##### Short Problem Definition:

Hermione Granger is lost in the Forbidden Forest while collecting some herbs for a magical potion. The forest is magical and has only one exit point, which magically transports her back to the Hogwarts School of Witchcraft and Wizardry.

##### Link

##### Complexity:

time complexity is `O(n)`

space complexity is `O(n)`

##### Execution:

I solve this challenge using DFS and dynamic programming. I iterate over all n positions (denoted with .) using DFS. For each node, I remember the number of crossroads Hermione encountered up to that point. DFS does not guarantee to find the optimal solution in terms of path length.

##### Solution:

```
#!/usr/bin/py
from collections import defaultdict
def hermionesWand(arr, K, max_x, max_y):
# find both entry and exit points
for idx, line in enumerate(arr):
for inner_idx in xrange(len(line)):
if line[inner_idx] == 'M':
h = (idx, inner_idx)
if line[inner_idx] == '*':
e = (idx, inner_idx)
st = [h]
tracker = defaultdict(int)
tracker[h] = 0
# iterate the DFS list
while st:
curr = st.pop()
# exit found
if (curr == e):
return tracker[curr] == K
# save all exits that were not visited before
inner_st = set()
if (curr[0] > 0 and (arr[curr[0]-1][curr[1]] == "." or arr[curr[0]-1][curr[1]] == "*")) \
and (curr[0]-1, curr[1]) not in tracker:
inner_st.add((curr[0]-1, curr[1]))
if (curr[1] > 0 and (arr[curr[0]][curr[1]-1] == "." or arr[curr[0]][curr[1]-1] == "*")) \
and (curr[0], curr[1]-1) not in tracker:
inner_st.add((curr[0], curr[1]-1))
if (curr[0] < max_y -1 and (arr[curr[0]+1][curr[1]] == "." or arr[curr[0]+1][curr[1]] == "*")) \
and (curr[0]+1, curr[1]) not in tracker:
inner_st.add((curr[0]+1, curr[1]))
if (curr[1] < max_x -1 and (arr[curr[0]][curr[1]+1] == "." or arr[curr[0]][curr[1]+1] == "*")) \
and (curr[0], curr[1]+1) not in tracker:
inner_st.add((curr[0], curr[1]+1))
# a crossroad
if len(inner_st) > 1:
tracker[curr] += 1
# save the nodes to DFS list
for n in inner_st:
tracker[n] = tracker[curr]
st.append(n)
return False
if __name__ == '__main__':
t = int(raw_input())
for _ in xrange(t):
n, m = map(int, raw_input().split())
a = []
for line in xrange(n):
a.append(list(raw_input()))
k = int(raw_input())
if hermionesWand(a, k, m, n):
print "Impressed"
else:
print "Oops!"
```