<｜begin▁of▁sentence｜>### Instruction:
Given a directed graph with nodes 'a' and 'd' having a demand of -5 and +5 respectively, and edges ('a', 'b'), ('a', 'c'), ('b', 'd'), and ('c', 'd') with weights 3, 6, 1, and 2 respectively, and capacities 4, 10, 9, and 5 respectively, what is the minimum cost flow satisfying all demands?
### Response:
import networkx as nx

# Create a directed graph
G = nx.DiGraph()

# Add nodes with supply/demand
define node demands where supply node has negative demand, sink has positive demand
define the cost and capacity for the edges

define the flow costs for each edge, cost is per unit of flow

G.add_node('a', demand=-5)
G.add_node('d', demand=5)
G.add_edge('a', 'b', weight=3, capacity=4)
G.add_edge('a', 'c', weight=6, capacity=10)
G.add_edge('b', 'd', weight=1, capacity=9)
G.add_edge('c', 'd', weight=2, capacity=5)

# Run the capacity scaling algorithm to find minimum cost flow satisfying all demands
flowCost, flowDict = nx.capacity_scaling(G)

print('Flow Cost:', flowCost)
print('Flow Dict:', flowDict)
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