HanoiState | Topcoder Archive

Problem Statement

In the classic Towers of Hanoi problem, there are three pegs, labeled A, B and C, and n discs, of sizes 1 to n. Each disc has a hole in the center, so that it can be placed on a peg. Initially, all the discs are stacked on peg A in order of size, with the smallest disc on top. Only one disc may be moved at a time. In each move, you remove the top disc from one of the pegs, and place it on another peg. A disc may be placed on an empty peg or stacked on top of a larger disc, but it may not be placed on top of a smaller disc.

target is a string consisting of n characters, each of which is either A, B or C. The goal of the game is to make the minimum number of moves so that character i of target is the peg containing the disc of size i + 1. There is only one shortest sequence of moves. Return the state of the game after making moves of these moves, in the same format as target.

Definition

Class:: HanoiState
Method:: partwayState
Parameters:: String, int
Returns:: String
Method signature:: String partwayState(String target, int moves)
(be sure your method is public)

Constraints

target will contain between 1 and 30 characters, inclusive.
Each character of target will be either 'A', 'B' or 'C'.
moves will be between 0 and m, inclusive, where the shortest solution to the game takes m moves.

Examples

```
"CCC"
```
```
4
```
```
Returns: "BBC"
```
The full sequence of states is AAA, CAA, CBA, BBA, BBC, ABC, ACC, CCC. After 4 moves the state is BBC.
```
"AAC"
```
```
7
```
```
Returns: "AAC"
```

"AAAAAAAAAAAAAAAAAAAAAAAAAAAA"

Returns: "AAAAAAAAAAAAAAAAAAAAAAAAAAAA"

"ABCABCABCABCABCABCABCABCABCABC"

100000000

Returns: "CCCCCCCCBAAAABBBBACBAAAAACBAAA"

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