# Sort ugly numbers in an array at their relative positions

Given an integer array arr[], the task is to sort only those elements which are ugly numbers at their relative positions in the array (positions of other elements must not be affected).
Ugly numbers are numbers whose only prime factors are 2, 3 or 5.
The sequence 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, ….. shows first few ugly numbers. By convention, 1 is included.

Examples:

Input: arr[] = {13, 9, 11, 3, 2}
Output: 13 2 11 3 9
9, 3 and 2 are the only ugly numbers in the given array.

Input: arr[] = {1, 2, 3, 7, 12, 10}
Output: 1 2 3 7 10 12

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Start traversing the array and for every element arr[i], if arr[i] is an ugly number then store it in an ArrayList and update arr[i] = -1
• After all the ugly numbers have been stored in the ArrayList, sort the updated ArrayList.
• Again traverse the array and for every element,
• If arr[i] = -1 then print the first element from the ArrayList that hasn’t been printed before.
• Else, print arr[i].

Below is the implementation of the above approach:

## C++

 `// CPP implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function that returns true if n is an ugly number ` `bool` `isUgly(``int` `n) ` `{ ` `    ``// While divisible by 2, keep dividing ` `    ``while` `(n % 2 == 0) ` `        ``n = n / 2; ` ` `  `    ``// While divisible by 3, keep dividing ` `    ``while` `(n % 3 == 0) ` `        ``n = n / 3; ` ` `  `    ``// While divisible by 5, keep dividing ` `    ``while` `(n % 5 == 0) ` `        ``n = n / 5; ` ` `  `    ``// n must be 1 if it was ugly ` `    ``if` `(n == 1) ` `        ``return` `true``; ` `    ``return` `false``; ` `} ` ` `  `// Function to sort ugly numbers ` `// in their relative positions ` `void` `sortUglyNumbers(``int` `arr[], ``int` `n) ` `{ ` ` `  `    ``// To store the ugly numbers from the array ` `    ``vector<``int``> list; ` ` `  `    ``int` `i; ` `    ``for` `(i = 0; i < n; i++) ` `    ``{ ` ` `  `        ``// If current element is an ugly number ` `        ``if` `(isUgly(arr[i]))  ` `        ``{ ` ` `  `            ``// Add it to the ArrayList ` `            ``// and set arr[i] to -1 ` `            ``list.push_back(arr[i]); ` `            ``arr[i] = -1; ` `        ``} ` `    ``} ` ` `  `    ``// Sort the ugly numbers ` `    ``sort(list.begin(),list.end()); ` ` `  `    ``int` `j = 0; ` `    ``for` `(i = 0; i < n; i++) ` `    ``{ ` ` `  `        ``// Position of an ugly number ` `        ``if` `(arr[i] == -1) ` `            ``cout << list[j++] << ``" "``; ` `        ``else` `            ``cout << arr[i] << ``" "``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3, 7, 12, 10 }; ` `    ``int` `n = ``sizeof``(arr)/``sizeof``(arr); ` `    ``sortUglyNumbers(arr, n); ` `} ` ` `  `// This code is contributed by ` `// Surendra_Gangwar `

## Java

 `// Java implementation of the approach ` `import` `java.util.ArrayList; ` `import` `java.util.Collections; ` ` `  `class` `GFG { ` ` `  `    ``// Function that returns true if n is an ugly number ` `    ``static` `boolean` `isUgly(``int` `n) ` `    ``{ ` `        ``// While divisible by 2, keep dividing ` `        ``while` `(n % ``2` `== ``0``) ` `            ``n = n / ``2``; ` ` `  `        ``// While divisible by 3, keep dividing ` `        ``while` `(n % ``3` `== ``0``) ` `            ``n = n / ``3``; ` ` `  `        ``// While divisible by 5, keep dividing ` `        ``while` `(n % ``5` `== ``0``) ` `            ``n = n / ``5``; ` ` `  `        ``// n must be 1 if it was ugly ` `        ``if` `(n == ``1``) ` `            ``return` `true``; ` `        ``return` `false``; ` `    ``} ` ` `  `    ``// Function to sort ugly numbers ` `    ``// in their relative positions ` `    ``static` `void` `sortUglyNumbers(``int` `arr[], ``int` `n) ` `    ``{ ` ` `  `        ``// To store the ugly numbers from the array ` `        ``ArrayList list = ``new` `ArrayList<>(); ` ` `  `        ``int` `i; ` `        ``for` `(i = ``0``; i < n; i++) { ` ` `  `            ``// If current element is an ugly number ` `            ``if` `(isUgly(arr[i])) { ` ` `  `                ``// Add it to the ArrayList ` `                ``// and set arr[i] to -1 ` `                ``list.add(arr[i]); ` `                ``arr[i] = -``1``; ` `            ``} ` `        ``} ` ` `  `        ``// Sort the ugly numbers ` `        ``Collections.sort(list); ` ` `  `        ``int` `j = ``0``; ` `        ``for` `(i = ``0``; i < n; i++) { ` ` `  `            ``// Position of an ugly number ` `            ``if` `(arr[i] == -``1``) ` `                ``System.out.print(list.get(j++) + ``" "``); ` `            ``else` `                ``System.out.print(arr[i] + ``" "``); ` `        ``} ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = { ``1``, ``2``, ``3``, ``7``, ``12``, ``10` `}; ` `        ``int` `n = arr.length; ` `        ``sortUglyNumbers(arr, n); ` `    ``} ` `} `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Function that returns true if n is an ugly number  ` `def` `isUgly(n):  ` ` `  `    ``# While divisible by 2, keep dividing  ` `    ``while` `n ``%` `2` `=``=` `0``:  ` `        ``n ``=` `n ``/``/` `2` ` `  `    ``# While divisible by 3, keep dividing  ` `    ``while` `n ``%` `3` `=``=` `0``:  ` `        ``n ``=` `n ``/``/` `3` ` `  `    ``# While divisible by 5, keep dividing  ` `    ``while` `n ``%` `5` `=``=` `0``:  ` `        ``n ``=` `n ``/``/` `5` ` `  `    ``# n must be 1 if it was ugly  ` `    ``if` `n ``=``=` `1``: ` `        ``return` `True` `    ``return` `False` ` `  `# Function to sort ugly numbers  ` `# in their relative positions  ` `def` `sortUglyNumbers(arr, n):  ` ` `  `    ``# To store the ugly numbers from the array  ` `    ``list` `=` `[]  ` ` `  `    ``for` `i ``in` `range``(``0``, n):  ` ` `  `        ``# If current element is an ugly number  ` `        ``if` `isUgly(arr[i]):  ` ` `  `            ``# Add it to the ArrayList  ` `            ``# and set arr[i] to -1  ` `            ``list``.append(arr[i])  ` `            ``arr[i] ``=` `-``1` ` `  `    ``# Sort the ugly numbers  ` `    ``list``.sort()  ` ` `  `    ``j ``=` `0` `    ``for` `i ``in` `range``(``0``, n):  ` `     `  `        ``# Position of an ugly number  ` `        ``if` `arr[i] ``=``=` `-``1``:  ` `            ``print``(``list``[j], end ``=` `" "``) ` `            ``j ``+``=` `1` `        ``else``: ` `            ``print``(arr[i], end ``=` `" "``)  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"``: ` ` `  `    ``arr ``=` `[``1``, ``2``, ``3``, ``7``, ``12``, ``10``]  ` `    ``n ``=` `len``(arr)  ` `    ``sortUglyNumbers(arr, n)  ` ` `  `# This code is contributed by Rituraj Jain `

## C#

 `// C# implementation of the approach ` `using` `System; ` `using` `System.Collections.Generic; ` `     `  `class` `GFG  ` `{ ` ` `  `    ``// Function that returns true  ` `    ``// if n is an ugly number ` `    ``static` `bool` `isUgly(``int` `n) ` `    ``{ ` `        ``// While divisible by 2, keep dividing ` `        ``while` `(n % 2 == 0) ` `            ``n = n / 2; ` ` `  `        ``// While divisible by 3, keep dividing ` `        ``while` `(n % 3 == 0) ` `            ``n = n / 3; ` ` `  `        ``// While divisible by 5, keep dividing ` `        ``while` `(n % 5 == 0) ` `            ``n = n / 5; ` ` `  `        ``// n must be 1 if it was ugly ` `        ``if` `(n == 1) ` `            ``return` `true``; ` `        ``return` `false``; ` `    ``} ` ` `  `    ``// Function to sort ugly numbers ` `    ``// in their relative positions ` `    ``static` `void` `sortUglyNumbers(``int` `[]arr, ``int` `n) ` `    ``{ ` ` `  `        ``// To store the ugly numbers from the array ` `        ``List<``int``> list = ``new` `List<``int``>(); ` ` `  `        ``int` `i; ` `        ``for` `(i = 0; i < n; i++) ` `        ``{ ` ` `  `            ``// If current element is an ugly number ` `            ``if` `(isUgly(arr[i])) ` `            ``{ ` ` `  `                ``// Add it to the ArrayList ` `                ``// and set arr[i] to -1 ` `                ``list.Add(arr[i]); ` `                ``arr[i] = -1; ` `            ``} ` `        ``} ` ` `  `        ``// Sort the ugly numbers ` `        ``list.Sort(); ` ` `  `        ``int` `j = 0; ` `        ``for` `(i = 0; i < n; i++) ` `        ``{ ` ` `  `            ``// Position of an ugly number ` `            ``if` `(arr[i] == -1) ` `                ``Console.Write(list[j++] + ``" "``); ` `            ``else` `                ``Console.Write(arr[i] + ``" "``); ` `        ``} ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``int` `[]arr = { 1, 2, 3, 7, 12, 10 }; ` `        ``int` `n = arr.Length; ` `        ``sortUglyNumbers(arr, n); ` `    ``} ` `} ` ` `  `// This code contributed by Rajput-Ji `

Output:

```1 2 3 7 10 12
```

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