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Check if it is possible to create a polygon with given n sides
• Difficulty Level : Medium
• Last Updated : 01 Apr, 2019

Given an array arr[] that contain the lengths of n sides that may or may not form a polygon. The task is to determine whether it is possible to form a polygon with all the given sides. Print Yes if possible else print No.

Examples:

Input: arr[] = {2, 3, 4}
Output: Yes

Input: arr[] = {3, 4, 9, 2}
Output: No

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

Approach: In order to create a polygon with given n sides, there is a certain property that must be satisfied by the sides of the polygon.

Property: The length of the every given side must be less than the sum of the other remaining sides.

Find the largest side among the given sides. Then, check whether it is smaller than the sum of the other sides or not. If it is smaller then print Yes else print No.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;`` ` `// Function that returns true if it is possible``// to form a polygon with the given sides``bool` `isPossible(``int` `a[], ``int` `n)``{`` ` `    ``// Sum stores the sum of all the sides``    ``// and maxS stores the length of``    ``// the largest side``    ``int` `sum = 0, maxS = 0;``    ``for` `(``int` `i = 0; i < n; i++) {``        ``sum += a[i];``        ``maxS = max(a[i], maxS);``    ``}`` ` `    ``// If the length of the largest side``    ``// is less than the sum of the``    ``// other remaining sides``    ``if` `((sum - maxS) > maxS)``        ``return` `true``;`` ` `    ``return` `false``;``}`` ` `// Driver code``int` `main()``{``    ``int` `a[] = { 2, 3, 4 };``    ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]);`` ` `    ``if` `(isPossible(a, n))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;`` ` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG {`` ` `    ``// Function that returns true if it is possible``    ``// to form a polygon with the given sides``    ``static` `boolean` `isPossible(``int` `a[], ``int` `n)``    ``{``        ``// Sum stores the sum of all the sides``        ``// and maxS stores the length of``        ``// the largest side``        ``int` `sum = ``0``, maxS = ``0``;``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``sum += a[i];``            ``maxS = Math.max(a[i], maxS);``        ``}`` ` `        ``// If the length of the largest side``        ``// is less than the sum of the``        ``// other remaining sides``        ``if` `((sum - maxS) > maxS)``            ``return` `true``;`` ` `        ``return` `false``;``    ``}`` ` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `a[] = { ``2``, ``3``, ``4` `};``        ``int` `n = a.length;`` ` `        ``if` `(isPossible(a, n))``            ``System.out.print(``"Yes"``);``        ``else``            ``System.out.print(``"No"``);``    ``}``}`

## Python

 `# Python 3 implementation of the approach `` ` `# Function to check whether ``# it is possible to create a ``# polygon with given sides length ``def` `isPossible(a, n):``    ``# Sum stores the sum of all the sides``    ``# and maxS stores the length of ``    ``# the largest side``    ``sum` `=` `0``    ``maxS ``=` `0``    ``for` `i ``in` `range``(n):``        ``sum` `+``=` `a[i]``        ``maxS ``=` `max``(a[i], maxS)`` ` `    ``# If the length of the largest side ``    ``# is less than the sum of the ``    ``# other remaining sides``    ``if` `((``sum` `-` `maxS) > maxS):``        ``return` `True``     ` `    ``return` `False`` ` `# Driver code``a ``=``[``2``, ``3``, ``4``]``n ``=` `len``(a)`` ` `if``(isPossible(a, n)):``    ``print``(``"Yes"``)``else``:``    ``print``(``"No"``)`

## C#

 `// C# implementation of the approach``using` `System;``class` `GFG {`` ` `    ``// Function that returns true if it is possible``    ``// to form a polygon with the given sides``    ``static` `bool` `isPossible(``int``[] a, ``int` `n)``    ``{``        ``// Sum stores the sum of all the sides``        ``// and maxS stores the length of``        ``// the largest side``        ``int` `sum = 0, maxS = 0;``        ``for` `(``int` `i = 0; i < n; i++) {``            ``sum += a[i];``            ``maxS = Math.Max(a[i], maxS);``        ``}`` ` `        ``// If the length of the largest side``        ``// is less than the sum of the``        ``// other remaining sides``        ``if` `((sum - maxS) > maxS)``            ``return` `true``;`` ` `        ``return` `false``;``    ``}`` ` `    ``// Driver code``    ``static` `void` `Main()``    ``{``        ``int``[] a = { 2, 3, 4 };``        ``int` `n = a.Length;`` ` `        ``if` `(isPossible(a, n))``            ``Console.Write(``"Yes"``);``        ``else``            ``Console.Write(``"No"``);``    ``}``}`

## PHP

 ` ``\$maxS``)``        ``return` `true;``     ` `    ``return` `false;``}`` ` `// Driver code ``\$a` `= ``array``(2, 3, 4);``\$n` `= ``count``(``\$a``);`` ` `if``(isPossible(``\$a``, ``\$n``))``    ``echo` `"Yes"``;``else``    ``echo` `"No"``;``?>`
Output:
```Yes
```

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