TopCoder Statistics - Problem Statement

Problem Statement

We are going to plant a tree on level ground near a streetlight, and we want to know how big a shadow it will cast. We will model the tree as a (possibly degenerate) rectangular solid, and treat the streetlight as casting rays from a single point. We will use an x,y,z coordinate system that is aligned with the rectangular solid and in which y is the distance above ground level.

int[] tree contains exactly 6 elements, namely the x,y,z coordinates of one corner of the rectangular solid followed by the coordinates of the diagonally opposite corner. int[] light contains exactly 3 elements, the x,y,z coordinates of the streetlight. Given tree and light, return the area of the shadow, or return -1 to indicate that the shadow has an infinite area. If the shadow is an infinitely long line, return 0 as its area.

Definition

Class:: Shadow
Method:: area
Parameters:: int[], int[]
Returns:: double
Method signature:: double area(int[] tree, int[] light)
(be sure your method is public)

Notes

A return value with either an absolute or relative error of less than 1.0E-9 is considered correct.

Constraints

tree will contain exactly 6 elements.
light will contain exactly 3 elements.
Each element of tree and of light will be between 1 and 10, inclusive.
The coordinates of the light will not lie on the boundary of the tree.

Examples

{1,1,1, 10,1,1}

{5,5,5}

Returns: 0.0

This tree is just a line so its shadow has no area.
{1,3,1, 10,1,1}

{2,2,2}

Returns: -1.0

This tree is just a rectangle. Its shadow covers an infinite rectangular area on the ground.
{1,1,1, 2,2,2}

{3,3,3}

Returns: 15.75

This is a unit cube one unit above the ground. The shadowed area is a six-sided polygon.
{1,1,1, 3,3,3}

{2,2,2}

Returns: -1.0

When the light is inside the tree the shadow extends everywhere.
{1,1,1, 3,3,3}

{2,5,2}

Returns: 25.0
{1,1,1, 3,1,3}

{2,2,2}

Returns: 16.0
{8,1,1,8,3,3}

{10,5,2}

Returns: 9.375
{1,1,2, 2,2,2}

{3,3,3}

Returns: 3.375
{2,1,1, 2,2,2}

{3,3,3}

Returns: 3.375
{1,1,2, 2,2,2}

{3,3,3}

Returns: 3.375

111 222 333 top: 121 222 333 = 9 rhs: 211 222 333 = 3.375 z=2: 112 222 333 = 3.375 total = 15.75
{4, 7, 3, 7, 5, 9}

{2, 8, 8}

Returns: 1493.3333333333335
{5, 3, 2, 2, 1, 10}

{6, 6, 10}

Returns: 106.24000000000001
{4, 10, 5, 9, 10, 6}

{9, 2, 1}

Returns: 0.0
{3, 10, 6, 7, 9, 2}

{10, 7, 10}

Returns: 0.0
{9, 1, 6, 8, 3, 7}

{9, 6, 4}

Returns: 6.5600000000000005
{2, 1, 3, 10, 9, 5}

{1, 7, 2}

Returns: -1.0
{5, 3, 6, 5, 9, 7}

{5, 5, 8}

Returns: 0.0
{8, 9, 2, 10, 4, 4}

{6, 9, 5}

Returns: -1.0
{1, 9, 1, 3, 10, 3}

{3, 7, 3}

Returns: 0.0
{3, 2, 4, 4, 1, 9}

{7, 1, 4}

Returns: 0.0
{8, 8, 7, 5, 10, 8}

{10, 9, 1}

Returns: -1.0
{4, 3, 9, 10, 10, 8}

{2, 2, 10}

Returns: 0.0
{1, 3, 4, 10, 9, 4}

{10, 6, 3}

Returns: -1.0
{3, 3, 3, 2, 7, 2}

{7, 2, 4}

Returns: 0.0
{8, 3, 7, 6, 2, 5}

{4, 4, 7}

Returns: 88.0
{9, 8, 1, 2, 4, 5}

{7, 5, 7}

Returns: -1.0
{3, 8, 5, 3, 7, 9}

{1, 3, 3}

Returns: 0.0
{7, 9, 8, 6, 1, 8}

{6, 2, 1}

Returns: -1.0
{1, 7, 5, 4, 6, 7}

{10, 3, 8}

Returns: 0.0
{7, 6, 7, 3, 6, 4}

{10, 4, 6}

Returns: 0.0
{6, 4, 8, 7, 7, 2}

{9, 10, 9}

Returns: 120.83333333333334
{1, 2, 9, 10, 10, 8}

{7, 8, 6}

Returns: -1.0
{8, 10, 8, 6, 4, 1}

{10, 8, 7}

Returns: -1.0
{6, 8, 9, 10, 2, 5}

{5, 2, 9}

Returns: 0.0
{7, 6, 9, 6, 5, 2}

{9, 3, 1}

Returns: 0.0
{1, 7, 5, 5, 1, 2}

{2, 5, 10}

Returns: -1.0
{9, 10, 9, 8, 1, 2}

{3, 2, 7}

Returns: -1.0
{6, 1, 8, 10, 1, 5}

{9, 7, 10}

Returns: 16.333333333333336
{4, 6, 6, 7, 4, 2}

{10, 3, 2}

Returns: 0.0
{1, 2, 1, 7, 3, 5}

{9, 7, 2}

Returns: 77.91
{8, 10, 2, 7, 5, 8}

{6, 5, 2}

Returns: 0.0
{1, 9, 5, 4, 1, 10}

{2, 5, 6}

Returns: -1.0
{6, 6, 7, 3, 7, 5}

{8, 3, 4}

Returns: 0.0
{1, 1, 1, 5, 10, 1 }

{8, 2, 1 }

Returns: 0.0
{5, 1, 7, 5, 9, 8 }

{5, 5, 5 }

Returns: 0.0
{3, 5, 3, 5, 7, 3 }

{1, 6, 3 }

Returns: 0.0
{1, 3, 1, 10, 4, 5 }

{5, 2, 5 }

Returns: 0.0
{5, 5, 5, 5, 7, 5 }

{6, 6, 6 }

Returns: 0.0
{5, 5, 5, 6, 5, 6 }

{3, 3, 3 }

Returns: 0.0
{1, 1, 1, 1, 5, 5 }

{1, 3, 6 }

Returns: 0.0
{2, 2, 2, 3, 3, 3 }

{1, 1, 1 }

Returns: 0.0
{1, 1, 1, 3, 3, 1 }

{4, 2, 1 }

Returns: 0.0
{1, 1, 1, 1, 10, 1 }

{2, 2, 2 }

Returns: 0.0
{2, 2, 2, 2, 4, 2 }

{1, 3, 2 }

Returns: 0.0
{1, 1, 1, 1, 1, 3 }

{1, 1, 10 }

Returns: 0.0
{5, 1, 5, 6, 2, 6 }

{2, 1, 2 }

Returns: 0.0
{1, 1, 1, 2, 2, 2 }

{3, 3, 5 }

Returns: 22.5

Statistics

Problem Statement for "Shadow"

Problem Statement

Definition

Notes

Constraints

Examples