TopCoder Statistics - Problem Statement

Problem Statement

When data is collected at regular intervals, trends in the data are sometimes easier to see by looking at a moving average. The moving average of length k at a particular time is the average of the k most recently collected data values. So at time t it is the average of the data reported at times t,t-1,...,t-(k-1). The moving average is not defined at time t unless we have data for the preceding k-1 times.

We have a sequence of data values and want to look at the moving averages of length k of those values. Specifically, we want to know how much the largest moving average exceeds the smallest moving average.

Create a class MovingAvg that contains a method difference that is given k and double[] data. It returns the difference between the largest and smallest moving average of length k in data.

Definition

Class:: MovingAvg
Method:: difference
Parameters:: int, double[]
Returns:: double
Method signature:: double difference(int k, double[] data)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

k will be between 1 and 10, inclusive.
data will contain between k and 50 elements, inclusive.
Each element of data will be between 0.0 and 1000.0 inclusive.

Examples

2

{3,8,9,15}

Returns: 6.5

The moving averages are (3+8)/2, (8+9)/2, and (9+15)/2 which are 5.5, 8.5, and 12.0. So the difference between the largest and smallest is 12.0 - 5.5 = 6.5
3

{17,6.2,19,3.4}

Returns: 4.533333333333335

The moving averages are (17+6.2+19)/3 and (6.2+19+3.4)/3 which are 14.0666666... and 9.533333...
3

{6,2.5,3.5}

Returns: 0.0

There is only 1 moving average of length 3, so the smallest and biggest moving average are the same.
2

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

Returns: 8.0
5

{6,2,7,3,4,9,2,7,3,4,9,4,9,2,7,3,4,9}

Returns: 1.7999999999999998
10

{500,500,500,500,500,500,500,500,500,500}

Returns: 0.0
10

{600,500,500,500,500,500,500,500,500,500}

Returns: 0.0
10

{500,500,500,500,500,500,500,500,500,600}

Returns: 0.0
10

{500,500,500,500,500,500,500,500,500,500,600}

Returns: 10.0
1

{3,9,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8}

Returns: 6.0
1

{3,9,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,2}

Returns: 7.0
3

{.01,.02,.03,.001,.001}

Returns: 0.009333333333333334
5

{0,0.0,0,0.0,0.0,0.000001}

Returns: 2.0E-7
1

{15.492}

Returns: 0.0
2

{0,1000,0,0,1000,1000,0}

Returns: 1000.0
9

{17.0, 6.2, 19.0, 3.4, 4.4, 5.5, 6.6, 0.0, 0.1, 17.0 }

Returns: 0.0
1

{2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 }

Returns: 7.0
1

{10.0 }

Returns: 0.0
1

{1.0, 3.0, 2.0 }

Returns: 2.0
2

{3.0, 8.0, 9.0, 15.0 }

Returns: 6.5
1

{6.0, 2.5, 3.5 }

Returns: 3.5
1

{5.0, 6.0, 7.0, 0.0, 3.0 }

Returns: 7.0
1

{1.0 }

Returns: 0.0
2

{1.0, 2.0, 5.0, 87.0, 4.0, 4.0, 4.0, 987.0, 1.0, 1.0, 1.0 }

Returns: 494.5
3

{1.0, 1.0, 1.0, 12.0, 12.0, 12.0, 1.0, 1.0, 1.0 }

Returns: 11.0
1

{1.0, 2.0, 5.0, 2.0, 1.0 }

Returns: 4.0
9

{17.0, 6.2, 19.0, 3.4, 4.4, 5.5, 6.6, 0.0, 0.1, 17.0 }

Returns: 0.0
1

{2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 }

Returns: 7.0
1

{10.0 }

Returns: 0.0
1

{1.0, 3.0, 2.0 }

Returns: 2.0
2

{3.0, 8.0, 9.0, 15.0 }

Returns: 6.5
1

{6.0, 2.5, 3.5 }

Returns: 3.5
1

{5.0, 6.0, 7.0, 0.0, 3.0 }

Returns: 7.0
1

{1.0 }

Returns: 0.0
2

{1.0, 2.0, 5.0, 87.0, 4.0, 4.0, 4.0, 987.0, 1.0, 1.0, 1.0 }

Returns: 494.5
3

{1.0, 1.0, 1.0, 12.0, 12.0, 12.0, 1.0, 1.0, 1.0 }

Returns: 11.0
1

{1.0, 2.0, 5.0, 2.0, 1.0 }

Returns: 4.0

Statistics

Problem Statement for "MovingAvg"

Problem Statement

Definition

Notes

Constraints

Examples