# Leetcode: Sliding Puzzle

Sliding Puzzle Similar Problems:

On a 2×3 board, there are 5 tiles represented by the integers 1 through 5, and an empty square represented by 0.

A move consists of choosing 0 and a 4-directionally adjacent number and swapping it.

The state of the board is solved if and only if the board is [[1,2,3],[4,5,0]].

Given a puzzle board, return the least number of moves required so that the state of the board is solved. If it is impossible for the state of the board to be solved, return -1.

Examples:

```Input: board = [[1,2,3],[4,0,5]]
Output: 1
Explanation: Swap the 0 and the 5 in one move.
```
```Input: board = [[1,2,3],[5,4,0]]
Output: -1
Explanation: No number of moves will make the board solved.
```
```Input: board = [[4,1,2],[5,0,3]]
Output: 5
Explanation: 5 is the smallest number of moves that solves the board.
An example path:
After move 0: [[4,1,2],[5,0,3]]
After move 1: [[4,1,2],[0,5,3]]
After move 2: [[0,1,2],[4,5,3]]
After move 3: [[1,0,2],[4,5,3]]
After move 4: [[1,2,0],[4,5,3]]
After move 5: [[1,2,3],[4,5,0]]
Input: board = [[3,2,4],[1,5,0]]
Output: 14
```

Note:

• board will be a 2 x 3 array as described above.
• board[i][j] will be a permutation of [0, 1, 2, 3, 4, 5].

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

```## Blog link: https://code.dennyzhang.com/sliding-puzzle
## Basic Ideas: BFS: find the mininum path from point1 to point2
##
## Complexity:
class Solution(object):
def slidingPuzzle(self, board):
"""
:type board: List[List[int]]
:rtype: int
"""
target = '123450'
queue, visited = [], set()
queue.append(self.toString(board))

level = 0
while len(queue) != 0:
for i in range(len(queue)):
state = queue
if state == target: return level
del queue
# move to next
# print queue
level += 1
return -1

def toString(self, board):
res = ''
for i in range(2):
for j in range(3):
res = res + str(board[i][j])
return res

# change back state to board
matrix = [[None for j in range(3)] for i in range(2)]
index = 0
i0, j0 = None, None
for i in range(2):
for j in range(3):
matrix[i][j] = state[index]
index += 1
if matrix[i][j] == '0':
i0, j0 = i, j
# get next:
for (ik, jk) in [(-1, 0), (1, 0), (0, 1), (0, -1)]:
i2, j2 = i0+ik, j0+jk
if i2<0 or i2 >= 2 or j2<0 or j2>=3: continue
matrix[i0][j0], matrix[i2][j2] = matrix[i2][j2], matrix[i0][j0]
newState = self.toString(matrix)
if newState not in visited:
queue.append(newState)
# change back
matrix[i0][j0], matrix[i2][j2] = matrix[i2][j2], matrix[i0][j0]
```

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