# Sort the numbers according to their product of digits

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

Input:arr[] = {12, 10, 102, 31, 15}Output:10 102 12 31 15

10 -> 1 * 0 = 0

102 -> 1 * 0 * 2 = 0

12 -> 1 * 2 = 2

31 -> 3 * 1 = 3

15 -> 1 * 5 = 5Input:arr[] = {12, 10}Output:10 12

**Approach:** The idea is to store each element with its product of digits in a vector pair and then sort all the elements of the vector according to the digit products stored. Finally, print the elements in order.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to return the product` `// of the digits of n` `int` `productOfDigit(` `int` `n)` `{` ` ` `int` `product = 1;` ` ` `while` `(n > 0) {` ` ` `product *= n % 10;` ` ` `n = n / 10;` ` ` `}` ` ` `return` `product;` `}` `// Function to sort the array according to` `// the product of the digits of elements` `void` `sortArr(` `int` `arr[], ` `int` `n)` `{` ` ` `// Vector to store the digit product` ` ` `// with respective elements` ` ` `vector<pair<` `int` `, ` `int` `> > vp;` ` ` `// Inserting digit product with elements` ` ` `// in the vector pair` ` ` `for` `(` `int` `i = 0; i < n; i++) {` ` ` `vp.push_back(make_pair(productOfDigit(arr[i]), arr[i]));` ` ` `}` ` ` `// Sort the vector, this will sort the pair` ` ` `// according to the product of the digits` ` ` `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[] = { 12, 10, 102, 31, 15 };` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` `sortArr(arr, n);` ` ` `return` `0;` `}` |

## Python3

`# Python3 implementation of the approach ` `# Function to return the product ` `# of the digits of n ` `def` `productOfDigit(n) :` ` ` `product ` `=` `1` `; ` ` ` `while` `(n > ` `0` `) :` ` ` `product ` `*` `=` `(n ` `%` `10` `); ` ` ` `n ` `=` `n ` `/` `/` `10` `; ` ` ` `return` `product; ` `# Function to sort the array according to ` `# the product of the digits of elements ` `def` `sortArr(arr, n) :` ` ` ` ` `# Vector to store the digit product ` ` ` `# with respective elements ` ` ` `vp ` `=` `[]; ` ` ` `# Inserting digit product with elements ` ` ` `# in the vector pair ` ` ` `for` `i ` `in` `range` `(n) :` ` ` `vp.append((productOfDigit(arr[i]), arr[i])); ` ` ` ` ` `# Sort the vector, this will sort the pair ` ` ` `# according to the product of the digits ` ` ` `vp.sort(); ` ` ` `# Print the sorted vector content ` ` ` `for` `i ` `in` `range` `(` `len` `(vp)) :` ` ` `print` `(vp[i][` `1` `], end ` `=` `" "` `); ` `# Driver code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` `arr ` `=` `[ ` `12` `, ` `10` `, ` `102` `, ` `31` `, ` `15` `]; ` ` ` `n ` `=` `len` `(arr); ` ` ` `sortArr(arr, n); ` `# This code is contributed by AnkitRai01` |

## Javascript

`<script>` `// Javascript implementation of the` `// above approach` `// Function to return the product` `// of the digits of n` `function` `productOfDigit(n)` `{` ` ` `var` `product = 1;` ` ` `while` `(n > 0) {` ` ` `product *= n % 10;` ` ` `n = Math.floor(n / 10);` ` ` `}` ` ` `return` `product;` `}` ` ` `// Function to sort the array according to` `// the product of the digits of elements` `function` `sortArr(arr, n)` `{` ` ` `// Vector to store the digit product` ` ` `// with respective elements` ` ` `var` `vp = ` `new` `Array(n);` ` ` `// Loop to create 2D array using 1D array` ` ` `for` `(` `var` `i = 0; i < vp.length; i++) {` ` ` `vp[i] = [];` ` ` `}` ` ` ` ` `// Inserting digit product with elements` ` ` `// in the vector pair` ` ` `for` `(` `var` `i = 0; i < n; i++) {` ` ` `vp[i].push(productOfDigit(arr[i]));` ` ` `vp[i].push(arr[i]);` ` ` `}` ` ` ` ` `// Sort the vector, this will sort the pair` ` ` `// according to the product of the digits` ` ` `vp.sort();` ` ` ` ` `// Print the sorted vector content` ` ` `for` `(` `var` `i = 0; i < n; i++)` ` ` `document.write(vp[i][1] + ` `" "` `);` `}` `// Driver code` `var` `arr = [ 12, 10, 102, 31, 15];` `var` `n = arr.length;` `sortArr(arr, n);` `// This code is contributed by ShubhamSingh10` `</script>` |

**Output:**

10 102 12 31 15

**Time Complexity:** O(nlogn)

**Auxiliary Space: **O(n)