Maze Pathfinder

Problem #64

Tags: graphs games arrays

Who solved this?

This problem is very simple: just find the way out of the maze.

Hint: you can choose any algorithm you know/like but a kind of wave propagation method is recommended.

Maze is given as a rectangular matrix of 0 and 1 characters. Exit is in top-left corner. You are to find the ways from top-right, bottom-left and bottom-right corners, i.e.

X-----A            1110001
-------            0010001
-------            1111111
-------            0000101
B-----C            1111101

For example in 7 * 5 rectangle (on the left) we should find ways from corners A, B and C to corner X. And for topology given (on the right) paths should be:

from A: DDLLLLUULL
from B: RRRRUULLUULL
from C: UULLLLUULL

Where U denotes step up, L is one step left, R and D are steps right and down respectively. We will use short form like:

from A: 2D4L2U2L
from B: 4R2U2L2U2L
from C: 2U4L2U2L

You see, each letter is preceded by amount of steps in this direction, like - 2 down, 4 left, 2 up, 2 left etc.

Input data will contain width and height of the maze in first line (both are odd values).
Then maze itself will follow, with 1 depicting passages and 0 for impassable walls.
Answer should contain three paths, space separated, in the format explained above.

Example:

input data:
13 9
1111101110111
0010001000001
1011111111111
1000000010100
1111111110101
0010000010001
1111101010111
1010001000100
1011111111111

answer:
2D10L2U2L 2U2R2U6R2U6L2U2L 10L4U6R2U6L2U2L
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