【coding】Breadth-first Search 广度优先搜索（原理+代码实现）

回顾了运筹课写的图搜索作业，并重新编程实现了一下。

1. 广度优先搜索

1.1 题目描述

Use Breath-first search and Depth-first search to search graph below. Illustrate each execution step.

1.2 题解

• For G = (V;E) and a source vertex s, it systematically explores the edges of G to discover every vertex that is reachable from s
• Breadth-first search expands the frontier between discovered and undiscovered vertices uniformly across the breadth of the frontier
• color[u]:
  • white (undiscovered),
  • gray (discovered but not scanned)
  • black (discovered and scanned)

① V={s,u,v,w,x,y,z}
② Adjacency-list：

③

1.3 编程实现

数据准备

def primalData():
    graph = {
    
    
        's': ['v', 'x'],
        'u': ['v', 'x', 'y', 'z'],
        'v': ['s', 'u', 'w'],
        'w': ['v'],
        'x': ['s', 'u', 'y'],
        'y': ['u', 'x', 'z'],
        'z': ['u', 'y']
    }
    return graph

from collections import deque


class Search():
    def __init__(self, graph, start_point):
        self.graph = graph
        self.start_point = start_point

    def BFS(self):
        res = []  # 储存搜索结果
        queue = deque(self.start_point)  # 广度优先搜索的辅助队列，用collections.deque实现
        visited_set = set()  # 储存访问过的点集合，防止重复访问
        while queue:
            n = len(queue)
            temp = []  # 放这一层的元素
            for _ in range(n):
                cur = queue.popleft()
                temp.append(cur)
                visited_set.add(cur)
                neighbours = self.graph[cur]  # cur的临接点
                for neighbour in neighbours:
                    if neighbour not in visited_set:
                        queue.append(neighbour)
                        visited_set.add(neighbour)
            res.append(temp)
        return res


if __name__ == '__main__':
    search = Search(primalData(), 's')
    res = search.BFS()
    print(res)

# 输出展示：
[['s'], ['v', 'x'], ['u', 'w', 'y'], ['z']]

2. 其他图搜索资料

2.1 Dijkstra

适用范围：无负权重边
参考文章链接：有概念讲解
参考文章链接：有示例