Connection Status:
Competition Arena > PolygonRotation

PolygonRotation

TCO17 Round 1A · 2017-03-31 · by Nickolas

TCO17 Round 1A · 2017-03-31 · by Nickolas · Geometry
Class Name: PolygonRotation
Return Type: double
Method Name: getVolume
Arg Types: (vector<int>, vector<int>)
Problem Statement

Problem Statement

We have a convex polygon in the XY plane. The vertices of the polygon are the points (x[0], y[0]), (x[1], y[1]), ... in clockwise order. You are given the int[]s x and y.
In order to make the implementation simpler the polygon and its representation satisfy some additional constraints. Please read the Constraints section carefully.
A three-dimensional solid is obtained by rotating this polygon around the Y axis. Compute and return the volume of the resulting solid.

Notes

  • The returned value must have an absolute or relative error less than 1e-9.

Constraints

  • x will contain between 3 and 50 elements, inclusive.
  • y will contain the same number of elements as x.
  • Each element of x and y will be between -100 and 100, inclusive.
  • The polygon will be convex.
  • All vertices of the polygon will be distinct.
  • The polygon will have exactly two vertices on the Y axis. Let's denote them (0, Ymin) and (0, Ymax) with Ymin < Ymax.
  • The vertices will be listed in clockwise order, starting with (0, Ymax).
  • The y-coordinates of all vertices will be between Ymin and Ymax, inclusive.
  • No three points will lie on the same line.
Examples
0)
{0, 1, 1, 0}
{1, 1, 0, 0}
Returns: 3.141592653589793

The polygon is a square with sides parallel to the coordinate axes. One of the sides of the square belongs to the Y axis. The resulting solid of revolution is a right cylinder of height 1 and radius 1.

1)
{0, 1, 0, -1}
{2, 1, 0, 1}
Returns: 2.0943951023931953

This polygon is also a square. Each of its sides is angled at 45 degrees to the coordinate axes. The resulting solid of revolution is the union of two cones, each with base radius 1 and height 1.

2)
{0, 3, 0, -2, -2}
{2, 0, -3, -1, 1}
Returns: 49.91641660703782
3)
{0, 3, 3, 0, -1, -1}
{2, 2, -2, -2, -1, 1}
Returns: 113.09733552923255
4)
{0, 1, 1, 0, -2}
{3, 2, 0, -1, 1}
Returns: 16.755160819145562
8)
{0, 100, 100, 0}
{100, 100, -100, -100}
Returns: 6283185.307179586

max volume

9)
{0, 0, -1}
{100, 99, 100}
Returns: 1.0471975511965976

min volume? can't have 0

11)
{0, 3, 8, 11, 13, 14, 11, 6, 0, -2, -9, -13, -14, -12, -9, -5}
{25, 24, 21, 17, 12, 7, 3, 1, 0, 0, 2, 5, 8, 15, 20, 23}
Returns: 9198.382026237112

edges intersections

Submissions are judged against all 72 archived test cases, of which 8 are shown here. Case numbers match the judge’s.

Coding Area

Language: C++17 · define a public class PolygonRotation with a public method double getVolume(vector<int> x, vector<int> y) · 72 test cases · 2 s / 256 MB per case

Submitting as anonymous