (index > n)
            return;
   
        // If number becomes n-digit
        if (index == n)
        {
            // if absolute difference between sum of even and
            // odd digits is 1, print the number
            if (Math.abs(evenSum - oddSum) == 1)
            {
                out[index] = '';
                System.out.print(out);
                System.out.print(" ");
            }
            return;
        }
   
        // If current index is odd, then add it to odd sum and recurse
        if (index % 2 != 0)
        {
            for (int i = 0; i <= 9; i++)
            {
                out[index] = (char)(i + '0');
                findNDigitNumsUtil(n, out, index + 1, evenSum, oddSum + i);
            }
        }
        else // else add to even sum and recurse
        {
            for (int i = 0; i <= 9; i++)
            {
                out[index] = (char)(i + '0');
                findNDigitNumsUtil(n, out, index + 1, evenSum + i, oddSum);
            }
        }
    }
      
    // This is mainly a wrapper over findNDigitNumsUtil.
    // It explicitly handles leading digit and calls
    // findNDigitNumsUtil() for remaining indexes
    static void findNDigitNums(int n)
    {
        // output array to store n-digit numbers
        char[] out = new char[n + 1];
   
        // Initialize number index considered so far
        int index = 0;
   
        // Initialize even and odd sums
        int evenSum = 0, oddSum = 0;
   
        // Explicitly handle first digit and call recursive function
        // findNDigitNumsUtil for remaining indexes. Note that the
        // first digit is considered to be present in even position
        for (int i = 1; i <= 9; i++)
        {
            out[index] = (char)(i + '0');
            findNDigitNumsUtil(n, out, index + 1, evenSum + i, oddSum);
        }
    }
      
    // Driver program
    public static void main (String[] args) 
    {
        int n = 3;
        findNDigitNums(n);
    }
}
  
// This code is contributed by Pramod Kumar

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Python 3

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# Python 3 recursive program to print all N-digit 
# numbers with absolute difference between sum of
# even and odd digits is 1
  
# Recursive function to print all N-digit numbers 
# with absolute difference between sum of even and 
# odd digits is 1. This function considers leading 
# zero as a digit
  
# n --> value of input
# out --> output array
# index --> index of next digit to be filled 
#           in output array
# evenSum, oddSum --> sum of even and odd 
#                     digits so far
def findNDigitNumsUtil(n, out, index, 
                       evenSum, oddSum):
  
    # Base case
    if (index > n):
        return
  
    # If number becomes n-digit
    if (index == n):
      
        # if absolute difference between sum of even
        # and odd digits is 1, print the number
        if (abs(evenSum - oddSum) == 1):
            out[index] = ''
            out = ''.join(out)
            print(out, end = " ")
        return
  
    # If current index is odd, then add it
    # to odd sum and recurse
    if (index & 1):
        for i in range(10):
            out[index] = chr(i + ord('0'))
            findNDigitNumsUtil(n, out, index + 1
                               evenSum, oddSum + i)
                                 
    else: # else add to even sum and recurse
        for i in range(10):
            out[index] = chr(i + ord('0'))
            findNDigitNumsUtil(n, out, index + 1
                               evenSum + i, oddSum)
  
# This is mainly a wrapper over findNDigitNumsUtil.
# It explicitly handles leading digit and calls
# findNDigitNumsUtil() for remaining indexes.
def findNDigitNums(n):
  
    # output array to store n-digit numbers
    out = [0] * (n + 1)
  
    # Initialize number index considered 
    # so far
    index = 0
  
    # Initialize even and odd sums
    evenSum = 0
    oddSum = 0
  
    # Explicitly handle first digit and call 
    # recursive function findNDigitNumsUtil 
    # for remaining indexes. Note that the
    # first digit is considered to be present 
    # in even position.
    for i in range(1, 10):
        out[index] = chr(i + ord('0'))
        findNDigitNumsUtil(n, out, index + 1
                           evenSum + i, oddSum)
  
# Driver Code
if __name__ == "__main__":
      
    n = 3
    findNDigitNums(n)
  
# This code is contributed by ita_c

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C#

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// C# program to print all n-digit numbers 
// with absolute difference between sum 
// of even and odd digits is 1
using System;
  
class GFG {
      
    // Recursive function to print all N-digit
    // numbers with absolute difference between
    // sum of even and odd digits is 1. This 
    // function considers leading zero as a
    // digit
  
    // n --> value of input
    // out --> output array
    // index --> index of next digit to be 
    // filled in output array
    // evenSum, oddSum --> sum of even and 
    // odd digits so far
    static void findNDigitNumsUtil(int n, char []ou,
                 int index, int evenSum, int oddSum)
    {
          
        // Base case
        if (index > n)
            return;
  
        // If number becomes n-digit
        if (index == n)
        {
            // if absolute difference between sum
            // of even and odd digits is 1, print
            // the number
            if (Math.Abs(evenSum - oddSum) == 1)
            {
                ou[index] = '\0';
                Console.Write(ou);
                Console.Write(" ");
            }
            return;
        }
  
        // If current index is odd, then add it
        // to odd sum and recurse
        if (index % 2 != 0)
        {
            for (int i = 0; i <= 9; i++)
            {
                ou[index] = (char)(i + '0');
                findNDigitNumsUtil(n, ou, index + 1,
                               evenSum, oddSum + i);
            }
        }
        else // else add to even sum and recurse
        {
            for (int i = 0; i <= 9; i++)
            {
                ou[index] = (char)(i + '0');
                findNDigitNumsUtil(n, ou, index + 1,
                               evenSum + i, oddSum);
            }
        }
    }
      
    // This is mainly a wrapper over findNDigitNumsUtil.
    // It explicitly handles leading digit and calls
    // findNDigitNumsUtil() for remaining indexes
    static void findNDigitNums(int n)
    {
        // output array to store n-digit numbers
        char []ou = new char[n + 1];
  
        // Initialize number index considered so far
        int index = 0;
  
        // Initialize even and odd sums
        int evenSum = 0, oddSum = 0;
  
        // Explicitly handle first digit and call 
        // recursive function findNDigitNumsUtil for
        // remaining indexes. Note that the first 
        // digit is considered to be present in even
        // position
        for (int i = 1; i <= 9; i++)
        {
            ou[index] = (char)(i + '0');
            findNDigitNumsUtil(n, ou, index + 1, 
                               evenSum + i, oddSum);
        }
    }
      
    // Driver program
    public static void Main () 
    {
        int n = 3;
        findNDigitNums(n);
    }
}
  
// This code is contributed by nitin mittal.

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PHP

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<?php
// A PHP recursive program to print 
// all N-digit numbers with absolute 
// difference between sum of even 
// and odd digits is 1
  
// Recursive function to print all
// N-digit numbers with absolute
// difference between sum of even 
// and odd digits is 1. This function 
// considers leading zero as a digit
  
// n --> value of input
// out --> output array
// index --> index of next digit 
// to be filled in output array
// evenSum, oddSum --> sum of even 
// and odd digits so far
function findNDigitNumsUtil($n,$out, $index, $evenSum,$oddSum)
{
    // Base case
    if ($index > $n)
        return;
  
    // If number becomes n-digit
    if ($index == $n)
    {
        // if absolute difference between sum of even and
        // odd digits is 1, print the number
        if (abs($evenSum - $oddSum) == 1)
        {
            echo implode("",$out)." ";
        }
        return;
    }
  
    // If current index is odd, then 
    // add it to odd sum and recurse
    if ($index & 1)
    {
        for ($i = 0; $i <= 9; $i++)
        {
            $out[$index] = $i + '0';
            findNDigitNumsUtil($n, $out, $index + 1, 
                                $evenSum, $oddSum + $i);
        }
    }
    else // else add to even sum and recurse
    {
        for ($i = 0; $i <= 9; $i++)
        {
            $out[$index] = $i + '0';
            findNDigitNumsUtil($n, $out, $index + 1, 
                                $evenSum + $i, $oddSum);
        }
    }
}
  
// This is mainly a wrapper over findNDigitNumsUtil.
// It explicitly handles leading digit and calls
// findNDigitNumsUtil() for remaining indexes.
function findNDigitNums($n)
{
    // output array to store n-digit numbers
    $out=array_fill(0,$n + 1,"");
  
    // Initialize number index considered so far
    $index = 0;
  
    // Initialize even and odd sums
    $evenSum = 0;
    $oddSum = 0;
  
    // Explicitly handle first digit and
    // call recursive function findNDigitNumsUtil 
    // for remaining indexes. Note that the
    // first digit is considered to be present in even position.
    for ($i = 1; $i <= 9; $i++)
    {
        $out[$index] = $i + '0';
        findNDigitNumsUtil($n, $out, $index + 1, 
                            $evenSum + $i, $oddSum);
    }
}
  
    // Driver program
    $n = 3;
  
    findNDigitNums($n);
  
// This code is contributed by chandan_jnu
?>

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Output:

100 111 120 122 131 133 142 144 153 155 164 166 175 177 186 
188 197 199 210 221 230 232 241 243 252 254 263 265 274 276 
285 287 296 298 320 331 340 342 351 353 362 364 373 375 384 
386 395 397 430 441 450 452 461 463 472 474 483 485 494 496 
540 551 560 562 571 573 582 584 593 595 650 661 670 672 681 
683 692 694 760 771 780 782 791 793 870 881 890 892 980 991 

We can avoid using two variables evenSum and oddSum. Instead we can maintain single variable diff that stores difference between sum of even and odd digits. The implementation can be seen here.

This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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