# Maximum length of a sub-array with ugly numbers

Given an array arr[] of N elements (0 ≤ arr[i] ≤ 1000). The task is to find the maximum length of the sub-array that contains only ugly numbers. 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[] = {1, 2, 7, 9, 120, 810, 374}
Output: 3
Longest possible sub-array of ugly number sis {9, 120, 810}

Input: arr[] = {109, 480, 320, 142, 121, 1}
Output: 2

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

Approach:

• Take a unordered_set, and insert all the ugly numbers which are less than 1000 in the set.
• Traverse the array with two variables named current_max and max_so_far.
• Check for each element if it is present in the set.
• If an ugly number is found then increment current_max and compare it with max_so_far.
• If current_max > max_so_far then max_so_far = current_max.
• Every time a non ugly element is found, reset current_max = 0.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to get the nth ugly number ` `unsigned uglyNumber(``int` `n) ` `{ ` `    ``// To store ugly numbers ` `    ``int` `ugly[n]; ` `    ``int` `i2 = 0, i3 = 0, i5 = 0; ` `    ``int` `next_multiple_of_2 = 2; ` `    ``int` `next_multiple_of_3 = 3; ` `    ``int` `next_multiple_of_5 = 5; ` `    ``int` `next_ugly_no = 1; ` ` `  `    ``ugly = 1; ` `    ``for` `(``int` `i = 1; i < n; i++) { ` `        ``next_ugly_no = min(next_multiple_of_2, ` `                           ``min(next_multiple_of_3, ` `                               ``next_multiple_of_5)); ` `        ``ugly[i] = next_ugly_no; ` `        ``if` `(next_ugly_no == next_multiple_of_2) { ` `            ``i2 = i2 + 1; ` `            ``next_multiple_of_2 = ugly[i2] * 2; ` `        ``} ` `        ``if` `(next_ugly_no == next_multiple_of_3) { ` `            ``i3 = i3 + 1; ` `            ``next_multiple_of_3 = ugly[i3] * 3; ` `        ``} ` `        ``if` `(next_ugly_no == next_multiple_of_5) { ` `            ``i5 = i5 + 1; ` `            ``next_multiple_of_5 = ugly[i5] * 5; ` `        ``} ` `    ``} ` ` `  `    ``return` `next_ugly_no; ` `} ` ` `  `// Function to return the length of the ` `// maximum sub-array of ugly numbers ` `int` `maxUglySubarray(``int` `arr[], ``int` `n) ` `{ ` `    ``unordered_set<``int``> s; ` `    ``int` `i = 1; ` ` `  `    ``// Insert ugly numbers in set ` `    ``// which are less than 1000 ` `    ``while` `(1) { ` `        ``int` `next_ugly_number = uglyNumber(i); ` `        ``if` `(next_ugly_number > 1000) ` `            ``break``; ` `        ``s.insert(next_ugly_number); ` `        ``i++; ` `    ``} ` ` `  `    ``int` `current_max = 0, max_so_far = 0; ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// Check if element is non ugly ` `        ``if` `(s.find(arr[i]) == s.end()) ` `            ``current_max = 0; ` ` `  `        ``// If element is ugly, than update ` `        ``// current_max and max_so_far accordingly ` `        ``else` `{ ` `            ``current_max++; ` `            ``max_so_far = max(current_max, max_so_far); ` `        ``} ` `    ``} ` ` `  `    ``return` `max_so_far; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `arr[] = { 1, 0, 6, 7, 320, 800, 100, 648 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `    ``cout << maxUglySubarray(arr, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` ` `  `// Function to get the nth ugly number ` `static` `int` `uglyNumber(``int` `n) ` `{ ` `    ``// To store ugly numbers ` `    ``int` `[]ugly = ``new` `int``[n]; ` `    ``int` `i2 = ``0``, i3 = ``0``, i5 = ``0``; ` `    ``int` `next_multiple_of_2 = ``2``; ` `    ``int` `next_multiple_of_3 = ``3``; ` `    ``int` `next_multiple_of_5 = ``5``; ` `    ``int` `next_ugly_no = ``1``; ` ` `  `    ``ugly[``0``] = ``1``; ` `    ``for` `(``int` `i = ``1``; i < n; i++) ` `    ``{ ` `        ``next_ugly_no = Math.min(next_multiple_of_2, ` `                       ``Math.min(next_multiple_of_3, ` `                                ``next_multiple_of_5)); ` `        ``ugly[i] = next_ugly_no; ` `        ``if` `(next_ugly_no == next_multiple_of_2)  ` `        ``{ ` `            ``i2 = i2 + ``1``; ` `            ``next_multiple_of_2 = ugly[i2] * ``2``; ` `        ``} ` `        ``if` `(next_ugly_no == next_multiple_of_3)  ` `        ``{ ` `            ``i3 = i3 + ``1``; ` `            ``next_multiple_of_3 = ugly[i3] * ``3``; ` `        ``} ` `        ``if` `(next_ugly_no == next_multiple_of_5) ` `        ``{ ` `            ``i5 = i5 + ``1``; ` `            ``next_multiple_of_5 = ugly[i5] * ``5``; ` `        ``} ` `    ``} ` `    ``return` `next_ugly_no; ` `} ` ` `  `// Function to return the length of the ` `// maximum sub-array of ugly numbers ` `static` `int` `maxUglySubarray(``int` `arr[], ``int` `n) ` `{ ` `    ``HashSet s = ``new` `HashSet<>(); ` `    ``int` `i = ``1``; ` ` `  `    ``// Insert ugly numbers in set ` `    ``// which are less than 1000 ` `    ``while` `(``true``) ` `    ``{ ` `        ``int` `next_ugly_number = uglyNumber(i); ` `        ``if` `(next_ugly_number > ``1000``) ` `            ``break``; ` `        ``s.add(next_ugly_number); ` `        ``i++; ` `    ``} ` ` `  `    ``int` `current_max = ``0``, max_so_far = ``0``; ` ` `  `    ``for` `(i = ``0``; i < n; i++)  ` `    ``{ ` ` `  `        ``// Check if element is non ugly ` `        ``if` `(!s.contains(arr[i])) ` `            ``current_max = ``0``; ` ` `  `        ``// If element is ugly, than update ` `        ``// current_max and max_so_far accordingly ` `        ``else` `        ``{ ` `            ``current_max++; ` `            ``max_so_far = Math.max(current_max,  ` `                                  ``max_so_far); ` `        ``} ` `    ``} ` `    ``return` `max_so_far; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{ ` `    ``int` `arr[] = { ``1``, ``0``, ``6``, ``7``, ``320``, ``800``, ``100``, ``648` `}; ` `    ``int` `n = arr.length; ` `    ``System.out.println(maxUglySubarray(arr, n)); ` `} ` `}  ` ` `  `// This code is contributed by Rajput-Ji `

## Python3

 `# Python 3 implementation of the approach ` ` `  `# Function to get the nth ugly number ` `def` `uglyNumber(n): ` `     `  `    ``# To store ugly numbers ` `    ``ugly ``=` `[``None` `for` `i ``in` `range``(n)] ` `    ``i2 ``=` `0` `    ``i3 ``=` `0` `    ``i5 ``=` `0` `    ``next_multiple_of_2 ``=` `2` `    ``next_multiple_of_3 ``=` `3` `    ``next_multiple_of_5 ``=` `5` `    ``next_ugly_no ``=` `1` ` `  `    ``ugly[``0``] ``=` `1` `    ``for` `i ``in` `range``(``1``, n, ``1``): ` `        ``next_ugly_no ``=` `min``(next_multiple_of_2,  ` `                       ``min``(next_multiple_of_3,  ` `                           ``next_multiple_of_5)) ` `        ``ugly[i] ``=` `next_ugly_no ` `        ``if` `(next_ugly_no ``=``=` `next_multiple_of_2): ` `            ``i2 ``=` `i2 ``+` `1` `            ``next_multiple_of_2 ``=` `ugly[i2] ``*` `2` `        ``if` `(next_ugly_no ``=``=` `next_multiple_of_3): ` `            ``i3 ``=` `i3 ``+` `1` `            ``next_multiple_of_3 ``=` `ugly[i3] ``*` `3` `        ``if` `(next_ugly_no ``=``=` `next_multiple_of_5): ` `            ``i5 ``=` `i5 ``+` `1` `            ``next_multiple_of_5 ``=` `ugly[i5] ``*` `5` ` `  `    ``return` `next_ugly_no ` ` `  `# Function to return the length of the ` `# maximum sub-array of ugly numbers ` `def` `maxUglySubarray(arr, n): ` `    ``s ``=` `set``() ` `    ``i ``=` `1` ` `  `    ``# Insert ugly numbers in set ` `    ``# which are less than 1000 ` `    ``while` `(``1``): ` `        ``next_ugly_number ``=` `uglyNumber(i) ` `        ``if` `(next_ugly_number >``=` `1000``): ` `            ``break` `        ``s.add(next_ugly_number) ` `        ``i ``+``=` `1` ` `  `    ``current_max ``=` `0` `    ``max_so_far ``=` `0` ` `  `    ``for` `i ``in` `range``(n): ` `         `  `        ``# Check if element is non ugly ` `        ``if` `(arr[i] ``not` `in` `s): ` `            ``current_max ``=` `0` ` `  `        ``# If element is ugly, than update ` `        ``# current_max and max_so_far accordingly ` `        ``else``: ` `            ``current_max ``+``=` `1` `            ``max_so_far ``=` `max``(current_max,  ` `                              ``max_so_far) ` ` `  `    ``return` `max_so_far ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[``1``, ``0``, ``6``, ``7``, ``320``, ``800``, ``100``, ``648``] ` `    ``n ``=` `len``(arr) ` `    ``print``(maxUglySubarray(arr, n)) ` `     `  `# This code is contributed by ` `# Surendra_Gangwar `

## C#

 `// C# implementation of the approach ` `using` `System; ` `using` `System.Collections.Generic;  ` `     `  `class` `GFG  ` `{ ` ` `  `// Function to get the nth ugly number ` `static` `int` `uglyNumber(``int` `n) ` `{ ` `    ``// To store ugly numbers ` `    ``int` `[]ugly = ``new` `int``[n]; ` `    ``int` `i2 = 0, i3 = 0, i5 = 0; ` `    ``int` `next_multiple_of_2 = 2; ` `    ``int` `next_multiple_of_3 = 3; ` `    ``int` `next_multiple_of_5 = 5; ` `    ``int` `next_ugly_no = 1; ` ` `  `    ``ugly = 1; ` `    ``for` `(``int` `i = 1; i < n; i++) ` `    ``{ ` `        ``next_ugly_no = Math.Min(next_multiple_of_2, ` `                       ``Math.Min(next_multiple_of_3, ` `                                ``next_multiple_of_5)); ` `        ``ugly[i] = next_ugly_no; ` `        ``if` `(next_ugly_no == next_multiple_of_2)  ` `        ``{ ` `            ``i2 = i2 + 1; ` `            ``next_multiple_of_2 = ugly[i2] * 2; ` `        ``} ` `        ``if` `(next_ugly_no == next_multiple_of_3)  ` `        ``{ ` `            ``i3 = i3 + 1; ` `            ``next_multiple_of_3 = ugly[i3] * 3; ` `        ``} ` `        ``if` `(next_ugly_no == next_multiple_of_5) ` `        ``{ ` `            ``i5 = i5 + 1; ` `            ``next_multiple_of_5 = ugly[i5] * 5; ` `        ``} ` `    ``} ` `    ``return` `next_ugly_no; ` `} ` ` `  `// Function to return the length of the ` `// maximum sub-array of ugly numbers ` `static` `int` `maxUglySubarray(``int` `[]arr, ``int` `n) ` `{ ` `    ``HashSet<``int``> s = ``new` `HashSet<``int``>(); ` `    ``int` `i = 1; ` ` `  `    ``// Insert ugly numbers in set ` `    ``// which are less than 1000 ` `    ``while` `(``true``) ` `    ``{ ` `        ``int` `next_ugly_number = uglyNumber(i); ` `        ``if` `(next_ugly_number > 1000) ` `            ``break``; ` `        ``s.Add(next_ugly_number); ` `        ``i++; ` `    ``} ` ` `  `    ``int` `current_max = 0, max_so_far = 0; ` ` `  `    ``for` `(i = 0; i < n; i++)  ` `    ``{ ` ` `  `        ``// Check if element is non ugly ` `        ``if` `(!s.Contains(arr[i])) ` `            ``current_max = 0; ` ` `  `        ``// If element is ugly, than update ` `        ``// current_max and max_so_far accordingly ` `        ``else` `        ``{ ` `            ``current_max++; ` `            ``max_so_far = Math.Max(current_max,  ` `                                  ``max_so_far); ` `        ``} ` `    ``} ` `    ``return` `max_so_far; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args)  ` `{ ` `    ``int` `[]arr = { 1, 0, 6, 7, 320, 800, 100, 648 }; ` `    ``int` `n = arr.Length; ` `    ``Console.WriteLine(maxUglySubarray(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by Princi Singh `

Output:

```4
```

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