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#!/usr/bin/env python
# -*- coding: utf-8 -*-
from itertools import permutations
from collections import deque
def knight_moves(start, end):
# Calculate the knight distance between start and end using a breadth-first search
moves = [(2, 1), (1, 2), (-1, 2), (-2, 1),
(-2, -1), (-1, -2), (1, -2), (2, -1)]
visited = set()
queue = deque([(start, 0)])
while queue:
pos, dist = queue.popleft()
if pos == end:
return dist
if pos in visited:
continue
visited.add(pos)
for move in moves:
next_pos = (pos[0] + move[0], pos[1] + move[1])
if 0 <= next_pos[0] < 8 and 0 <= next_pos[1] < 8:
queue.append((next_pos, dist + 1))
def shortest_path(treasures):
# Find the permutation of treasures with the shortest total distance
start = (0, 0)
shortest_dist = float('inf')
shortest_perm = None
for perm in permutations(treasures):
total_dist = sum(knight_moves(perm[i], perm[i+1])
for i in range(len(perm) - 1))
total_dist += knight_moves(start,
perm[0]) + knight_moves(perm[-1], start)
if total_dist < shortest_dist:
shortest_dist = total_dist
shortest_perm = perm
return shortest_perm
# The treasures' positions
treasures = [(1, 1), (1, 0), (2, 0), (2, 1), (3, 1), (5, 3)]
print(shortest_path(treasures))
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