Check if an N-sided Polygon is possible from N given angles

Given an array arr[] of N elements, where each element represents an angle(in degrees) of a polygon, the task is to check whether it is possible to make an N-sided polygon with all the given angles or not. If it is possible then print Yes else print No.

Examples:

Input: N = 3, arr[] = {60, 60, 60}
Output: Yes
Explanation: There exists a triangle(i.e. a polygon) satisfying the above angles. Hence the output is Yes.

Input: N = 4, arr[] = {90, 90, 90, 100}
Output: No
Explanation: There does not exist any polygon satisfying the above angles. Hence the output is No.

Approach: A N-sided polygon is only possible if the sum of all the given angles is equal to 180*(N-2). Therefore the ides is to find the sum of all the angles given in the array arr[] and if the sum is equal to 180*(N-2) then print Yes, else print No.

Below is the implementation of the above approach:

// C++ program for the above approach 
#include <iostream> 
using namespace std; 

// Function to check if the polygon 
// exists or not 
void checkValidPolygon(int arr[], int N) 
{ 
    // Initialize a variable to 
    // store the sum of angles 
    int sum = 0; 

    // Loop through the array and 
    // calculate the sum of angles 
    for (int i = 0; i < N; i++) { 
        sum += arr[i]; 
    } 

    // Check the condition for 
    // an N-side polygon 
    if (sum == 180 * (N - 2)) 
        cout << "Yes"; 
    else
        cout << "No"; 
} 

// Driver Code 
int main() 
{ 
    int N = 3; 

    // Given array arr[] 
    int arr[] = { 60, 60, 60 }; 

    // Function Call 
    checkValidPolygon(arr, N); 

    return 0; 
}

// Java program for the above approach 
import java.util.*; 

class GFG{ 
    
// Function to check if the polygon 
// exists or not 
static void checkValidPolygon(int arr[], int N) 
{ 
    
    // Initialize a variable to 
    // store the sum of angles 
    int sum = 0; 

    // Loop through the array and 
    // calculate the sum of angles 
    for(int i = 0; i < N; i++) 
    { 
        sum += arr[i]; 
    } 

    // Check the condition for 
    // an N-side polygon 
    if (sum == 180 * (N - 2)) 
        System.out.println("Yes"); 
    else
        System.out.println("No"); 
} 
    
// Driver code 
public static void main(String[] args) 
{ 
    int N = 3; 
    
    // Given array arr[] 
    int arr[] = { 60, 60, 60 }; 

    // Function call 
    checkValidPolygon(arr, N); 
} 
} 

// This code is contributed by offbeat 

# Python3 program for the above approach

# Function to check if the polygon 
# exists or not 
def checkValidPolygon(arr, N): 

    # Initialize a variable to 
    # store the sum of angles 
    Sum = 0

    # Loop through the array and 
    # calculate the sum of angles 
    for i in range(N): 
        Sum += arr[i] 

    # Check the condition for 
    # an N-side polygon 
    if Sum == 180 * (N - 2): 
        print("Yes")
    else:
        print("No")
        
# Driver Code
N = 3

# Given array arr[] 
arr = [ 60, 60, 60 ] 

# Function Call 
checkValidPolygon(arr, N) 

# This code is contributed by divyeshrabadiya07

// C# program for the above approach
using System;

class GFG{
    
// Function to check if the polygon
// exists or not
static void checkValidPolygon(int []arr, int N)
{
    
    // Initialize a variable to
    // store the sum of angles
    int sum = 0;

    // Loop through the array and
    // calculate the sum of angles
    for(int i = 0; i < N; i++)
    {
        sum += arr[i];
    }

    // Check the condition for
    // an N-side polygon
    if (sum == 180 * (N - 2))
        Console.Write("Yes");
    else
        Console.Write("No");
}
    
// Driver code
public static void Main(string[] args)
{
    int N = 3;
    
    // Given array arr[]
    int []arr = { 60, 60, 60 };

    // Function call
    checkValidPolygon(arr, N);
}
}

// This code is contributed by rutvik_56

<script>

// Javascript program for the above approach 

// Function to check if the polygon 
// exists or not 
function checkValidPolygon(arr, N) 
{ 
    
    // Initialize a variable to 
    // store the sum of angles 
    var sum = 0; 

    // Loop through the array and 
    // calculate the sum of angles 
    for(var i = 0; i < N; i++) 
    { 
        sum += arr[i]; 
    } 

    // Check the condition for 
    // an N-side polygon 
    if (sum == 180 * (N - 2)) 
        document.write("Yes"); 
    else
        document.write("No"); 
} 

// Driver code
var N = 3; 
    
// Given array arr[] 
var arr = [ 60, 60, 60 ]; 

// Function call 
checkValidPolygon(arr, N); 
           
// This code is contributed by Kirti

</script>                    

Yes

Time Complexity: O(N), where N is the length of the array. 
Auxiliary Space: O(1)