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# 組合せ最適化 - 典型問題 - 最短路問題

Last updated at Posted at 2015-07-10

## 最短路問題

グラフ$G=(V,E)$の各辺$e_{ij}=(v_i,v_j)\in E$が重み$a_{ij}$をもつとき、始点$v_s \in V$から終点$v_t \in V$への路の中で最も重みの和の小さいものを求めよ。

## 実行方法

usage
Signature: nx.dijkstra_path(G, source, target, weight='weight')
Docstring:
Returns the shortest path from source to target in a weighted graph G.

python
# CSVデータ
import pandas as pd, networkx as nx
from ortoolpy import graph_from_table
g = graph_from_table(tbn, tbe)[0]
print(nx.dijkstra_path(g, 5, 2))


[5, 4, 0, 2]

python
# pandas.DataFrame
from ortoolpy.optimization import DijkstraPath
DijkstraPath('data/edge0.csv', 5, 2)

node1 node2 capacity weight
9 4 5 2 1
3 0 4 2 2
1 0 2 2 4
python
# 乱数データ
import networkx as nx
g = nx.fast_gnp_random_graph(8, 0.26, 1)
print(nx.dijkstra_path(g, 0, 2))


[0, 1, 6, 3, 5, 2]


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