77 lines
2.3 KiB
Python
77 lines
2.3 KiB
Python
|
from itertools import permutations
|
||
|
|
from heapq import heappush, heappop
|
||
|
|
|
||
|
|
|
||
|
|
m1 = """ 7 53 183 439 863
|
||
|
|
497 383 563 79 973
|
||
|
|
287 63 343 169 583
|
||
|
|
627 343 773 959 943
|
||
|
|
767 473 103 699 303"""
|
||
|
|
|
||
|
|
|
||
|
|
m2 = """ 7 53 183 439 863 497 383 563 79 973 287 63 343 169 583
|
||
|
|
627 343 773 959 943 767 473 103 699 303 957 703 583 639 913
|
||
|
|
447 283 463 29 23 487 463 993 119 883 327 493 423 159 743
|
||
|
|
217 623 3 399 853 407 103 983 89 463 290 516 212 462 350
|
||
|
|
960 376 682 962 300 780 486 502 912 800 250 346 172 812 350
|
||
|
|
870 456 192 162 593 473 915 45 989 873 823 965 425 329 803
|
||
|
|
973 965 905 919 133 673 665 235 509 613 673 815 165 992 326
|
||
|
|
322 148 972 962 286 255 941 541 265 323 925 281 601 95 973
|
||
|
|
445 721 11 525 473 65 511 164 138 672 18 428 154 448 848
|
||
|
|
414 456 310 312 798 104 566 520 302 248 694 976 430 392 198
|
||
|
|
184 829 373 181 631 101 969 613 840 740 778 458 284 760 390
|
||
|
|
821 461 843 513 17 901 711 993 293 157 274 94 192 156 574
|
||
|
|
34 124 4 878 450 476 712 914 838 669 875 299 823 329 699
|
||
|
|
815 559 813 459 522 788 168 586 966 232 308 833 251 631 107
|
||
|
|
813 883 451 509 615 77 281 613 459 205 380 274 302 35 805
|
||
|
|
"""
|
||
|
|
|
||
|
|
|
||
|
|
def brute_force(m):
|
||
|
|
idxs = [i for i in range(len(m))]
|
||
|
|
max_sum = 0
|
||
|
|
for idx in permutations(idxs):
|
||
|
|
temp_sum = 0
|
||
|
|
for i, j in enumerate(idx):
|
||
|
|
temp_sum += m[j][i]
|
||
|
|
if temp_sum > max_sum:
|
||
|
|
max_sum = temp_sum
|
||
|
|
return max_sum
|
||
|
|
|
||
|
|
|
||
|
|
def a_star(m):
|
||
|
|
# init heuristic function
|
||
|
|
h = {}
|
||
|
|
for i in range(len(m)):
|
||
|
|
h[i] = sum(map(min, m[i:]))
|
||
|
|
h[i + 1] = 0
|
||
|
|
|
||
|
|
states = []
|
||
|
|
for i, r in enumerate(m[0]):
|
||
|
|
state = (r + h[1], r, 1, [i])
|
||
|
|
heappush(states, state)
|
||
|
|
|
||
|
|
while states:
|
||
|
|
_, gscore, index, seen = heappop(states)
|
||
|
|
if index == len(m):
|
||
|
|
return -gscore
|
||
|
|
|
||
|
|
for row_index, row_score in enumerate(m[index]):
|
||
|
|
if row_index in seen:
|
||
|
|
continue
|
||
|
|
ngscore = gscore + row_score
|
||
|
|
nfscore = ngscore + h[index + 1]
|
||
|
|
nstate = (nfscore, ngscore, index + 1, seen + [row_index])
|
||
|
|
heappush(states, nstate)
|
||
|
|
|
||
|
|
|
||
|
|
def euler_345():
|
||
|
|
m = list(zip(*map(lambda line: list(map(lambda n: -int(n), line.split())), m2.splitlines())))
|
||
|
|
return a_star(m)
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
solution = euler_345()
|
||
|
|
print("e345.py: " + str(solution))
|
||
|
|
assert(solution == 13938)
|