CarrotJumping | Topcoder Archive

Problem Statement

Rabbits often feel hungry, so when they go out to eat carrots, they jump as quickly as possible.

Initially, rabbit Hanako stands at position init. From position x, she can jump to either position 4*x+3 or 8*x+7 in a single jump. She can jump at most 100,000 times because she gets tired by jumping.

Carrots are planted at position x if and only if x is divisible by 1,000,000,007 (i.e. carrots are planted at position 0, position 1,000,000,007, position 2,000,000,014, and so on). Return the minimal number of jumps required to reach a carrot. If it's impossible to reach a carrot using at most 100,000 jumps, return -1.

Definition

Class:: CarrotJumping
Method:: theJump
Parameters:: int
Returns:: int
Method signature:: int theJump(int init)
(be sure your method is public)

Constraints

init will be between 1 and 1,000,000,006, inclusive.

Examples

```
125000000
```
```
Returns: 1
```
She can jump from 125000000 to 1000000007.
```
281250001
```
```
Returns: 2
```
281250001 -> 1125000007 -> 9000000063
```
18426114
```
```
Returns: 58
```
```
4530664
```
```
Returns: 478
```
```
705616876
```
```
Returns: 100000
```
```
852808441
```
```
Returns: -1
```
She can't reach any carrot by making at most 100,000 jumps.

This problem statement is the exclusive and proprietary property of Topcoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of Topcoder, Inc. is strictly prohibited. (c)2024, Topcoder, Inc. All rights reserved.