TopCoder Statistics - Problem Statement

Problem Statement

We have n straight lines drawn in the Cartesian plane each described by two distinct points (x1[i], y1[i]) and (x2[i], y2[i]) lying on it. A center of symmetry is such a point that under a symmetry centered at this point the given configuration of lines goes into itself (i.e., the image of every given line under this symmetry is again one of the given lines). Return the number of centers of symmetry that the given system of lines has. Return -1 if there are infinitely many centers of symmetry.

Definition

Class:: CentersOfSymmetry
Method:: lineConfigurations
Parameters:: int[], int[], int[], int[]
Returns:: int
Method signature:: int lineConfigurations(int[] x1, int[] y1, int[] x2, int[] y2)
(be sure your method is public)

Notes

A symmetry centered at point X works as follows. The image of a point A is such a point B that X is the midpoint of the line segment AB (note that if A = X, then also B = X). The image of a line is the union of images of all points on this line.

Constraints

x1 will contain between 1 and 50 elements, inclusive.
x1, y1, x2, y2 will all contain the same number of elements.
All the elements of x1, y1, x2 and y2 will be between -50 and 50, inclusive.
For each i either x1[i] and x2[i] or y1[i] and y2[i] will be distinct (i.e., two points defining a line will be distinct).
All the lines defined by (x1[i], y1[i]) and (x2[i], y2[i]) will be distinct.

Examples

{0, 0}

{0, 0}

{1, -1}

{1, 1}

Returns: 1

A configuration of two intersecting lines has a single center of symmetry - their intersection point.
{0, 0, 0, 0, 0, 0, 0, 0, 0}

{0, 0, 0, 0, 0, 0, 0, 0, 0}

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

{1, 2, 3, 4, 5, 6, 7, 8, 9}

Returns: 1

All the lines pass through the origin.
{0, 1, 2}

{0, 1, -1}

{1, 2, 0}

{1, -1, 0}

Returns: 0
{-10, 10}

{10, -10}

{-10, 10}

{-10, 10}

Returns: -1

Two parallel lines produce infinitely many centers of symmetry.
{-50, -50, -50, -50}

{-50, -49, -48, -46}

{50, 49, 48, 46}

{50, 50, 50, 50}

Returns: 0

4 parallel lines with no centers of symmetry.
{7}

{11}

{10}

{-7}

Returns: -1

A single line.
{0,0,0,0}

{0,7,4,3}

{10,20,30,40}

{0,7,4,3}

Returns: -1

Next 4 don't delete
{0,0,0,0}

{0,7,5,3}

{40,30,20,10}

{0,7,5,3}

Returns: 0
{1,1,3,3}

{1,1,3,3}

{1,3,1,3}

{3,1,3,1}

Returns: 1
{2, -9, 1, 21, -15, 13, 6, -3, -3, 1, 0, 0, 12, 9, 29}

{13, -2, 5, -27, -4, 2, 3, 10, 0, 11, 0, 3, -5, 8, -19}

{5, -5, 2, 24, -11, 10, 3, -5, -5, 3, 8, 2, 0, -11, 32}

{1, 0, 5, -31, -2, 3, 6, 10, 0, 7, 10, 4, 10, -4, -23}

Returns: 1

next 11 are random configurations with a center of symmetry
{2, 3, -7, 5, -5, 3, 14, 2, 7, 6, 2, 6, 15, 7, -2, -6, 3, -1, 4, -3}

{-11, 0, 13, 3, -2, 7, -8, 4, 2, 2, -5, 5, -5, 1, 26, 18, 5, 0, 7, -2}

{6, 6, 9, 5, 0, 7, 8, 6, 8, 2, 4, 2, 18, 10, -3, -7, 11, -4, 2, 9}

{9, 6, 1, 5, 1, 1, 0, 4, 1, 10, 1, 1, -8, -2, 28, 20, 1, -2, 13, 7}

Returns: 1
{-4, -32, -2, -2, -2, -7, -5, -8, -13, -3, 2, -13, -3, -3, -3, -5, 1, -1, 1, -6, -8, -9, -2, -10, -12, -2, -6, -36}

{-3, -25, -2, -6, -3, -14, 1, -4, -7, -1, -10, -13, 1, 0, -5, 2, -11, -4, -2, -11, 0, -3, 2, -4, -11, -11, -7, -17}

{-4, -23, 2, 0, -1, -7, -7, 0, -10, -5, -6, -7, -5, -7, -6, -6, 1, -1, 6, -7, 4, -9, -8, -2, -16, -2, -6, -27}

{0, -19, -4, -11, -4, -15, 5, 2, -5, -1, 2, -5, -3, -4, 7, 5, -13, -5, -3, -16, -3, -5, -7, 0, -16, -9, -5, -11}

Returns: 1
{-19, -11, -13, -3, -4, -5, -2, -10, -25, -44, -3, -2, -7, -1, -25, -7, -3, -10, -15, -34, 6, 8, -1, -30, -32, 2}

{-4, 37, -10, 6, 3, 5, 10, -3, -14, 22, 1, 3, 11, 4, -4, 14, 9, 2, 27, 16, 3, 2, 1, -26, -36, 2}

{-9, -10, -1, -6, -4, -6, -8, -13, -34, -39, -5, -5, -3, -7, -34, -3, -5, -8, -14, -29, 11, 0, 2, -21, -23, -6}

{2, 34, 10, 3, 6, 5, -5, -7, -20, 20, 9, 6, 3, 6, -10, 2, 1, 3, 24, 14, 2, 4, -3, -14, -24, 6}

Returns: 1
{-35, -12, -39, -19, -17, -43, 21, -13, -37, -11, -11, 23, -17}

{-12, -7, -4, -13, -14, 23, -36, 36, 33, -4, -7, -36, 44}

{-43, -13, -47, -16, -16, -48, 12, -12, -42, -10, -8, 14, -16}

{-14, -8, -6, -10, -13, 27, -24, 32, 37, -3, -4, -24, 40}

Returns: 1
{20, -16, -10, -12, -2, -17, 5, -9, 18, -3, -6, -6, 3, 11, -2, 11, 1, 11, -7, -10, 19, -26, -4, -6, -8}

{-4, 38, -23, -19, 17, -13, -6, -3, -12, 21, 2, -2, 1, -13, -33, -8, -10, -3, 27, -39, -4, 42, -13, -3, 15}

{16, -19, -8, -10, 0, -21, 5, -13, 14, -1, -7, -7, 3, 9, 1, 13, 1, 9, -5, -7, 21, -29, -3, -5, -6}

{-2, 43, -20, -16, 13, -15, -8, -5, -10, 15, 2, -2, -2, -11, -21, -9, -12, -1, 21, -27, -5, 47, -12, -2, 11}

Returns: 1
{34, 0, -11, 10, -7, -16, -16, -6, 9, -3, -8, 1, -1, 2, 11, -10, -23, -15, 4, -18, 38, 18, -2, 3, 24}

{-10, -3, -5, -13, -8, -14, -23, -6, -16, -4, -14, -4, -5, -2, -6, -4, -28, -36, -3, -29, -8, -27, 2, -4, -37}

{39, 2, 5, 11, 5, -18, -28, -5, 8, -1, -7, 1, -3, 0, 10, -12, -17, -9, 5, -30, 43, 10, 7, 0, 16}

{-11, -1, -1, -14, 1, -15, -39, -5, -15, -3, -13, -5, -8, -2, -5, -5, -19, -27, -4, -45, -9, -15, -10, -1, -25}

Returns: 1
{-9, -6, -15, 5, -8, -14, -6, -8, -4, -1, -1, -11, 6, 15, -2, -12, 0, -14, -25, -20, -10, -23, -19, -21, -8, -1, 5, -6, -19}

{-13, 18, -4, -7, 20, -3, 19, 19, -1, 22, 1, 12, -5, -5, -3, -8, 32, 0, 24, -9, 22, -10, -24, 14, 25, -17, 4, 29, -30}

{-11, -5, -13, 6, -7, -12, -4, -6, -4, 0, 0, -10, 6, 16, 0, -18, -3, -20, -28, -18, -13, -21, -15, -24, -7, -3, -11, -5, -15}

{-19, 16, -3, -8, 18, -2, 15, 15, -5, 20, 2, 10, -9, -6, 1, -11, 44, -3, 26, -8, 34, -9, -18, 16, 22, -23, 0, 26, -24}

Returns: 1
{10, -35, -8, 7, -5, -8, -9, -50, -17, -18, -17, -26, -5, 23, 18, -7, -8, -6, -8, -12, 22, -7, 17, -48, -6, -16, -12, -14, 13, 30, 11, 17, -3, -5, -27, -30}

{-27, -25, -17, -26, -3, -19, -20, -33, -22, -21, -23, -38, -2, -32, -27, -8, -2, -5, -21, -7, -15, -15, -5, -27, 0, -19, -25, 1, -22, -11, -13, -38, -1, -6, -17, -32}

{16, -32, -11, 11, -3, -9, -8, -45, -16, -15, -19, -29, -2, 20, 24, -1, 4, -7, -5, -13, 16, -9, 29, -43, 2, -17, -15, -15, 17, 24, 23, 14, -7, -3, -24, -33}

{-35, -23, -26, -32, -3, -21, -18, -30, -20, -15, -27, -42, -5, -28, -35, 2, -5, -6, -15, -7, -13, -19, -9, -24, -12, -21, -34, 1, -28, -9, -17, -34, -9, 0, -15, -36}

Returns: 1
{3, 3, 1, -5, 3, 5, 20, -24, -6, 8, 38, 12, -4, -24, 42, 26, -10, 18, -13, -5, 2, 37, -28, 2, 0, -23, -8, -4, -6, 0, -29, 26, -4, -16, -33, 18, -6, -11, -39, -2}

{4, -2, -9, 0, 5, -4, 2, -24, -12, 8, -37, -8, -11, 12, -47, -5, -2, -22, 0, -9, 3, -41, 18, -6, -9, -13, -17, 24, -3, -19, -21, -26, 9, -34, -34, -7, 18, -10, -24, 8}

{7, 3, 2, -2, 5, 5, 24, -27, -10, -8, 30, 16, -7, -44, 34, 22, -6, 16, -11, 1, 5, 28, -48, -2, 1, -14, -7, -3, -11, -3, -20, 24, -8, -19, -28, 14, -5, -9, -34, 2}

{0, -6, -5, 1, 1, -8, 0, -28, -20, -12, -27, -10, -20, 20, -37, -3, -2, -19, 1, -1, 3, -29, 26, -14, -7, -7, -15, 22, -6, -28, -15, -23, 12, -38, -30, -5, 16, -9, -20, 8}

Returns: 1
{-11, -3, -8, -19, -17, -8, 0, -4, 16, -10, -3, -12, -33, -18, 15, -39, -4, 21, 20, -41, -6, -3, -10, -12, -10, -27, -4, -9, -18, -8, -15, -1, 4, 15, 24, 12, -8, -12, 3, -14, -17, 4, -7, -5, -13, 3, 24}

{-1, -8, -2, -22, -24, 10, 2, -2, -3, -8, -5, -4, -2, 3, -9, 40, 9, -1, -1, 32, -6, 8, 2, 3, -1, -2, -27, 0, -7, -14, -23, 4, -2, 1, -9, 1, -8, -7, 0, -19, -5, 7, 3, -29, 5, -1, 1}

{-17, -2, -9, -13, -11, -4, 0, -4, 19, -11, -3, -9, -38, -27, 17, -34, -3, 23, 23, -36, -7, -4, -5, -16, -9, -32, -3, -10, -27, -9, -13, -2, 4, 5, 27, -4, -5, -16, 9, -13, -23, -8, -5, -3, -11, 3, 27}

{-4, -4, -3, -13, -15, 7, 5, -6, -4, -9, -8, -1, -3, 0, -10, 36, 9, -2, -2, 28, -8, 8, 3, 1, -1, -3, -24, 0, -10, -16, -17, 4, -6, 3, -10, 5, -5, -9, -8, -16, -8, -2, 3, -23, 5, -4, 0}

Returns: 1
{-24, 45, 28, -15, -50, 16}

{-42, 39, -13, 29, 2, -2}

{5, -33, -16, 40, -4, -26}

{35, 9, 37, 28, -33, 46}

Returns: 0

next 19 are random lines
{-36, 9, 0, 12, -39, -24, -6}

{22, 29, 49, 23, 35, -3, 35}

{-39, 48, -18, 15, 40, -13, -44}

{13, 50, -47, 45, -34, 22, 44}

Returns: 0
{-47, 3, 15, -18, -45, -6, -12, -33, -39}

{-3, -19, 49, 5, 29, 26, 3, 2, 4}

{-20, -50, 11, 21, -40, 28, 43, -42, 42}

{46, -12, -32, -27, 21, -7, -41, -19, -40}

Returns: 0
{-21, -42, -34, -46, -23, -28, -23}

{9, -8, -7, 17, 43, -20, 4}

{-40, -19, -32, -18, 17, 50, -24}

{-20, 22, -34, -3, 4, 9, 8}

Returns: 0
{36, 44, -23, 33, -21, -36, -8, -48, 2, 15, -1, -7}

{-47, 46, -27, 11, -11, -23, -19, 29, 50, -8, -23, 40}

{-50, 28, -35, -34, 21, -34, -35, -6, 20, -26, 26, -34}

{39, 48, -43, -49, -16, -38, -27, 29, 31, 9, -39, 25}

Returns: 0
{-44, 6, -12, -14, -25, 11, 20, -26, 29, 31, 14, -31, -19, -49, 45, -27}

{-10, -26, 35, 31, 42, 15, 2, -33, 12, 31, 21, 19, 5, -33, 7, -30}

{12, -40, -28, 11, 48, 22, 50, 33, -40, -47, -44, -25, -38, -36, 14, -28}

{46, 20, 40, 18, -31, 24, 27, 41, 41, 29, 37, 22, -31, 10, -2, 47}

Returns: 0
{-19, -46, 41, -30, 24, 34, 49, -4, 5, 39, -2, -16, 13}

{-8, 19, -1, 2, -43, 22, 29, 11, 0, 33, -18, -16, 24}

{13, -21, -2, -27, -23, 6, -40, -8, 15, 19, -23, 39, 38}

{-9, -26, 27, -25, 33, -24, 38, 8, 8, 6, -31, 1, -5}

Returns: 0
{-38, -17, 46, -36, -25, -3, -8, 34, -17, -50, 44, -31, 40, 16, 2, -31, -39, 14, 1, -13}

{-28, -24, 17, 2, 6, 28, -41, 13, -27, -19, -19, 26, 0, 12, 11, -42, -49, -44, 42, -50}

{40, 16, -27, 21, 32, 37, -17, -32, -21, 39, -37, -41, 5, -33, -34, -28, 11, 35, 12, 43}

{23, 36, -1, -7, -8, -18, -39, 31, 45, 10, -42, 28, 37, -45, -7, -35, 11, 10, 0, -46}

Returns: 0
{-42, -16, 33, 27, -28, 47, -44, 30, 30, 7, -16, -20, -14, 5, -16, 26, -27, 16, 23}

{33, -18, -34, -46, -23, 26, 44, 21, -33, 21, 17, 38, 5, -41, 3, 23, 26, 2, -39}

{38, 15, -5, 47, 46, 48, 28, -35, 2, -38, -8, -34, 38, 42, 41, -30, 26, 17, -19}

{22, 11, 14, -26, -45, -14, -1, 40, -4, -5, 49, -1, -35, -23, -2, 29, 22, 33, 48}

Returns: 0
{-50, 19, -44, 15, -40, 42, -33, 18, 32, -30, 46, 5, -19, 50, -48, 27, 2, -32, -23}

{46, -8, -25, -48, -11, 24, -30, -33, -34, 34, -23, -31, 5, 3, 35, -42, -43, -42, 40}

{33, -1, -30, -46, -30, -21, 1, 0, 42, -35, 42, -47, 22, 44, -12, -11, 15, 39, -31}

{-40, -15, -18, -16, -45, -8, 8, -41, 34, -41, -8, -34, 17, -29, -4, 1, -25, -28, -10}

Returns: 0
{-11, 48, -32, 19, -33, 21, -37, -36, 26, 8, 26, 25, -9, -43, -36, -20, -15, -4, -27, -36, 38, -22, -25, -31, -26, 16, 34, 37, 12}

{-25, -20, 5, -31, -11, 29, -10, 31, 2, 23, 46, 33, -11, -31, 4, 13, 7, 27, 38, -45, -38, 15, -31, 2, -9, -12, -26, 24, -7}

{27, 26, 25, 38, 44, 42, -23, 25, 19, 30, 6, -9, -42, -26, 38, 45, 15, -4, -40, 14, -10, 50, 6, 9, -50, -35, -41, -37, 1}

{24, -25, -28, 16, 10, -45, -49, -45, 2, -39, -27, 10, -34, -35, 27, -15, -48, 24, -24, 43, 20, 24, 24, 11, 5, -1, 20, -43, -9}

Returns: 0
{44, -40, -33, 17, -34, 18, 8, -39, 50, -33, -5, -23, -43, -31, 1, -42, -7, -45, -29, 44, 38, 1, -18, 49, -20, 25}

{15, 47, -15, -4, 6, 48, 0, 37, 21, 3, 12, -2, -26, -12, -29, -32, 35, 39, -42, 19, 21, 35, 37, 41, 6, 6}

{-43, -28, -13, 0, 29, 35, -29, 11, 8, 11, 30, -43, 38, 50, 28, 16, 1, -40, -29, 17, 44, -5, 42, 38, -29, -41}

{-15, -47, -2, -16, -4, -47, 28, -22, 8, 23, -38, -5, -16, 17, -17, -23, -50, 7, -35, -42, -6, 37, -6, -16, 28, -11}

Returns: 0
{-18, 11, 3, 41, -47, 17, -17, -31, 32, 30, -20, -32, -29, -50, 42, -27, -35, 37, 0, -29, -44, 3, 24, -21, 43, -14, 31, 5, -41}

{49, 7, -1, 2, -42, 6, 45, 30, -15, -42, 28, 7, 2, -50, -47, 18, 17, 0, -44, 32, 6, 0, 35, 47, -15, -28, 19, 16, 7}

{30, -24, 32, 14, -45, 1, 27, -11, 45, -34, 5, -41, -17, 38, -28, 17, 25, 33, 18, -17, -25, 4, -40, -36, -17, -25, -24, -13, 45}

{9, -15, -5, 20, 24, -32, 39, -27, 45, -12, 35, 19, -35, -47, -3, -29, 33, 22, -8, 38, 47, 15, -36, 38, -44, -26, -33, -37, -42}

Returns: 0
{-5, 12, 44, -1, -6, 50, -11, 29, -46, 20, 50, 10, -2, -27, -20, 6, 19, -6, -16, 35, 29, 25, 20, -37, 18, -43, -5, 7, 0, 30, 47, 37, -28}

{2, -2, 44, 20, -4, -12, -27, -1, 34, -9, -36, 30, 13, -34, -49, 35, 8, 46, 28, 38, 30, 9, 33, -43, 38, -24, 45, 41, 38, 22, 18, -9, 13}

{28, 32, 50, -2, 23, 25, -16, -26, -29, -28, 3, 38, 45, 47, -16, -15, 42, -23, -42, -41, 27, 24, 25, -37, 14, 20, 19, 45, -45, 30, 9, -8, -41}

{-14, -49, 11, 41, 21, 22, 48, -43, -4, 33, 39, 45, 30, -16, -41, -16, -5, -3, -25, -48, 15, 48, -46, -46, 50, -22, -13, 35, 25, -37, 0, 13, 8}

Returns: 0
{-21, 25, 44, -35, 20, 8, 25, -37, -29, -38, -38, 6, 0, 23, -28, -27, 48, -26, -6, -23, -24, -44, 31, -31, 15, -36, 45, -36, 39, 26, 24, 36, -12, 33, 20, -5, 18, 26}

{-18, 46, -33, 0, 46, 16, -39, -28, -46, 42, 17, 46, -37, 14, 37, 30, 1, -34, -34, -29, 47, -11, 8, 2, 23, 8, 9, -28, -4, 28, -43, -17, -16, -39, 7, 17, -26, -1}

{50, 6, 38, 28, -4, 45, 23, 39, -46, 16, 23, -36, -2, 48, 48, -19, -35, -50, 45, 10, 24, -35, 31, 12, 17, -17, -44, 4, 27, 50, 35, -30, -17, -35, 22, 16, -30, -36}

{-5, -29, -41, 32, -19, -32, 29, -6, 23, 44, 28, -45, -37, -25, 18, 27, 16, -35, 35, 35, 22, -9, -40, -22, -3, -44, 19, -4, -13, 42, -4, -26, -5, -44, 11, -36, -11, -22}

Returns: 0
{-32, -40, -17, -14, -39, -18, -26, -2, 12, -7, -14, -23, 46, -44, -23, 3, -20, -14, -17, 22, 40, 25, -44, 1, 47, -2, 47, -20, 28, -36, 3, -42, -7, 27, -40}

{14, 17, 24, 46, -17, -8, 8, -47, 32, 8, -23, -10, 6, -7, 1, -10, 32, 2, 5, 50, -49, -32, -13, 7, -24, -43, -22, -28, -36, -8, 47, -11, 30, 33, 34}

{46, -42, -42, 3, 31, -8, -43, 10, 46, -46, -3, 10, 27, -13, 30, -21, 38, -11, -48, 22, 20, 0, 29, 20, 42, 5, -47, -27, 39, 49, -7, 50, -13, 20, 38}

{-8, -35, -9, 34, -38, 4, -27, -5, 50, -50, 48, -15, -25, 2, -37, -6, -1, -32, 6, -13, 46, 27, 13, -49, -39, 8, -24, 39, -25, -26, 26, -44, 37, -27, -50}

Returns: 0
{36, 8, -4, 23, -33, 36, -33, 35, -22, 45, -43, -29, 18, 49, 38, 42, -32, 19, 26, -47, -18, 39, -15, 10, -46, -15, 49, 15, 17, -39, -24, -7, -14, 14, -6, 27, -10, -40, -41, 45, 31}

{-20, 24, -34, -49, 19, 13, -25, 37, -15, -4, -12, 35, 46, 49, -3, -30, 15, -7, 49, -19, -37, 25, 21, -22, 3, -47, -36, 12, -2, -38, -21, -11, -26, -10, -14, -44, -7, 8, -11, 34, -27}

{44, -36, -38, 2, 23, 29, -19, -44, 19, 33, -6, -47, -43, 46, 37, -21, -32, -27, -24, -21, -35, -11, 37, 37, -9, 5, 7, 1, -47, -20, -3, 41, 1, 21, 0, 10, 28, 10, 22, -17, -5}

{-8, -46, -10, -45, 11, -44, 14, 9, 4, -19, 8, -5, -28, 49, -10, 35, -45, 21, 22, 38, -41, 6, -48, 20, 29, -48, 32, -31, -45, -10, -7, 33, -3, -29, 10, -24, 42, -5, 2, -49, 43}

Returns: 0
{9, -45, 1, -28, -44, -30, -38, -39, -35, 25, 35, -38, -18, 30, -22, 4, 6, 31, -1, -38, -48, 32, -20, -39, 33, -24, 25, -21, -23, -27, -10, 38, -26, -31, -7, 19, -41, -40}

{16, 14, 20, -35, 3, -36, -29, 20, 33, 45, -44, -4, -6, 47, -20, 10, 26, 27, 10, 44, 10, -34, -43, 17, -20, 34, -24, -2, 27, 15, -19, 13, -24, -44, 32, 34, 31, -43}

{-13, -38, -24, -43, 50, 44, 48, 24, -23, 48, 20, -46, 21, -9, -18, -43, -30, 36, 35, 32, -30, -19, -42, 16, 24, -13, -32, -31, -37, -42, 42, 45, -4, 49, -12, 14, -50, -24}

{44, 2, -24, 6, -44, -20, 42, -17, 19, 24, 48, -44, 7, 15, -25, 43, 26, -23, -37, -13, -45, -2, 9, -8, 7, 3, -40, 18, 47, -34, -7, -39, -11, 30, -37, -21, 5, -48}

Returns: 0
{38, -19, 7, -32, -45, 23, 1, -17, 6, -6, 42, -49, 42, -34, 14, -24, -38, -49, -42, -4, -49, 28, -36, 9, 3, 19, -48, -25, -21, -3, 23, -28, -3, -15, -8, -37, 3, -42, -34, 49, 20}

{-18, 6, 37, -9, 36, 17, -12, -2, 37, -38, 3, -41, -14, 34, 28, -24, -44, -32, -46, 8, -20, 35, 35, -34, 8, -32, -43, 7, -25, -43, -41, 30, 49, 33, 44, 2, 40, -28, -41, 21, 20}

{47, -28, 5, -22, 5, 1, -35, -17, 11, -38, -19, -2, 22, 13, 44, -9, 13, -38, -39, -1, 38, -47, -8, 4, -24, 2, -40, 39, -13, -47, 28, -38, 46, 20, 14, 20, 5, 42, -15, -14, 46}

{48, 14, 7, 25, -14, -2, 8, 33, -20, -29, 12, 21, -3, -4, 13, -30, -41, -44, -19, -8, 39, -18, -10, 47, -28, -38, 13, 40, 36, 40, 46, 46, 44, -1, 31, -26, -15, -12, -23, -14, -30}

Returns: 0
{-27, -24, -21, -36, -43, -42, -26, -26}

{20, 16, 23, 24, 35, 32, 22, 24}

{-31, -28, -25, -24, -35, -38, -30, -34}

{23, 19, 26, 15, 29, 29, 25, 30}

Returns: 0

next 9 are random parallel
{13, 9, 5, 9, 11, 9, 12, 2, 11}

{-22, -35, -26, -22, -15, -31, -29, -13, -13}

{14, 7, 4, 11, 15, 10, 9, 5, 13}

{-25, -29, -23, -28, -27, -34, -20, -22, -19}

Returns: 0
{-19, -9, -21, -13, -18, -7, -9, -11, -16, -12, -7, -11, -17, -7}

{36, 22, 34, 20, 42, 21, 19, 30, 34, 37, 26, 37, 23, 19}

{-15, -13, -19, -17, -12, -15, -13, -15, -18, -8, -15, -13, -21, -13}

{28, 30, 30, 28, 30, 37, 27, 38, 38, 29, 42, 41, 31, 31}

Returns: 0
{-2, -4, 5, -5, -1, -3, 0, 4}

{25, 31, 31, 35, 27, 27, 32, 39}

{-2, -4, 5, -5, -1, -3, 0, 4}

{33, 43, 35, 31, 31, 31, 28, 35}

Returns: 0
{33, 29, 31, 23, 37, 33, 22, 40, 45, 44, 23, 28, 33}

{33, 32, 33, 24, 43, 38, 29, 38, 40, 41, 19, 22, 32}

{41, 41, 23, 39, 21, 25, 26, 28, 41, 32, 27, 32, 25}

{41, 44, 25, 40, 27, 30, 33, 26, 36, 29, 23, 26, 24}

Returns: 0
{26, 41, 34, 35, 27, 20, 19, 38, 28, 32, 26, 35, 27, 20, 31, 33, 26, 44, 19}

{7, 7, 13, 8, 11, 8, 5, 13, 8, 13, 4, 5, 5, 4, 10, 4, 12, 15, 10}

{30, 29, 38, 19, 43, 28, 23, 34, 20, 28, 30, 27, 23, 28, 19, 45, 38, 40, 27}

{8, 4, 14, 4, 15, 10, 6, 12, 6, 12, 5, 3, 4, 6, 7, 7, 15, 14, 12}

Returns: 0
{-18, -17, -16, -21, -12, -17, -17, -20, -8, -12, -13}

{-3, 4, 2, 0, 3, -2, 1, -1, -4, -5, 5}

{-22, -19, -10, -25, -16, -19, -23, -18, -10, -18, -9}

{-3, 4, 2, 0, 3, -2, 1, -1, -4, -5, 5}

Returns: -1
{13, 7, 9, 8, 10, 10, 6, 6, 6, 9, 8, 10, 12, 5, 4, 11, 12, 4, 6, 8, 6, 13, 12, 2, 1, 7, 6}

{32, 34, 32, 29, 33, 34, 23, 34, 27, 19, 36, 42, 26, 36, 40, 31, 39, 37, 35, 41, 31, 34, 37, 28, 22, 28, 39}

{11, 5, 8, 10, 7, 11, 9, 5, 10, 11, 4, 6, 14, 6, 1, 14, 11, 1, 8, 7, 9, 12, 10, 4, 2, 10, 7}

{24, 26, 28, 37, 21, 38, 35, 30, 43, 27, 20, 26, 34, 40, 28, 43, 35, 25, 43, 37, 43, 30, 29, 36, 26, 40, 43}

Returns: 0
{-13, 32, 28, 26, -26, 31, 37}

{-26, 40, 44, 36, -9, -45, 11}

{-15, 34, 26, 28, -30, 33, 39}

{-26, 40, 44, 36, -9, -45, 11}

Returns: 0

next 2 are random parallel horizontal
{10, 13, -32, -2, -46, -33, 12, -46, 18, 36, -39}

{8, 20, 40, -10, 38, 14, 42, 13, -39, 26, 45}

{9, 14, -33, 1, -44, -32, 13, -47, 17, 34, -36}

{8, 20, 40, -10, 38, 14, 42, 13, -39, 26, 45}

Returns: 0
{-6, 40, 36, 34, -20, 45}

{-33, 32, 36, 28, -15, 3}

{-6, 40, 36, 34, -20, 45}

{-35, 34, 34, 30, -19, 5}

Returns: 0

next 4 are random parallel vertical
{17, 23, -26, 7, -36, -23, 21, -10, -40, 24, 43, -30}

{1, 10, 34, -19, 28, 4, 33, 0, 7, -45, 19, 36}

{17, 23, -26, 7, -36, -23, 21, -10, -40, 24, 43, -30}

{0, 11, 33, -16, 30, 5, 34, 2, 6, -46, 17, 39}

Returns: 0
{38, 42, -29, -28, -31, -15, -10, 8, -7, 43, -38, -2, -43, -8, -35, -33, -39, 24, -6, 12}

{-31, -39, -33, 14, -27, 21, -8, 32, -34, -7, -31, -23, -39, 26, 36, -18, 25, -19, 14, 25}

{38, 42, -29, -28, -31, -15, -10, 8, -7, 43, -38, -2, -43, -8, -35, -33, -39, 24, -6, 12}

{-28, -38, -35, 11, -30, 24, -5, 31, -32, -10, -29, -22, -42, 27, 37, -19, 23, -20, 15, 28}

Returns: 0
{-17, -35, -19, 3, -2, 38, -8, 20, 43, -11, -15, -18, 44, 11, 36, 15, -43, -33, 17, 30, 26, -37, -34}

{6, -13, -21, -5, 29, -28, -29, 6, -34, 10, 21, 10, -42, 10, 5, -20, 6, -35, -39, -48, -31, 24, 19}

{-17, -35, -19, 3, -2, 38, -8, 20, 43, -11, -15, -18, 44, 11, 36, 15, -43, -33, 17, 30, 26, -37, -34}

{8, -14, -19, -2, 30, -29, -30, 7, -36, 7, 17, 11, -40, 8, 2, -17, 4, -36, -36, -46, -28, 21, 18}

Returns: 0
{16, 1, 3, 11, 5, -10, -5}

{-15, 39, 2, 9, 5, 28, -16}

{16, 1, 3, 11, 5, -10, -5}

{29, -33, -4, 28, 35, -50, 37}

Returns: -1

next 8 are random vertical parallel symmetrically spaced
{32, -18, -14, 1, 45, 36, -27, 17}

{13, -39, 48, 22, 0, 23, -47, 46}

{32, -18, -14, 1, 45, 36, -27, 17}

{9, 35, 50, -39, 49, 15, 12, -17}

Returns: -1
{10, 14, -23, -34, -30, -19, -10, 2, -22, 3, -1}

{5, 44, -50, -3, -45, 35, -7, 15, 26, 46, -13}

{10, 14, -23, -34, -30, -19, -10, 2, -22, 3, -1}

{21, 32, -12, -20, 29, -44, -12, 49, 28, 3, 22}

Returns: -1
{-2, 27, 22, 11, -36, 26, -29, -28, -24, -1, 0, -13, 34}

{-21, 22, -46, -40, -28, 50, -32, 4, -3, 8, 42, -8, 43}

{-2, 27, 22, 11, -36, 26, -29, -28, -24, -1, 0, -13, 34}

{9, -34, 17, -20, -20, 9, -34, -24, -23, -39, -40, -19, 17}

Returns: -1
{-9, -7, 8, 23, -22, -15, -31, 6, 2, 29, 25, 10, 14, -13, 38, 47, 31}

{-34, -27, -44, -8, 2, 26, 33, 25, -8, 44, -16, -7, -34, 48, 29, -27, 9}

{-9, -7, 8, 23, -22, -15, -31, 6, 2, 29, 25, 10, 14, -13, 38, 47, 31}

{-38, -48, -10, -19, 50, -39, 11, -2, -26, 46, -36, 40, -49, -23, -6, -35, -1}

Returns: -1
{42, 25, -7, -23, -11, -28, 21, -21, 37, 33, 41, -19, -27, 35}

{50, -25, -40, 35, -31, -33, 15, -36, 45, -30, -25, 41, 5, -31}

{42, 25, -7, -23, -11, -28, 21, -21, 37, 33, 41, -19, -27, 35}

{27, 42, 41, -28, 11, 33, 22, 10, 7, -28, 22, -19, -38, -49}

Returns: -1
{2, -9, 23, 9, 8, 14, 1, -32, 5, -1, 34, 11, 35, 19, 32, -22, -13, -25, 42, -7, -4, -24, 17}

{19, -31, -2, 34, 8, 29, -24, -27, -36, -38, 19, 38, -25, -2, 40, -24, 2, -23, 36, 0, -4, 41, -8}

{2, -9, 23, 9, 8, 14, 1, -32, 5, -1, 34, 11, 35, 19, 32, -22, -13, -25, 42, -7, -4, -24, 17}

{6, -16, 27, 22, 39, -40, 49, -1, 2, -28, -21, -5, 24, -18, 23, 16, -27, 33, 46, 15, 11, -1, 8}

Returns: -1
{6, -40, -45, 11, -1, 17, -31, 27, -35, -44, 10, -17, -33, -8, -24, -28, -27, 9, 25, 5, -23, 20, -43, 22, -38, -47, 15, -10, 13, 26, 29, -29}

{46, -16, 26, 41, 24, -40, 5, 29, -45, 28, -14, -33, 33, -38, 19, -35, -27, -39, -23, 49, -34, -41, -25, -41, 42, -33, 16, 17, -47, -14, 1, 23}

{6, -40, -45, 11, -1, 17, -31, 27, -35, -44, 10, -17, -33, -8, -24, -28, -27, 9, 25, 5, -23, 20, -43, 22, -38, -47, 15, -10, 13, 26, 29, -29}

{33, 3, 22, -2, -21, -11, 22, -27, 42, -1, 5, -30, 23, -5, -8, 5, -50, -19, 42, -20, -1, 32, -30, 42, 34, 0, 2, -8, -34, -44, 8, -30}

Returns: -1
{-20, -24, 1, 19, 50, 4, -17}

{-9, -2, -1, -1, 8, 1, -1}

{1, -3, -8, -2, 44, -2, -14}

{-2, 5, -4, -8, 6, -1, 0}

Returns: -1

next 3 are random symetrically spaced parallel
{27, 13, -25, -9, 20, -20}

{4, 1, -1, 3, -1, 3}

{29, 1, -23, -19, 18, -32}

{5, -5, 0, -2, -2, -3}

Returns: -1
{-4, -4, 9, 32, 11, -1, -28, 28, -16, -4, -1, 35, -24, 2, -17, -1, 0}

{-1, -8, 7, 1, -6, 1, 1, 6, -1, -3, -4, 9, 0, 1, 3, -6, 0}

{0, 7, -5, 34, 25, 2, -31, 31, -20, -2, 9, 24, -27, 1, -25, 15, -4}

{3, 3, -7, 3, 8, 4, -2, 9, -5, -1, 6, -2, -3, 0, -5, 10, -4}

Returns: -1
{-15, 39, 2, 9, 5, 28, -16}

{16, 1, 3, 11, 5, -10, -5}

{29, -33, -4, 28, 35, -50, 37}

{16, 1, 3, 11, 5, -10, -5}

Returns: -1

next 8 are horizontal parallel symetrically spaced
{13, -39, 48, 22, 0, 23, -47, 46}

{32, -18, -14, 1, 45, 36, -27, 17}

{9, 35, 50, -39, 49, 15, 12, -17}

{32, -18, -14, 1, 45, 36, -27, 17}

Returns: -1
{5, 44, -50, -3, -45, 35, 43, 15, 26, -12, 46, -32, -13}

{30, 34, -3, -14, -10, 1, 10, 22, 15, 5, 23, -2, 19}

{21, 32, -12, -20, 29, -44, -41, 49, 28, 3, 3, -18, 22}

{30, 34, -3, -14, -10, 1, 10, 22, 15, 5, 23, -2, 19}

Returns: -1
{-20, 17, 17, -8, 36, -50, -23, -39, -20, -40, -24, -21, -34}

{-32, 28, 39, 40, -9, 5, -18, 25, -29, -15, 19, 42, -30}

{-42, -18, 4, -19, -47, 39, 43, 4, 50, 11, 8, 9, -7}

{-32, 28, 39, 40, -9, 5, -18, 25, -29, -15, 19, 42, -30}

Returns: -1
{-23, 11, -34, -23, -23, 12, -48, 15, -14, -38, 11, 20, -44, -43, -21, -26, 22, 18, 21, 2, -7, 42, 29, -35, 50, -28}

{13, 19, 24, -27, 18, 11, 27, -12, 22, 5, -39, 32, -28, -17, -23, -15, 14, -26, 23, -18, -22, 35, -31, -9, 8, -36}

{-27, -34, 25, -34, 26, 46, 29, -8, 31, -8, 15, -12, -10, 33, -11, -40, 24, -25, -16, 50, 40, 48, 2, -27, 20, 40}

{13, 19, 24, -27, 18, 11, 27, -12, 22, 5, -39, 32, -28, -17, -23, -15, 14, -26, 23, -18, -22, 35, -31, -9, 8, -36}

Returns: -1
{10, -28, 6, -25, 7, -26, -27, -44, -30, 34, 19, -40, -8, 38, -43, 41, 29, -49, -2, 29, -19, 13, -31, 22}

{-16, 38, 43, -23, 35, 31, -21, -30, 37, -25, 6, -7, 4, 10, 39, 21, -29, 30, -17, 44, -24, 8, 23, -9}

{45, 47, -24, 24, 14, 41, -30, 37, 2, 22, -21, 41, 8, -4, -23, 29, -40, -33, 27, 14, -8, -9, 19, -19}

{-16, 38, 43, -23, 35, 31, -21, -30, 37, -25, 6, -7, 4, 10, 39, 21, -29, 30, -17, 44, -24, 8, 23, -9}

Returns: -1
{-42, 21, 25, -12, 45, -26, -10, -11, -8, -43, 3, -11, 27, -19, -30, -11, 15, -31, -31, 4, -39, 27, -20, 16, 22, -31, 25, 44, -35, 42, -48, -36, 46, -21, -42, -45, -34, 0, 34, 10, -15, 8}

{-13, -4, 30, 3, -27, 2, 25, 11, -30, -8, -44, -2, 17, -36, -17, -14, 32, -7, 26, -12, -34, 8, -18, 21, 34, 4, -3, -31, -28, -21, -20, -35, 20, 7, -42, -6, -23, 13, 18, -40, 10, 24}

{-11, 29, 33, -4, -15, -35, -23, -30, 5, -31, 44, -42, -20, 5, 1, -25, -25, 38, -47, 38, 26, 24, 26, -33, 17, -10, -28, 10, -41, 24, -4, 31, -23, -8, 39, -37, 42, -41, -30, -9, 7, 23}

{-13, -4, 30, 3, -27, 2, 25, 11, -30, -8, -44, -2, 17, -36, -17, -14, 32, -7, 26, -12, -34, 8, -18, 21, 34, 4, -3, -31, -28, -21, -20, -35, 20, 7, -42, -6, -23, 13, 18, -40, 10, 24}

Returns: -1
{-12, -25, -38, -29, -7, -2, 11, -16, 0, 0, -50, 50, 38, -41, 8, 28, -36, -2, -1, 2, -5, 37, 24, -26, 17, -40, 15, -12, -43, -29, 39, 28, 38, -28, 14, 50, 35, -15, 20, 3, -43}

{-4, 32, 9, -9, 22, 47, -22, -2, 7, 5, 24, -18, 35, -23, 4, -30, -10, 13, 43, 41, 3, 21, -12, -21, 50, -5, 25, -15, -1, 10, 29, 42, 30, 14, 11, 16, 15, 6, 38, 17, -27}

{-35, -31, -10, -42, 1, -43, -22, 44, -16, -29, 5, 24, -16, 20, -33, -17, -45, 17, 34, 9, 12, 24, -31, -9, 1, 47, -43, 50, 12, -35, -40, -39, -40, -47, 43, 21, -47, -13, -22, 11, -26}

{-4, 32, 9, -9, 22, 47, -22, -2, 7, 5, 24, -18, 35, -23, 4, -30, -10, 13, 43, 41, 3, 21, -12, -21, 50, -5, 25, -15, -1, 10, 29, 42, 30, 14, 11, 16, 15, 6, 38, 17, -27}

Returns: -1
{0, 1, 0, 0 }

{0, 0, 0, 1 }

{0, 1, 1, 1 }

{1, 1, 0, 1 }

Returns: 1
{10, -35, -8, 7, -5, -8, -9, -50, -17, -18, -17, -26, -5, 23, 18, -7, -8, -6, -8, -12, 22, -7, 17, -48, -6, -16, -12, -14, 13, 30, 11, 17, -3, -5, -27, -30 }

{-27, -25, -17, -26, -3, -19, -20, -33, -22, -21, -23, -38, -2, -32, -27, -8, -2, -5, -21, -7, -15, -15, -5, -27, 0, -19, -25, 1, -22, -11, -13, -38, -1, -6, -17, -32 }

{16, -32, -11, 11, -3, -9, -8, -45, -16, -15, -19, -29, -2, 20, 24, -1, 4, -7, -5, -13, 16, -9, 29, -43, 2, -17, -15, -15, 17, 24, 23, 14, -7, -3, -24, -33 }

{-35, -23, -26, -32, -3, -21, -18, -30, -20, -15, -27, -42, -5, -28, -35, 2, -5, -6, -15, -7, -13, -19, -9, -24, -12, -21, -34, 1, -28, -9, -17, -34, -9, 0, -15, -36 }

Returns: 1
{0, 0, 0, 1 }

{0, 0, 1, 0 }

{0, 1, 1, 1 }

{1, 0, 1, 1 }

Returns: 1
{0, 0, 1, 0 }

{0, 0, 0, 1 }

{0, 1, 1, 1 }

{1, 0, 1, 1 }

Returns: 1
{0, 1, 2, 0, 0, 0, 0, 0, 3 }

{0, 0, 0, 1, 2, 0, 0, 3, 0 }

{0, 1, 2, 1, 1, 1, 1, 1, 3 }

{1, 1, 1, 1, 2, 0, 1, 3, 1 }

Returns: 1
{1, 2, 4 }

{0, 0, 0 }

{0, 0, 0 }

{2, 4, 8 }

Returns: 0
{0, -1, -2, 3 }

{0, 0, 0, 0 }

{0, -1, -2, 3 }

{1, 1, 1, 1 }

Returns: 0
{0, 0, 0, 0, 0 }

{0, 1, 3, 5, 6 }

{1, 2, 3, 4, 5 }

{0, 1, 3, 5, 6 }

Returns: -1
{-50, -50 }

{50, -50 }

{50, 50 }

{49, -49 }

Returns: 1
{-1, 3, -2, -6 }

{5, 5, 5, 4 }

{1, 3, -2, 7 }

{5, 4, 4, 4 }

Returns: 1

Statistics

Problem Statement for "CentersOfSymmetry"

Problem Statement

Definition

Notes

Constraints

Examples