TopCoder Statistics - Problem Statement

Problem Statement

A dog is standing at point (0, 0), and a rabbit is standing at point (distanceToRabbit, 0). The rabbit starts running in a straight line toward his home, which is located at (distanceToHome + distanceToRabbit, 0). At the same time, the dog starts running in a straight line toward the rabbit.

The rabbit runs at a constant speed of rabbitSpeed units per second. This means that in t seconds, he travels rabbitSpeed * t units. The dog starts running at an initial speed of 0 and a constant acceleration of dogAcceleration units per second². This means that in t seconds, he travels dogAcceleration * t² / 2 units.

Return "YES" if the dog can catch the rabbit before the rabbit enters its home, or "NO" otherwise (all quotes for clarity). The dog can catch the rabbit if there exists a point (x, 0) such that x <= distanceToHome + distanceToRabbit, and both the dog and the rabbit are at that same point at the same time.

Definition

Class:: DogAndRabbit
Method:: willCatch
Parameters:: int, int, int, int
Returns:: String
Method signature:: String willCatch(int distanceToRabbit, int distanceToHome, int rabbitSpeed, int dogAcceleration)
(be sure your method is public)

Constraints

distanceToRabbit will be between 0 and 1000000, inclusive.
distanceToHome will be between 0 and 1000000, inclusive.
distanceToRabbit and distanceToHome won't both be equal to 0.
rabbitSpeed will be between 0 and 1000000, inclusive.
dogAcceleration will be between 0 and 1000000, inclusive.

Examples

150

100

10

5

Returns: "YES"
100

200

20

10

Returns: "YES"

The dog will catch the rabbit about 62 units away from the rabbit's home.
1

100

1

0

Returns: "NO"

Here the dog is not so interested in the rabbit, so it stays in place.
0

5

1

2

Returns: "YES"

The dog got the rabbit already.
1000000

1000000

1000000

1000000

Returns: "NO"
1000000

1000000

499999

1000000

Returns: "YES"
1000000

1000000

500000

1000000

Returns: "YES"
999999

999997

499999

1000000

Returns: "NO"
999995

999997

499999

999998

Returns: "YES"
999984

999997

499999

999993

Returns: "YES"
1

1

1

5

Returns: "YES"
1

1

1

3

Returns: "NO"
56

86

50

96

Returns: "YES"
50

96

53

89

Returns: "NO"
103

194

101

161

Returns: "YES"
103

191

108

188

Returns: "NO"
100

211

184

473

Returns: "YES"
100

263

137

197

Returns: "NO"
999994

999996

499999

999999

Returns: "YES"
1

0

0

0

Returns: "NO"
0

1

0

0

Returns: "YES"
0

1

0

1

Returns: "YES"
0

1

1

0

Returns: "YES"
0

1

1

1

Returns: "YES"
1

0

0

1

Returns: "YES"
1

0

1

0

Returns: "NO"
1

0

1

1

Returns: "NO"
1

1

0

0

Returns: "NO"
1

1

0

1

Returns: "YES"
1

1

1

1

Returns: "NO"
2

499998

499998

1000000

Returns: "YES"
265432

234567

234567

999998

Returns: "YES"
605801

675735

212998

254659

Returns: "NO"
100

0

0

5

Returns: "YES"

The poor rabbit sleeps in front of his house, not aware of the dog.
200

10

5

10

Returns: "NO"

The dog is too far away from the rabbit to catch it.
10

10

0

0

Returns: "NO"
0

5

0

0

Returns: "YES"
10

0

0

10

Returns: "YES"
10

0

0

0

Returns: "NO"
0

5

1

0

Returns: "YES"
100

1

0

0

Returns: "NO"
100

100

10

4

Returns: "YES"
20

100

0

0

Returns: "NO"
10

0

1

0

Returns: "NO"
100

0

0

0

Returns: "NO"

Statistics

Problem Statement for "DogAndRabbit"

Problem Statement

Definition

Constraints

Examples