ConnectionPoint | Topcoder Archive

Problem Statement

You want to estimate the number of cars that are in range of a particular wireless connection point. All cars are described by their distances to the connection point and by their velocities. At time 0 all cars move towards the connection point, though they will all eventually pass and move away from it. Given radius, the maximum possible distance at which a connection is possible, return the maximal possible number of cars that will be in range at once.

Definition

Class:: ConnectionPoint
Method:: maximalConnections
Parameters:: int[], int[], int
Returns:: int
Method signature:: int maximalConnections(int[] position, int[] speed, int radius)
(be sure your method is public)

Notes

A device can connect to the connection point if its distance is exactly equal to radius.

Constraints

position and speed will contain the same number of elements.
position and speed will contain between 0 and 50 elements, inclusive.
All elements of position will be between 0 and 1000, inclusive.
All elements of speed will be between 1 and 1000, inclusive.
radius will be between 1 and 1000, inclusive.

Examples

```
{100, 20, 50}
```
```
{1, 10, 2}
```
```
10
```
```
Returns: 1
```
Car 0 will be in range from time 90 to 110. Car 1 will be in range from time 1 to 3. Car 2 will be in range from time 20 to 30. Clearly, no more than one car will ever be in range.
```
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
```
```
{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3}
```
```
2
```
```
Returns: 6
```
The last car goes slightly faster, and will be in range from time 8/3 to 4. At time 3.5, the car that starts 9 units away will have just come into range. The car that started 5 units away will have moved 7 units at time 3.5, and so it will be just on the edge of the range. The cars that started between 5 and 9 units away will all still be in range also, since they move at the same speed. Hence, the 6 cars starting between 5 and 10 units away, inclusive, will all be in range at exactly time 3.5.

{798, 892, 442, 458, 700, 95, 569, 754, 722, 407,
 62, 151, 648, 888, 501, 393, 574, 666, 909, 301,
 637, 36, 746, 256, 7, 265, 853, 536, 720, 856,
 168, 570, 525, 384, 527}

{451, 846, 677, 768, 767, 661, 737, 720, 548, 658,
 463, 951, 552, 988, 208, 990, 145, 950, 265, 952,
 534, 710, 630, 191, 703, 571, 543, 859, 202, 411,
 869, 615, 576, 251, 654}

Returns: 26

{50, 50, 50, 50, 50, 50, 50, 50}

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

Returns: 1

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