思路分析
本题迷宫只有一条通道,可以使用DFS,栈内元素正好为所走的路径,也是最短路径。
若迷宫不只一条通道,使用DFS走通的路径不一定是最短路径,最好采用BFS。
方法一:DFS
def DFS(start):
stack = []
stack.append(start)
maze[0][0] = 2 # 走过标记为2
while stack:
if stack[-1] == end: # 栈内元素为所走的路径
for i in stack:
print(f"({i[0]},{i[1]})")
break
r, c = stack[-1]
neighbors = [(r - 1, c), (r, c + 1), (r + 1, c), (r, c - 1)] # (r,c)的邻居
for neighbor in neighbors:
i, j = neighbor
if 0 <= i < N and 0 <= j < M: # 有效邻居
if maze[i][j] == 0:
stack.append((i, j))
maze[i][j] = 2 # 走过标记为2
break
else: # 无路可走,回退
stack.pop()
# 0.输入
N, M = map(int, input().split())
maze = [list(map(int, input().split())) for _ in range(N)]
# 1.起点与终点
start = (0, 0)
end = (N-1, M-1)
# 2.DFS
DFS(start)
方法二:BFS
def BFS(start):
queue = []
queue.append(start)
visited = set()
visited.add(start)
father[(0, 0)] = (-1, -1) # 任取(0,0)上一步(-1,-1)
while queue:
(r, c) = queue.pop(0)
if (r, c) == end:
return
for i, j in [(r - 1, c), (r, c + 1), (r + 1, c), (r, c - 1)]:
if 0 <= i < N and 0 <= j < M:
if maze[i][j] == 0 and (i, j) not in visited:
queue.append((i, j))
visited.add((i, j))
father[(i, j)] = (r, c)
# 0.输入
N, M = map(int, input().split())
maze = [list(map(int, input().split())) for _ in range(N)]
# 1.起点与终点
start = (0, 0)
end = (N-1, M-1)
# 2.BFS后得出路径坐标的映射关系
father = {} # 收集坐标与上一步映射关系,用字典来表示
BFS(start)
# 3.路径倒推
path = []
while end != (-1, -1):
path.append(end)
end = father[end]
for p in path[::-1]: # 路径的逆序,按格式输出
print(f"({p[0]},{p[1]})")

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