# 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:**

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

**Examples:**

Input:N = 6, A = 2, B = 4Output:Vertex = 3Explaination: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 = 2Output:Vertex = 3Explaination: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++

`// C++ implementation of above approach ` ` ` `#include <bits/stdc++.h> ` `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; ` `} ` |

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## Java

`// 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 ` |

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## Python

`# 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 ` |

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## C#

`// 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 */` |

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## PHP

`<?php ` `// PHP implementation of above approach ` ` ` ` ` `// Function to find out the ` `// number of that vertices ` `function` `vertices(` `$N` `, ` `$A` `, ` `$B` `) ` `{ ` ` ` `$position` `= 0; ` ` ` `$minisum` `= PHP_INT_MAX; ` ` ` `$sum` `= 0; ` ` ` `for` `(` `$i` `= 1; ` `$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` `{ ` ` ` ` ` `$x` `= ` `abs` `(` `$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; ` `$B` `= 2; ` ` ` ` ` `// Calling function ` ` ` `echo` `"Vertex = "` `,vertices(` `$N` `, ` `$A` `,` `$B` `); ` ` ` ` ` `// This code is contributed by Ryuga ` ` ` `?> ` |

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**Output:**

Vertex = 3

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