Add 015

Author: tobegit3hub

014LRU缓存.md

@@ -67,4 +67,6 @@ class LRUCache(object):
         else:
             self.data[key] = value
             self.keys.insert(0, key)
-```
+```
+
+这是本章内容，希望对你有所帮助。[进入下一章](./015图.md)

015图.md

@@ -0,0 +1,108 @@
+
+# 实现图数据结构
+
+## 什么是图
+
+图是类似树这样的数据结构，与树不同的是它可以没有根节点，而且根据类型不同可分为有向图和无向图等。
+
+在现实中可能存在这样的图，满足以下条件。
+
+```
+A -> B
+A -> C
+B -> C
+B -> D
+C -> D
+D -> C
+E -> F
+F -> C
+```
+
+这样的图用Python可以使用字典来表达这样的数据结构，如{A: [B, C], B: [C, D], C: [D], D: [C], E: [F], F: [C]}。
+
+## 如何实现图
+
+要实现图的遍历等功能，以上面的图为例，我们首先要定义数据结构和函数。因为要递归实现，我们需要把start、end传进去，而且还要给历史走过的path。
+
+```
+def find_path(graph, start, end, path=[]):
+  pass
+
+def find_all_paths(graph, start, end, path=[]):
+  pass
+
+def find_shortest_path(graph, start, end, path=[]):
+  pass
+
+graph = {'a':['b', 'c'], 'b': ['c', 'd'], 'c': ['d'], 'd': ['c'], 'e': ['f'], 'f': ['c']}
+```
+
+首先我们来实现find_path函数，用到了回溯法，从起点开始，如果起点就是终点那先返回，然后遍历每个子节点，注意要确保不是环路而且找了非空的路径才返回。
+
+```
+def find_path(graph, start, end, path=[]):
+  path = path + [start]
+
+  if start == end:
+    return [path]
+
+  for node in graph[start]:
+    if node not in path:
+      new_path = find_path(graph, node, end, path)
+      if new_path:
+        return new_path
+
+graph = {'a':['b', 'c'], 'b': ['c', 'd'], 'c': ['d'], 'd': ['c'], 'e': ['f'], 'f': ['c']}
+print(find_path(graph, 'a', 'd'))
+# Print [['a', 'b', 'c', 'd']]
+```
+
+然后我们来实现find_all_paths函数，
+
+```
+def find_all_paths(graph, start, end, path=[]):
+  path = path + [start]
+
+  if start == end:
+    return [path]
+
+  all_paths = []
+  for node in graph[start]:
+    if node not in path:
+      new_paths = find_all_paths(graph, node, end, path)
+      for new_path in new_paths:
+        all_paths.append(new_path)
+
+  return all_paths
+
+graph = {'a':['b', 'c'], 'b': ['c', 'd'], 'c': ['d'], 'd': ['c'], 'e': ['f'], 'f': ['c']}
+print(find_all_paths(graph, 'a', 'd'))
+# Print [['a', 'b', 'c', 'd'], ['a', 'b', 'd'], ['a', 'c', 'd']]
+```
+
+最后来实现获取最短路径。
+
+```
+def find_shortest_path(graph, start, end, path=[]):
+  path = path + [start]
+
+  if start == end:
+    return path
+
+  result_path = None
+  for node in graph[start]:
+    if node not in path:
+      new_path = find_shortest_path(graph, node, end, path)
+      if result_path == None:
+        result_path = new_path
+      elif len(result_path) > len(new_path):
+        result_path = new_path
+
+  return result_path
+
+graph = {'a':['b', 'c'], 'b': ['c', 'd'], 'c': ['d'], 'd': ['c'], 'e': ['f'], 'f': ['c']}
+print(find_shortest_path(graph, 'a', 'd'))
+# Print ['a', 'b', 'd']
+```
+
+这是本章内容，希望对你有所帮助。[进入下一章](./015图.md)