N条非平行线可划分平面的最大区域数

给定N ‘，非平行线的数量。任务是找到这些线可以划分平面的最大区域数。
例子：

Input : N = 3 
Output : 7
Input : N = 2 
Output : 4 
 

由于非平行线形成的平面上的最大区域数

方法：上图显示了一条线可以划分平面的最大区域数。一条线可以把一个平面分成两个区域，两条不平行的线可以把一个平面分成4个区域，三条不平行的线可以分成7个区域，以此类推。当将^第n 行添加到 (n-1) 行的集群中时，形成的额外区域的最大数量等于 n。
现在解决递归如下：

L(2) – L(1) = 2 … (i) 
L(3) – L(2) = 3 … (ii) 
L(4) – L(3) = 4 … (iii) 
. . . 
. . . 
L(n) – L(n-1) = n ; … (n) 
Adding all the above equation we get,
L(n) – L(1) = 2 + 3 + 4 + 5 + 6 + 7 + …… + n ; 
L(n) = L(1) + 2 + 3 + 4 + 5 + 6 + 7 + …… + n ; 
L(n) = 2 + 2 + 3 + 4 + 5 + 6 + 7 + …… + n ; 
L(n) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + …… + n + 1 ; 
L(n) = n ( n + 1 ) / 2 + 1 ;
 

N条非平行线可划分平面的区域数等于N*(N+1)/2+1 。
下面是上述方法的实现：

C++

// C++ program to implement the above problem
 
#include 
using namespace std;
 
// Function to find the maximum
// number of regions on a plane
void maxRegions(int n)
{
    int num;
    num = n * (n + 1) / 2 + 1;
 
    // print the maximum number of regions
    cout << num;
}
 
// Driver code
int main()
{
    int n = 10;
 
    maxRegions(n);
 
    return 0;
}

Java

// Java program to implement the above problem
class GFG
{
 
    // Function to find the maximum
    // number of regions on a plane
    static void maxRegions(int n)
    {
        int num;
        num = n * (n + 1) / 2 + 1;
 
        // print the maximum number of regions
        System.out.println(num);;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int n = 10;
        maxRegions(n);
    }
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 program to implement
# the above problem
 
# Function to find the maximum
# number of regions on a plane
def maxRegions(n):
    num = n * (n + 1) // 2 + 1
 
    # print the maximum number
    # of regions
    print(num)
 
# Driver code
n = 10
 
maxRegions(n)
 
# This code is contributed
# by Mohit Kumar

C#

// C# program to implement the above problem
using System;
     
class GFG
{
 
    // Function to find the maximum
    // number of regions on a plane
    static void maxRegions(int n)
    {
        int num;
        num = n * (n + 1) / 2 + 1;
 
        // print the maximum number of regions
        Console.WriteLine(num);
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        int n = 10;
        maxRegions(n);
    }
}
 
// This code is contributed by 29AjayKumar

Javascript

 
// Javascript program to implement the above problem
 
// Function to find the maximum
// number of regions on a plane
function maxRegions(n)
{
    let num;
    num = parseInt( n * (n + 1) / 2) + 1;
 
    // print the maximum number of regions
    document.write(num);
}
 
// Driver code
    let n = 10;
 
    maxRegions(n);
 

输出：

56

时间复杂度： O(1)