以codewars中3 kyu Path Finder #3: the Alpinist 为例

题干：

You are at start location [0, 0] in mountain area of NxN and you can only move in one of the four cardinal directions (i.e. North, East, South, West). Return minimal number of climb rounds to target location [N-1, N-1]. Number of climb rounds between adjacent locations is defined as difference of location altitudes (ascending or descending).

代码主体部分（构建图（dict），堆优化的Dijkstra算法）：

 1 import heapq
 2 
 3 
 4 def get_distance(a, b):
 5     return abs(int(a)-int(b))
 6 
 7 def get_G(area):
 8     G = {}
 9     area = area.splitlines()
10     N = len(area)
11     for i in range(N):
12         for j in range(N):
13             n = N * i + j
14             G[n] = {}
15             if i < N-1:
16                 G[n][n+N] = get_distance(area[i][j], area[i+1][j])
17             if j < N-1:
18                 G[n][n+1] = get_distance(area[i][j], area[i][j+1])
19             if i > 0:
20                 G[n][n-N] = get_distance(area[i][j], area[i-1][j])
21             if j > 0:
22                 G[n][n-1] = get_distance(area[i][j], area[i][j-1])
23     return G
24 
25 
26 def dijkstra(G, start):
27     dis = dict((key, float('inf')) for key in G)         # start 到每个点的距离
28     dis[start] = 0
29     vis = dict((key, False) for key in G)       # 是否访问过某个点
30 
31     ### 堆优化
32     pq = []
33     heapq.heappush(pq, [dis[start], start])
34 
35     path = dict((key, [start]) for key in G)     # 记录到每个点的路径
36     while len(pq) > 0:
37         v_dis, v = heapq.heappop(pq)      # 未访问的点中距离最近的点
38         if vis[v] is True:
39             continue
40         vis[v] = True
41         p = path[v].copy()   # 到v的最短路径
42         for node in G[v]:    # 与v直接相连的点
43             new_dis = dis[v] + G[v][node]     # 更新到下一个点的距离
44             if new_dis < dis[node] and (not vis[node]):   # 比较距离是否更近，是则更新相关信息
45                 dis[node] = new_dis
46                 heapq.heappush(pq, [dis[node], node])
47                 temp = p.copy()
48                 temp.append(node)
49                 path[node] = temp
50     return dis, path

测试部分：

 1 g = "\n".join([
 2   "000000",
 3   "000000",
 4   "000000",
 5   "000010",
 6   "000109",
 7   "001010"
 8 ])
 9 
10 def path_finder(area):
11     dis, path = dijkstra(get_G(g), 0)
12     print(list(dis.values())[-1])

其他作者解法：

 1 def path_finder(maze):
 2     grid = maze.splitlines()
 3     end = h, w = len(grid) - 1, len(grid[0]) - 1
 4     bag, seen = {(0, 0): 0}, set()
 5     while bag:
 6         x, y = min(bag, key=bag.get)
 7         rounds = bag.pop((x, y))
 8         seen.add((x, y))
 9         if (x, y) == end: return rounds
10         for u, v in (-1, 0), (0, 1), (1, 0), (0, -1):
11             m, n = x + u, y + v
12             if (m, n) in seen or not (0 <= m <= h and 0 <= n <= w): continue
13             new_rounds = rounds + abs(int(grid[x][y]) - int(grid[m][n]))
14             if new_rounds < bag.get((m, n), float('inf')): bag[m, n] = new_rounds