TopCoder Statistics - Problem Statement

Problem Statement

A triple (x, y, z) is called an arithmetic progression if the equality y - x = z - y holds.

You are given three ints a, b and c. Your goal is to change the triple (a, b, c) into an arithmetic progression. You are only allowed to change one of the three numbers. The change must proceed as follows: First, you choose a non-negative real (not necessarily integer) number r. Then, you either add r to one of the three given numbers, or you subtract r from one of them. Return the minimum value of r which allows you to create an arithmetic progression.

Definition

Class:: TheArithmeticProgression
Method:: minimumChange
Parameters:: int, int, int
Returns:: double
Method signature:: double minimumChange(int a, int b, int c)
(be sure your method is public)

Constraints

a will be between 0 and 1000, inclusive.
b will be between 0 and 1000, inclusive.
c will be between 0 and 1000, inclusive.

Examples

0

1

2

Returns: 0.0

The triple (0, 1, 2) is an arithmetic progression. Thus, you can choose r = 0.0 and add or subtract it from any of the given numbers without changing the triple.
0

2

1

Returns: 1.5

Note that while (0, 1, 2) is an arithmetic progression, you cannot rearrange the numbers within the triple. You can choose r = 1.5 and subtract it from b, obtaining the triple (0, 0.5, 1).
3

2

1

Returns: 0.0
4

4

8

Returns: 2.0
1000

0

0

Returns: 500.0
1000

1000

1000

Returns: 0.0
0

0

0

Returns: 0.0
0

1000

0

Returns: 1000.0
1000

0

1000

Returns: 1000.0
1000

0

0

Returns: 500.0
6

7

8

Returns: 0.0
125

882

114

Returns: 762.5
662

663

5

Returns: 329.5
999

122

679

Returns: 717.0
722

1000

900

Returns: 189.0
722

900

1000

Returns: 39.0
60

90

121

Returns: 0.5
500

301

901

Returns: 399.5
814

502

699

Returns: 254.5
10

1

2

Returns: 5.0
1

3

1

Returns: 2.0
1

2

5

Returns: 1.0
1

5

10

Returns: 0.5
0

1

0

Returns: 1.0
3

5

6

Returns: 0.5
1

2

1

Returns: 1.0
2

4

7

Returns: 0.5
3

1

0

Returns: 0.5
3

5

3

Returns: 2.0
1

2

100

Returns: 48.5
50

100

250

Returns: 50.0
1

4

10

Returns: 1.5
2

2

3

Returns: 0.5
0

0

2

Returns: 1.0
8

1

6

Returns: 6.0
17

10

14

Returns: 5.5
100

1

2

Returns: 50.0
0

0

1000

Returns: 500.0
4

2

1

Returns: 0.5
1

0

1

Returns: 1.0
1

2

2

Returns: 0.5
10

1

10

Returns: 9.0
1

1

3

Returns: 1.0
2

5

2

Returns: 3.0
5

6

8

Returns: 0.5
1

5

6

Returns: 1.5
1

2

4

Returns: 0.5
1

5

8

Returns: 0.5
0

2

0

Returns: 2.0
500

1

2

Returns: 250.0
9

10

4

Returns: 3.5
2

1

3

Returns: 1.5
4

10

30

Returns: 7.0
0

5

100

Returns: 45.0
1

0

2

Returns: 1.5
5

4

2

Returns: 0.5
3

2

2

Returns: 0.5
2

5

5

Returns: 1.5
2

0

1

Returns: 1.5
0

10

100

Returns: 40.0
1

2

8

Returns: 2.5

Statistics

Problem Statement for "TheArithmeticProgression"

Problem Statement

Definition

Constraints

Examples