Statistics

Problem Statement for "CheckPolygon"

Problem Statement

A simple polygon is a polygon with the following properties:

  • the length of each side is positive
  • no two consecutive sides are parallel
  • no two non-consecutive sides share a common point

You are given two int[]s X and Y, each with N elements. Find out whether there is a simple polygon whose vertices (in the order in which they lie on its boundary) are the points (X[0], Y[0]), (X[1], Y[1]), ... (X[N-1], Y[N-1]).

If the given points are the vertices of a simple polygon, calculate its area A and return a String that contains the decimal representation of A with one digit after the decimal point. If the given points are not the vertices of a simple polygon, return the String "Not simple" (quotes for clarity).

Definition

Class:
CheckPolygon
Method:
check
Parameters:
int[], int[]
Returns:
String
Method signature:
String check(int[] X, int[] Y)
(be sure your method is public)

Notes

  • The correct return value is always uniquely defined by problem statement. In particular, if the points represent a valid polygon, its area is always a rational number with at most one decimal digit.

Constraints

  • X will contain between 3 and 50 elements, inclusive.
  • Each element of X will be between -1,000,000,000 and 1,000,000,000, inclusive.
  • X and Y will contain same number of elements.
  • Each element of Y will be between -1,000,000,000 and 1,000,000,000, inclusive.

Examples

  1. {0,0,1}

    {0,1,0}

    Returns: "0.5"

    These three points are the vertices of a small triangle.

  2. {0,1,2,0,2}

    {0,2,0,1,1}

    Returns: "Not simple"

    These points, in the given order, are not the vertices of a simple polygon. The closed polyline that passes through these five points intersets itself five times.

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

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

    Returns: "2.0"

    Note that you must return the string "2.0". The printed number must have exactly one decimal place, even if that digit is zero. The string "2" is not a correct answer.

  4. {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    {1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000,1000000000}

    Returns: "Not simple"

  5. {0,1,1}

    {-1000000000,1000000000,999999999}

    Returns: "0.5"

  6. {-1000000000,0,1000000000}

    {-1000000000,0,1000000000}

    Returns: "Not simple"

  7. {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

    {0,20000000,40000000,60000000,80000000,100000000,120000000,140000000,160000000,180000000,200000000,220000000,240000000,260000000,280000000,300000000,320000000,340000000,360000000,380000000,400000000,420000000,440000000,460000000,480000000,500000000,520000000,540000000,560000000,580000000,600000000,620000000,640000000,660000000,680000000,700000000,720000000,740000000,760000000,780000000,800000000,820000000,840000000,860000000,880000000,900000000,920000000,940000000,960000000,980000000}

    Returns: "Not simple"

  8. {-1000000000,-1000000000,-999999999,-999999999,-999999998,-999999998,-999999997,-999999997,-999999996,-999999996,-999999995,-999999995,-999999994,-999999994,-999999993,-999999993,-999999992,-999999992,-999999991,-999999991,-999999990,-999999990}

    {-1000000000,-999999998,-999999998,-999999999,-999999999,-999999998,-999999998,-999999999,-999999999,-999999998,-999999998,-999999999,-999999999,-999999998,-999999998,-999999999,-999999999,-999999998,-999999998,-999999999,-999999999,-1000000000}

    Returns: "15.0"

  9. {-1000000000,-500000000,0,500000000,1000000000}

    {-1000000000,1000000000,-1000000000,1000000000,-1000000000}

    Returns: "Not simple"

  10. {-1000000000,-500000000,0,500000000,1000000000}

    {1000000000,-1000000000,999999999,-1000000000,1000000000}

    Returns: "2000000000500000000.0"

  11. {-1000000000,1000000000,1000000000,-1000000000}

    {1000000000,-1000000000,1000000000,-1000000000}

    Returns: "Not simple"

  12. {-500000000,-500000000,-499999999,-499999999,-500000001,-500000001,-499999998,-499999998,-500000002,-500000002,-499999997,-499999997,-500000003,-500000003,-499999996,-499999996,-500000004,-500000004,-499999995,-499999995,-500000005,-500000005,-499999994,-499999994,-500000006,-500000006,-499999993,-499999993,-500000007,-500000007,-499999992,-499999992,-500000008,-500000008,-499999991,-499999991,-500000009,-500000009,-499999990,-499999990,-500000010}

    {-500000000,-499999999,-499999999,-500000001,-500000001,-499999998,-499999998,-500000002,-500000002,-499999997,-499999997,-500000003,-500000003,-499999996,-499999996,-500000004,-500000004,-499999995,-499999995,-500000005,-500000005,-499999994,-499999994,-500000006,-500000006,-499999993,-499999993,-500000007,-500000007,-499999992,-499999992,-500000008,-500000008,-499999991,-499999991,-500000009,-500000009,-499999990,-499999990,-500000010,-500000010}

    Returns: "Not simple"

  13. {0,52631578,105263156,157894734,210526312,263157890,315789468,368421046,421052624,473684202,526315780,578947358,631578936,684210514,736842092,789473670,842105248,894736826,947368404,999999982,999999982,947368404,894736826,842105248,789473670,736842092,684210514,631578936,578947358,526315780,473684202,421052624,368421046,315789468,263157890,210526312,157894734,105263156,52631578,0}

    {-999999999,1000000000,-999999999,1000000000,-999999999,1000000000,-999999999,1000000000,-999999999,1000000000,-999999999,1000000000,-999999999,1000000000,-999999999,1000000000,-999999999,1000000000,-999999999,1000000000,999999999,-1000000000,999999999,-1000000000,999999999,-1000000000,999999999,-1000000000,999999999,-1000000000,999999999,-1000000000,999999999,-1000000000,999999999,-1000000000,999999999,-1000000000,999999999,-1000000000}

    Returns: "999999982.0"

  14. {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1}

    {0,13,25,36,46,55,63,70,76,81,85,88,90,89,87,84,80,75,69,62,54,45,35,24,12,0,-12,-24,-35,-45,-54,-62,-69,-75,-80,-84,-87,-89,-90,-88,-85,-81,-76,-70,-63,-55,-46,-36,-25,-13}

    Returns: "2900.0"

  15. {0, 100000, 100000, 0}

    {0, 0, 100000, 100000}

    Returns: "10000000000.0"

  16. {0, 1, 1, 0, -1, -1}

    {0, 0, 1, 0, 0, -1}

    Returns: "Not simple"

  17. {-999997458,-999997458,-999997460,999997460}

    {-999997458,-999997458,999997460,999997460}

    Returns: "Not simple"

  18. {-999993690,-999993688,-999993688,999993690}

    {-999993690,999993690,999993690,999993690}

    Returns: "Not simple"

  19. {-999995580,-999995580,999995580,999995580}

    {-999995580,999995580,999995578,999995578}

    Returns: "Not simple"

  20. {-999997183,-999997183,-999997183,999997183}

    {-999997183,1,999997183,999997183}

    Returns: "Not simple"

  21. {-999994662,-999994662,0,999994662}

    {-999994662,999994662,999994662,999994662}

    Returns: "Not simple"

  22. {-999988868,-999988868,0,999988868}

    {-999988868,999988868,0,999988868}

    Returns: "Not simple"

  23. {0,0,999997030,1,0,-999997030}

    {0,99,1,0,-1,-1}

    Returns: "49999851501.0"

  24. {0,99,1,0,-1,-1}

    {0,0,999997030,1,0,-999997030}

    Returns: "49999851501.0"

  25. {0,0,999988078,1,0,-999988078}

    {-1,99,1,0,0,-1}

    Returns: "Not simple"

  26. {-1,99,1,0,0,-1}

    {0,0,999988078,1,0,-999988078}

    Returns: "Not simple"

  27. {0,0,999995706,0,-1,-999995706}

    {-1,99,1,0,0,-1}

    Returns: "Not simple"

  28. {-1,99,1,0,0,-1}

    {0,0,999995706,0,-1,-999995706}

    Returns: "Not simple"

  29. {2,6,999996163,4,9,-999996163}

    {3,7,1,5,9,-1}

    Returns: "Not simple"

  30. {3,7,1,5,9,-1}

    {2,6,999996163,4,9,-999996163}

    Returns: "Not simple"

  31. {2,4,999998619,6,9,-999998619}

    {3,5,1,7,9,-1}

    Returns: "3999994466.0"

  32. {3,5,1,7,9,-1}

    {2,4,999998619,6,9,-999998619}

    Returns: "3999994466.0"

  33. {0, 1, 2 }

    {0, 1, 0 }

    Returns: "1.0"

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