問題描述：有兩個集合$\boldsymbol$，$\boldsymbol$，且$\boldsymbol$和$\boldsymbol$中元素的個數均為$d$。現給定$n$個由集合$\boldsymbol$中某元素到集合$\boldsymbol$中某元素的對映，期望找出所有可能的雙射的情形。
**：
import copy
import numpy as np
import matplotlib.pyplot as plt
def find_solutions(x_to_y_matrix, index_vectors,
connection_list, connection_index_list,
solution_set, solution_index_set):
""""""
start_pos = [-1, -1]
for i in range(x_to_y_matrix.shape[1]):
if x_to_y_matrix[0][i] == 1:
start_pos = [0, i]
reduced_matrix = np.zeros([x_to_y_matrix.shape[0] - 1, x_to_y_matrix.shape[1] - 1])
if reduced_matrix.shape[0] == 0 and reduced_matrix.shape[1] == 0:
connection_list.pop()
break
n = 0
for i in range(x_to_y_matrix.shape[0]):
if i != start_pos[0]:
current_row = np.array()
for j in range(x_to_y_matrix.shape[1]):
if j != start_pos[1]:
reduced_matrix[n, :] = current_row
n += 1
index_vectors[0][ : start_pos[0]], index_vectors[0][start_pos[0] + 1: ])
index_vectors[1][ : start_pos[1]], index_vectors[1][start_pos[1] + 1: ])
reduced_index_vectors = np.array([index_row, index_col])
find_solutions(reduced_matrix, reduced_index_vectors, \
connection_list, connection_index_list, \
solution_set, solution_index_set)
if len(connection_list) != 0:
connection_list.pop()
if len(connection_index_list) != 0:
connection_index_list.pop()
return none
def test():
""""""
dim_x_to_y_matrix = 5
x_to_y_connections = np.array([[0, 0],
[0, 2],
[0, 4],
[1, 0],
[1, 2],
[2, 1],
[2, 3],
[3, 1],
[3, 3],
[4, 0],
[4, 4]])
x_to_y_matrix = np.zeros([dim_x_to_y_matrix, dim_x_to_y_matrix])
for i in range(x_to_y_connections.shape[0]):
x_to_y_matrix[int(x_to_y_connections[i][0])][int(x_to_y_connections[i][1])] = 1
index_vectors = np.empty([2, dim_x_to_y_matrix])
index_vectors[0, :] = np.arange(0, dim_x_to_y_matrix, 1)
index_vectors[1, :] = np.arange(0, dim_x_to_y_matrix, 1)
connection_list =
connection_index_list =
solution_set =
solution_index_set =
find_solutions(x_to_y_matrix, index_vectors,
connection_list, connection_index_list,
solution_set, solution_index_set)
if len(solution_set) % 2 == 0:
plot_offset = 200 + (len(solution_set) + 2)/2 * 10
elif len(solution_set) % 2 == 1:
plot_offset = 200 + (len(solution_set) + 1)/2 * 10
plt.figure()
plt.subplot(plot_offset + 1)
for j in range(x_to_y_connections.shape[0]):
plt.plot([1, 2], x_to_y_connections[j, :], color='grey')
plt.grid()
plt.box()
plt.show()
for i in range(len(solution_set)):
x_to_y_list =
for j in range(len(solution_set[i])):
if j == 0:
elif j >= 1:
[int(solution_index_set[i][j - 1][0][int(solution_set[i][j][0])]), \
int(solution_index_set[i][j - 1][1][int(solution_set[i][j][1])])])
print(x_to_y_list)
plt.subplot(plot_offset + i + 2)
for j in range(len(x_to_y_list)):
plt.plot([1, 2], x_to_y_list[j], 'o-', linewidth=1)
plt.grid()
plt.box()
plt.show()
if __name__ == "__main__":
test()
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