EADST

Maximize the sum of the table where each number must come from the unique row and column. Maximum cost bipartite matching problem can be solved with the Hungarian algorithm.

from scipy.optimize import linear_sum_assignment
import numpy as np

cost =np.array(
    [
        [12,7,9,7,9],
        [8,9,6,6,6],
        [7,17,12,14,9],
        [15,14,6,6,10],
        [4,10,7,10,9]
    ])
row_ind, col_ind=linear_sum_assignment(cost)
res = np.zeros_like(cost) # np.ones_like
res[row_ind, col_ind] = 1
print(res)                          
#[[0 1 0 0 0]
# [0 0 1 0 0]
#[0 0 0 0 1]
#[0 0 0 1 0]
#[1 0 0 0 0]]
print(cost[row_ind,col_ind].sum())  # 32 total cost

Reference

StackOverflow

指派问题 —— 匈牙利算法