TopCoder Statistics - Problem Statement

Problem Statement

"Place popcorn bag into microwave and start at full power. After at least 3 kernels have popped, listen until more than T seconds have passed without popping. Remove bag from microwave oven."

We plan to put these instructions on our popcorn bag, with the T replaced by a number. We want to choose T so that at least 75% of the kernels will have popped if the user follows the instructions. A popcorn sample has been tested and we have recorded the time that it took for each kernel to pop. Create a class Popcorn that contains the method quietTime that takes the popTimes of the kernels in the sample as input and returns the smallest T that will yield at least 75%.

Definition

Class:: Popcorn
Method:: quietTime
Parameters:: int[]
Returns:: int
Method signature:: int quietTime(int[] popTimes)
(be sure your method is public)

Notes

popTimes are already sorted into non-descending order.
If exactly T seconds pass between pops, the user will continue popping.

Constraints

popTimes contains between 3 and 50 elements, inclusive.
Each element in popTimes is between 1 and 10,000, inclusive.
popTimes is in non-descending order.

Examples

{3,4,9,12,13,14,14,18,19,25,27}

Returns: 4

The intervals after the 3rd kernel has popped are 3,1,1,0,4,1,6,2. If T were 3, the user would stop at time 17, popping 7 of the 11 kernels which is less than 75%. So make T be 4. The user will stop at time 23, popping 9 of the 11 kernels.
{2,5,19}

Returns: 0

The user will stop at time 19, yielding 3 of 3.
{2,5,19,29,30}

Returns: 10
{2,5,19,29,30,42}

Returns: 10
{1000,5000,5000,5001}

Returns: 0
{1000,5000,5000,5001,5002}

Returns: 1
{1000,5000,5000,5001,5003}

Returns: 1
{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}

Returns: 0
{1,1,10000,10000,10000}

Returns: 0
{3,5,12,12,15}

Returns: 0
{1,1,10000,10000,10000,10000}

Returns: 0
{1,1,1,10000,10000}

Returns: 9999
{1,2,100,130,132,135,300,301}

Returns: 30
{1,2,100,130,132,135,300,301,302}

Returns: 165
{100,120,130,138,138,142,152,153}

Returns: 8
{ 1, 2, 3, 4, 5, 6 }

Returns: 1
{ 3, 4, 5, 15 }

Returns: 0
{ 1, 5, 6, 8, 9 }

Returns: 2
{ 1, 2, 3, 7, 15 }

Returns: 4
{ 1, 2, 3, 30, 31, 32, 33, 34, 35 }

Returns: 27
{ 1, 2, 3, 4, 19, 20, 21, 22, 23, 24, 25 }

Returns: 15
{ 1, 1, 1, 5, 5 }

Returns: 4
{ 1, 2, 3, 4, 5, 10, 18 }

Returns: 5
{ 3, 5, 9 }

Returns: 0
{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 18 }

Returns: 1
{ 1, 1, 1, 1, 1, 1, 5, 5, 5 }

Returns: 4
{ 1, 1, 1, 2 }

Returns: 0
{ 100, 120, 130, 138, 138, 142, 152, 153 }

Returns: 8
{ 1, 2, 3, 7, 8, 9, 10, 11, 12 }

Returns: 4
{ 3, 5, 8, 9 }

Returns: 0
{ 1, 2, 3, 15 }

Returns: 0
{ 12, 15, 15, 9394 }

Returns: 0
{ 2, 5, 19, 29, 30 }

Returns: 10
{ 1, 1, 1 }

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

Returns: 0

Statistics

Problem Statement for "Popcorn"

Problem Statement

Definition

Notes

Constraints

Examples