# Sort the numbers according to their sum of digits

• Difficulty Level : Medium
• Last Updated : 20 May, 2022

Given an array arr[] of N non-negative integers, the task is to sort these integers according to sum of their digits.
Examples:

Input: arr[] = {12, 10, 102, 31, 15}
Output: 10 12 102 31 15
10 => 1 + 0 = 1
12 => 1 + 2 = 3
102 => 1 + 0 + 2 = 3
31 => 3 + 1= 4
15 => 1 + 5 = 6
Input: arr[] = {14, 1101, 10, 35, 0}
Output: 0 10 1101 14 35

First Approach: The idea is to store each element with its sum of digits in a vector pair and then sort all the elements of the vector according to the digit sums stored. Finally, print the elements in order.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the sum``// of the digits of n``int` `sumOfDigit(``int` `n)``{``    ``int` `sum = 0;``    ``while` `(n > 0) {``        ``sum += n % 10;``        ``n = n / 10;``    ``}``    ``return` `sum;``}` `// Function to sort the array according to``// the sum of the digits of elements``void` `sortArr(``int` `arr[], ``int` `n)``{``    ``// Vector to store digit sum with respective element``    ``vector > vp;` `    ``// Inserting digit sum with element in the vector pair``    ``for` `(``int` `i = 0; i < n; i++) {``        ``vp.push_back(make_pair(sumOfDigit(arr[i]), arr[i]));``    ``}` `    ``// Quick sort the vector, this will sort the pair``    ``// according to sum of the digits of elements``    ``sort(vp.begin(), vp.end());` `    ``// Print the sorted vector content``    ``for` `(``int` `i = 0; i < vp.size(); i++)``        ``cout << vp[i].second << ``" "``;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 14, 1101, 10, 35, 0 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``sortArr(arr, n);` `    ``return` `0;``}`

## Java

 `/*package whatever //do not write package name here */``import` `java.io.*;``import` `java.util.ArrayList;``import` `java.util.Collections;``import` `java.util.Comparator;` `class` `GFG``{` `  ``// Function to return the sum``  ``// of the digits of n``  ``static` `int` `sumOfDigit(``int` `n)``  ``{``    ``int` `sum = ``0``;``    ``while` `(n > ``0``) {``      ``sum += n % ``10``;``      ``n = Math.floorDiv(n , ``10``);``    ``}``    ``return` `sum;``  ``}` `  ``// Function to sort the array according to``  ``// the sum of the digits of elements``  ``static` `void` `sortArr(``int``[] arr,``int` `n)``  ``{` `    ``// Vector to store digit sum with respective element``    ``ArrayList> vp = ``new` `ArrayList>();` `    ``// Inserting digit sum with element in the vector pair``    ``for` `(``int` `i = ``0``; i < n; i++) {``      ``ArrayListtemp = ``new` `ArrayList();``      ``temp.add(sumOfDigit(arr[i]));``      ``temp.add(arr[i]);``      ``vp.add(temp);``    ``}` `    ``// Quick sort the vector, this will sort the pair``    ``// according to sum of the digits of elements``    ``Collections.sort(vp,``new` `Comparator>(){``      ``@Override``      ``public` `int` `compare(ArrayList o1, ArrayList o2) {``        ``return` `o1.get(``0``) - o2.get(``0``);``      ``}  ``    ``});` `    ``// Print the sorted vector content``    ``for` `(``int` `i = ``0``; i < vp.size(); i++){``      ``System.out.printf(``"%d "``,vp.get(i).get(``1``));``    ``}``  ``}` `  ``// Driver code``  ``public` `static` `void` `main(String args[])``  ``{``    ``int``[] arr = { ``14``, ``1101``, ``10``, ``35``, ``0` `};``    ``int` `n = arr.length;``    ``sortArr(arr, n);``  ``}``}` `// This code is contributed by shinjanpatra`

## Python3

 `# Python3 implementation of the approach` `# Function to return the sum``# of the digits of n``def` `sumOfDigit(n) :``    ` `    ``sum` `=` `0``;``    ``while` `(n > ``0``) :``        ` `        ``sum` `+``=` `n ``%` `10``;``        ``n ``=` `n ``/``/` `10``;``        ` `    ``return` `sum``;` `# Function to sort the array according to``# the sum of the digits of elements``def` `sortArr(arr, n) :``    ` `    ``# Vector to store digit sum with``    ``# respective element``    ``vp ``=` `[];` `    ``# Inserting digit sum with element``    ``# in the vector pair``    ``for` `i ``in` `range``(n) :``        ``vp.append([sumOfDigit(arr[i]), arr[i]]);` `    ``# Quick sort the vector, this will``    ``# sort the pair according to sum``    ``# of the digits of elements``    ``vp.sort()` `    ``# Print the sorted vector content``    ``for` `i ``in` `range``(``len``(vp)) :``        ``print``(vp[i][``1``], end ``=` `" "``);` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``arr ``=` `[``14``, ``1101``, ``10``, ``35``, ``0``];``    ``n ``=` `len``(arr);``    ``sortArr(arr, n);` `# This code is contributed by Ryuga`

## Javascript

 ``

Output

`0 10 1101 14 35 `

Time Complexity: O(n log n) for merge sort and heap sort but O(n^2) for quick sort

Auxiliary Space: O(n)

Second Approach: The idea is to use built-in sort function with a comparator function that computes sum for each pair of comparing integers.

1. Pass the array arr into sort function with Sum_Compare comparator function.

2. Inside Sum_Compare function, calculate sum of digits of both numbers x and y as sumx and sumy by taking modulus by 10 and then dividing it by 10.

3. return whether sumx is less than sumy.

## C++14

 `#include ` `using` `namespace` `std;` `bool` `Sum_Compare(``int` `x,``int` `y)``{``    ``int` `tempx=x,tempy=y;``    ``int` `sumx=0,sumy=0;``    ` `    ``while``(tempx)``    ``{``        ``sumx+=tempx%10;``        ``tempx/=10;``    ``}``    ` `    ``while``(tempy)``    ``{``        ``sumy+=tempy%10;``        ``tempy/=10;``    ``}``    ` `    ``return` `sumx

## Python3

 `# Python3 code for the approach` `from` `functools ``import` `cmp_to_key`  `def` `Sum_Compare(x, y):` `    ``tempx,tempy ``=` `x,y``    ``sumx,sumy ``=` `0``,``0``    ` `    ``while``(tempx > ``0``):` `        ``sumx ``+``=` `tempx ``%` `10``        ``tempx ``=` `tempx ``/``/` `10``    ` `    ``while``(tempy > ``0``):``        ``sumy ``+``=` `tempy ``%` `10``        ``tempy ``=` `tempy ``/``/` `10``    ` `    ``return` `sumx ``-` `sumy`  `arr ``=` `[``12``, ``10``, ``102``, ``31``, ``15``]``n ``=` `len``(arr)``    ` `arr.sort(key ``=` `cmp_to_key(Sum_Compare))` `for` `x ``in` `arr:``    ``print``(x,end ``=` `" "``)``    ` `# This code is contributed by shinjanpatra`

## Javascript

 ``

Output

`10 12 102 31 15 `

Time Complexity: O(n (log n)^2) for merge sort and heap sort but O(n^2 log n) for quick sort.

Auxiliary Space: O(1) for quick sort and heap sort but O(n) for merge sort.

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