path_finder.py

origin ="""
S0110
01000
01010
00010
0001E
"""



grid = [[j for j in i] for i in origin.split("\n")][1:-1]

look = lambda p, grid=grid: list(filter(lambda x:grid[x[0]][x[1]]!="1", filter(lambda x: len(grid)>x[0]>=0 and len(grid[0])>x[1]>=0  , map(lambda x: (p[0]+x[0], p[1]+x[1]), [(0,1),(1,0),(0,-1),(-1,0)]))))

def walkpath(grid=grid, s=(0,0), e=(4,4)):
    def walk(grid, s, e, trac=[(0,0)], res=[]):
        if s==e:
            trac =trac[:]
            res.append(trac)
        look_ahead = look(s)
        for i in set(look_ahead)-set(trac):
            trac.append(i)
            walk(grid, i, e)
            trac.remove(i)
        return res
    return min(walk(grid, s, e), key=len)



for i in walkpath((0,0)):
    grid[i[0]][i[1]] = "#"


print(*["".join(i)for i in  grid], sep="\n")