python Hungarian Algorithm bipartite graph maximum matching code
时间: 2023-02-12 14:58:48 浏览: 86
下面是一个用 Python 实现的二分图最大匹配 (Hungarian Algorithm) 的示例代码:
```
import numpy as np
def hungarian(cost_matrix):
row_ind, col_ind = linear_sum_assignment(cost_matrix)
return np.sum(cost_matrix[row_ind, col_ind])
```
该算法依赖于scipy库,需要先运行 `pip install scipy` 进行安装
输入为代价矩阵,输出为最小代价。
相关问题
hungarian algorithm
匈牙利算法(Hungarian Algorithm)是一种求解二分图最大权匹配的算法。它的时间复杂度为O(n^3),是一种比较高效的算法。该算法的基本思想是通过不断的交替增广路径来寻找增广路,直到无法找到增广路为止。
最大匹配算法python代码
以下是基于匈牙利算法的最大匹配算法的Python代码:
```python
def max_matching(graph):
"""
Find the maximum matching in a bipartite graph using the Hungarian algorithm.
The graph is represented as an adjacency list, where the keys are the vertices on one side
of the bipartition and the values are lists of vertices on the other side of the bipartition that
are connected to the key vertex.
"""
# Initialize the matching to be empty
matching = {}
for u in graph.keys():
matching[u] = None
# Find the augmenting path using DFS
def dfs(u, visited):
for v in graph[u]:
if v not in visited:
visited.add(v)
if matching[v] is None or dfs(matching[v], visited):
matching[v] = u
return True
return False
# Find the maximum matching by iterating through all vertices in the first partition
for u in graph.keys():
dfs(u, set())
# Count the number of edges in the matching
num_edges = sum(1 for u in graph.keys() if matching[u] is not None)
return matching, num_edges
```
其中,`graph` 是一个字典,键为第一部分的顶点,值为与该顶点相连的第二部分的顶点列表。函数返回一个元组,第一个元素是匹配,第二个元素是匹配的边数。
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