EasyCalculusca-226

Optimal Transport Cost

Problem

The cost of a transport plan P with cost matrix C is the Frobenius inner product:

cost = sum over i, j of P_ij * C_ij

Given the plan and the cost matrix, return the total transport cost.

Hint

The optimal plan minimizes this inner product subject to the marginal constraints.

case 1

in: [[[0.5,0.5],[0,0]],[[1,2],[3,4]]]

expected: 1.5

case 2

in: [[[0,1],[1,0]],[[2,5],[7,3]]]

expected: 12

case 3

in: [[[1]],[[4]]]

expected: 4

case 4

in: [[[0.25,0.25],[0.25,0.25]],[[1,2],[3,4]]]

expected: 2.5

Starter codePython

def optimal_transport_cost(plan, cost):
    # Your code here
    pass

4 test cases · run your code against them in the editor