Package g2501_2600.s2550_count_collisions_of_monkeys_on_a_polygon

Class Solution

java.lang.Object
g2501_2600.s2550_count_collisions_of_monkeys_on_a_polygon.Solution
public class Solution extends java.lang.Object
2550 - Count Collisions of Monkeys on a Polygon.

Medium

There is a regular convex polygon with n vertices. The vertices are labeled from 0 to n - 1 in a clockwise direction, and each vertex has exactly one monkey. The following figure shows a convex polygon of 6 vertices.

Each monkey moves simultaneously to a neighboring vertex. A neighboring vertex for a vertex i can be:

  • the vertex (i + 1) % n in the clockwise direction, or
  • the vertex (i - 1 + n) % n in the counter-clockwise direction.

A collision happens if at least two monkeys reside on the same vertex after the movement or intersect on an edge.

Return the number of ways the monkeys can move so that at least one collision happens. Since the answer may be very large, return it modulo 109 + 7.

Note that each monkey can only move once.

Example 1:

Input: n = 3

Output: 6

Explanation: There are 8 total possible movements.

Two ways such that they collide at some point are:

  • Monkey 1 moves in a clockwise direction; monkey 2 moves in an anticlockwise direction; monkey 3 moves in a clockwise direction. Monkeys 1 and 2 collide.
  • Monkey 1 moves in an anticlockwise direction; monkey 2 moves in an anticlockwise direction; monkey 3 moves in a clockwise direction. Monkeys 1 and 3 collide. It can be shown 6 total movements result in a collision.

Example 2:

Input: n = 4

Output: 14

Explanation: It can be shown that there are 14 ways for the monkeys to collide.

Constraints:

  • 3 <= n <= 109

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    monkeyMove(int n)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • monkeyMove

      public int monkeyMove(int n)