图的遍历算法

前言

图的遍历算法是求解图的连通性问题、拓扑排序和求关键路径等算法的基础。

通常有两种遍历图的方式：广度优先和深度优先（有无向图和有向图都适用），下面以有向图为例给出基于python的两种实现。

已知图如下所示：

广度优先搜索

from collections import deque

VISITED = []

# breadth first search
def bfs(d):
	VISITED.append("v1")
	q = deque()
	q += d["v1"]
	while q:
		item = q.popleft()  # first in first out
		if item not in VISITED:
			VISITED.append(item)
			q += d[item]

if __name__ == "__main__":
	d = {}
	d["v1"] = ["v2", "v3", "v4"]
	d["v2"] = ["v5", "v6"]
	d["v3"] = ["v9"]
	d["v4"] = ["v7", "v8"]
	d["v5"] = ["v9"]
	d["v6"] = ["v9"]
	d["v7"] = []
	d["v8"] = ["v10"]
	d["v9"] = []
	d["v10"] = ["v9"]
	bfs(d)
	print(VISITED)

# ['v1', 'v2', 'v3', 'v4', 'v5', 'v6', 'v9', 'v7', 'v8', 'v10']

深度优先搜索

深度优先搜索存在一个回溯的过程，所以使用递归来实现，因为递归本身保存了调用栈。

VISITED = []

def recurse(items, d):
	if not items:
		return None
	for item in items:
		if item not in VISITED:
			VISITED.append(item)
			recurse(d[item], d)

# depth first search
def dfs(d):
	VISITED.append("v1")
	recurse(d["v1"], d)

if __name__ == "__main__":
	d = {}
	d["v1"] = ["v2", "v3", "v4"]
	d["v2"] = ["v5", "v6"]
	d["v3"] = ["v9"]
	d["v4"] = ["v7", "v8"]
	d["v5"] = ["v9"]
	d["v6"] = ["v9"]
	d["v7"] = []
	d["v8"] = ["v10"]
	d["v9"] = []
	d["v10"] = ["v9"]
	dfs(d)
	print(VISITED)

# ['v1', 'v2', 'v5', 'v9', 'v6', 'v3', 'v4', 'v7', 'v8', 'v10']