# Determine the position of the third person on regular N sided polygon

Given ‘N’ which represent the regular N sided polygon. Two children are standing on the vertex ‘A’ and ‘B’ of this Regular N sided polygon. The task is to determine the number of that vertex another person should stand on so that the sum of the minimum jumps required to reach A and minimum jumps required to reach B is minimized.

Note:

1. The vertices of this regular polygon are number from 1 to N in a clockwise manner.
2. If there are multiple answers, output the least numbered vertex.

Examples:

```Input: N = 6, A = 2, B = 4
Output: Vertex = 3
Explanation:
The another person should stand on 3rd vertex.
As from 3rd vertex,
1 jump is required to reach A
and 1 jump is required to reach B.
(See figure above)

Input: N = 4, A = 1, B = 2
Output: Vertex = 3
Explanation:
The another person should stand on 3rd or 4th vertex.
But, as mentioned above
we have to print least numbered vertex
that's why the output is 3.
```

Approach:

• Simply calculate jumps from each vertex except vertices A and B as on that vertices children are standing and store their sum in sum variable.
• Finally, print that position from where the sum of jumps is minimum.
 `// C++ implementation of above approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to find out the ` `// number of that vertices ` `int` `vertices(``int` `N, ``int` `A, ``int` `B) ` `{ ` `    ``int` `position = 0; ` `    ``int` `minisum = INT_MAX; ` `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 1; i <= N; i++) { ` ` `  `        ``// Another person can't stand on ` `        ``// vertex on which 2 children stand. ` `        ``if` `(i == A || i == B) ` `            ``continue``; ` ` `  `        ``// calculating minimum jumps from ` `        ``// each vertex. ` `        ``else` `{ ` ` `  `            ``int` `x = ``abs``(i - A); ` `            ``int` `y = ``abs``(i - B); ` ` `  `            ``// Calculate sum of jumps. ` `            ``sum = x + y; ` ` `  `            ``if` `(sum < minisum) { ` `                ``minisum = sum; ` `                ``position = i; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `position; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `N = 3, A = 1, B = 2; ` ` `  `    ``// Calling function ` `    ``cout << ``"Vertex = "` `<< vertices(N, A, B); ` ` `  `    ``return` `0; ` `} `

 `// Java implementation of above approach ` `class` `GFG  ` `{ ` `     `  `// Function to find out the ` `// number of that vertices ` `static` `int` `vertices(``int` `N, ``int` `A, ``int` `B) ` `{ ` `    ``int` `position = ``0``; ` `    ``int` `minisum = Integer.MAX_VALUE; ` `    ``int` `sum = ``0``; ` `    ``for` `(``int` `i = ``1``; i <= N; i++)  ` `    ``{ ` ` `  `        ``// Another person can't stand on ` `        ``// vertex on which 2 children stand. ` `        ``if` `(i == A || i == B) ` `            ``continue``; ` ` `  `        ``// calculating minimum jumps from ` `        ``// each vertex. ` `        ``else`  `        ``{ ` ` `  `            ``int` `x = Math.abs(i - A); ` `            ``int` `y = Math.abs(i - B); ` ` `  `            ``// Calculate sum of jumps. ` `            ``sum = x + y; ` ` `  `            ``if` `(sum < minisum)  ` `            ``{ ` `                ``minisum = sum; ` `                ``position = i; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `position; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `N = ``3``, A = ``1``, B = ``2``; ` ` `  `    ``// Calling function ` `    ``System.out.println(``"Vertex = "` `+ vertices(N, A, B)); ` `} ` `} ` ` `  `// This code contributed by Rajput-Ji `

 `# Python3 implementation of above approach ` ` `  `# Function to find out the ` `# number of that vertices ` `def` `vertices(N, A, B): ` ` `  `    ``position ``=` `0` `    ``miniSum ``=` `10``*``*``9` `    ``Sum` `=` `0` `    ``for` `i ``in` `range``(``1``, N ``+` `1``): ` ` `  `        ``# Another person can't stand on ` `        ``# vertex on which 2 children stand. ` `        ``if` `(i ``=``=` `A ``or` `i ``=``=` `B): ` `            ``continue` ` `  `        ``# calculating minimum jumps from ` `        ``# each vertex. ` `        ``else``: ` ` `  `            ``x ``=` `abs``(i ``-` `A) ` `            ``y ``=` `abs``(i ``-` `B) ` ` `  `            ``# Calculate Sum of jumps. ` `            ``Sum` `=` `x ``+` `y ` ` `  `            ``if` `(``Sum` `< miniSum): ` `                ``miniSum ``=` `Sum` `                ``position ``=` `i ` `             `  `    ``return` `position ` ` `  ` `  `# Driver code ` `N ``=` `3` `A ``=` `1` `B ``=` `2` ` `  `# Calling function ` `print``(``"Vertex = "``,vertices(N, A, B)) ` ` `  ` `  `# This code is contributed by mohit kumar `

 `// C# implementation of the approach  ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG  ` `{  ` `     `  `// Function to find out the  ` `// number of that vertices  ` `static` `int` `vertices(``int` `N, ``int` `A, ``int` `B)  ` `{  ` `    ``int` `position = 0;  ` `    ``int` `minisum = ``int``.MaxValue;  ` `    ``int` `sum = 0;  ` `    ``for` `(``int` `i = 1; i <= N; i++)  ` `    ``{  ` ` `  `        ``// Another person can't stand on  ` `        ``// vertex on which 2 children stand.  ` `        ``if` `(i == A || i == B)  ` `            ``continue``;  ` ` `  `        ``// calculating minimum jumps from  ` `        ``// each vertex.  ` `        ``else` `        ``{  ` ` `  `            ``int` `x = Math.Abs(i - A);  ` `            ``int` `y = Math.Abs(i - B);  ` ` `  `            ``// Calculate sum of jumps.  ` `            ``sum = x + y;  ` ` `  `            ``if` `(sum < minisum)  ` `            ``{  ` `                ``minisum = sum;  ` `                ``position = i;  ` `            ``}  ` `        ``}  ` `    ``}  ` `    ``return` `position;  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main(String[] args)  ` `{  ` `    ``int` `N = 3, A = 1, B = 2;  ` ` `  `    ``// Calling function  ` `    ``Console.WriteLine(``"Vertex = "` `+ vertices(N, A, B));  ` `}  ` `}  ` ` `  `/* This code contributed by PrinciRaj1992 */`

 ` `

Output:
```Vertex = 3
```

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