Expert · Graphs · 221 of 264
Shortest way out
Find the fewest steps from S to E in a maze; # is a wall, and you move up, down, left or right. Use breadth-first search.
Input: r and c, then r lines of the maze. Output: the number of steps, or -1 if E cannot be reached.
Examples
Input
3 4 S..# .#.. ...E
Output
5
Input
2 3 S#E .#.
Output
-1
Input
1 2 SE
Output
1
One more test checks other inputs when you press Check.
Stuck? The idea behind graphs
A graph is places (nodes) joined by edges. Keep it as a dictionary of neighbours: graph[a] is the list of nodes next to a.
Breadth-first search, with a queue, finds the shortest path when every step costs the same; Dijkstra's algorithm, with a heap, when steps cost different amounts.
from collections import deque
graph = {1: [2, 3], 2: [4], 3: [4], 4: []}
dist = {1: 0}
queue = deque([1])
while queue:
node = queue.popleft()
for nxt in graph[node]:
if nxt not in dist:
dist[nxt] = dist[node] + 1
queue.append(nxt)
print(dist[4])Watch for: Mark a node as seen when you add it to the queue, not when you take it out, or it is added many times.