TopCoder Statistics - Problem Statement

Problem Statement

The "taxicab distance" between two points in space is defined to be the distance that would need to be travelled to get from one to the other using segments that are parallel to the axes. This is generally longer than the (straight-line) distance between the two points.

We know the taxicab distance between two points. We want to know the maximum straight-line distance between them if they lie in the rectangular region { (x,y) | 0<=x<=maxX, 0<=y<=maxY }. Create a class Taxi that contains a method maxDis that is given maxX, maxY, and taxiDis and that returns the largest possible straight-line distance between the two points. If no two points within the given region have the given taxicab distance, return -1.0.

Definition

Class:: Taxi
Method:: maxDis
Parameters:: int, int, int
Returns:: double
Method signature:: double maxDis(int maxX, int maxY, int taxiDis)
(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

maxX and maxY are both between 1 and 1,000,000, inclusive.
taxiDis is between 0 and 1,000,000, inclusive.

Examples

10

3

3

Returns: 3.0

The two points could lie in a straight line parallel to one of the axes. Then the straight-line distance would be the same as the taxicab distance.
10

3

24

Returns: -1.0

No two points with 0<=x<=10, 0<=y<=3, have a taxicab distance between them that is as big as 24.
7

10

13

Returns: 10.44030650891055

(5,0) and (2,10) are two points in this region whose taxicab distance is |2-5| + |10-0| = 13 and whose straight-line distance is sqrt(3*3 + 10*10) = sqrt(109).
5

5

5

Returns: 5.0
4

4

7

Returns: 5.0
19

13

0

Returns: 0.0
1

20

21

Returns: 20.024984394500787
48

1

7

Returns: 7.0
12

12

17

Returns: 13.0
4

12

17

Returns: -1.0
4

12

16

Returns: 12.649110640673518
976421

976421

1000000

Returns: 976705.6560100387
1000000

22

24

Returns: 24.0
909

3292

4044

Returns: 3376.798483771278
7968

9804

5140

Returns: 5140.0
276

6051

3892

Returns: 3892.0
3691

1295

1245

Returns: 1245.0
5679

7879

4387

Returns: 4387.0
5256

7198

4869

Returns: 4869.0
5557

7452

2405

Returns: 2405.0
2982

4845

3820

Returns: 3820.0
8648

4609

6189

Returns: 6189.0
5042

1084

336

Returns: 336.0
1003

3822

2088

Returns: 2088.0
9055

2401

3352

Returns: 3352.0
9777

9637

12790

Returns: 10230.733013816753
2752

2185

3273

Returns: 2800.8828965167395
7268

255

3577

Returns: 3577.0
976421

976421

1000000

Returns: 976705.6560100387
999990

10

27

Returns: 27.0
10

200

50

Returns: 50.0
4

4

8

Returns: 5.656854249492381
1000000

1000000

999999

Returns: 999999.0
999990

10

999990

Returns: 999990.0
10

3

24

Returns: -1.0
10

3

7

Returns: 7.0
7

10

13

Returns: 10.44030650891055
976421

976422

1000000

Returns: 976706.6315777733
3

10

4

Returns: 4.0
10

10

1

Returns: 1.0
10

3

2

Returns: 2.0
6

1

5

Returns: 5.0
10

9

6

Returns: 6.0
3

4

7

Returns: 5.0
10

3

3

Returns: 3.0
4

4

3

Returns: 3.0
7

2

5

Returns: 5.0
490000

490000

1000000

Returns: -1.0
100

100

5

Returns: 5.0
499999

499999

999998

Returns: 707105.3669729851
1

7

5

Returns: 5.0
100

150

4

Returns: 4.0
5

10

13

Returns: 10.44030650891055
2

2

4

Returns: 2.8284271247461903
1000000

1000000

888888

Returns: 888888.0
1

1

2

Returns: 1.4142135623730951
3

3

6

Returns: 4.242640687119285
10

7

13

Returns: 10.44030650891055
4

2

3

Returns: 3.0
5

5

10

Returns: 7.0710678118654755
1

6

5

Returns: 5.0

Statistics

Problem Statement for "Taxi"

Problem Statement

Definition

Notes

Constraints

Examples