#coding=utf-8
def init_set():
r10=range(10)
return [(i, j, k, l)
for i in r10 for j in r10 for k in r10 for l in r10
if (i != j and i != k and i != l and j != k and j != l and k != l) ]
#对给定的两组数，计算xAyB.不知道能不能更快些
def get_match_ab(target, source):
la, lb = 0, 0
for (i, t) in enumerate(target):
for (j, s) in enumerate(source):
if s == t:
if i == j:
la += 1
else:
lb += 1
#break this loop since we already found match
break
return (la, lb)
#by lancer
#思路很好，把原来的16次比较变成了8次
#经过timeit验证确实速度有所提高
def get_match_ab2(target, source):
table = [-1] * 10
la, lb = 0, 0
for i in xrange(len(source)):
table[source[i]] = i
for i in xrange(len(target)):
if table[target[i]] == i:
la += 1
elif table[target[i]] != -1:
lb += 1
return (la, lb)
#nums: the number_set list to be checked
#guess: last guess
#a, b: the number of aAbB
#@return: the rest number_sets which matche last guess
def check_and_remove(nums, guess, a, b):
rest_nums = []
for num_set in nums:
if (a, b) == get_match_ab(num_set, guess):
rest_nums.append(num_set)
return rest_nums
#计算在nums中选择target以后，所有ab分支里面的剩余组合个数
def calc_ab_counts(target, nums):
#a * 10 + b is used to indicate an "a & b" combination
ab_map = {}
#init ab_map
abs = (0, 1, 2, 3, 4, 10, 11, 12, 13, 20, 21, 22, 30, 31, 40)
for ab in abs:
ab_map[ab] = 0
#let's do the calculation
for num_set in nums:
(a, b) = get_match_ab(num_set, target)
ab_map[a * 10 + b] += 1
return [ab_map[ab] for ab in abs]
#计算一个选择相对于选择集的“标准差”
def calc_standard_deviation(target, nums):
ab_counts = calc_ab_counts(target, nums)
total = sum(ab_counts)
avg = float(total) / len(ab_counts)
sd = sum([(abc - avg)**2 for abc in ab_counts])
return sd
#根据现有集合寻找下一个集合
#采用“最小标准差”作为衡量标准
def next_guess(nums):
min_sd = 0
min_set = ()
touched = False
for num_set in nums:
sd = calc_standard_deviation(num_set, nums)
if not touched or min_sd > sd:
touched = True
min_set = num_set
min_sd = sd
return min_set
#根据现有集合寻找下一个集合
#随机选取，会有4-5个超过八次
def next_guess2(nums):
return nums[0]
#折衷的方法：小于500用最小标准差
def next_guess3(nums):
if len(nums) > 500:
return大专栏 python猜数字游戏快速求解解决方案> next_guess2(nums)
else:
return next_guess(nums)
#计算熵
import math
def calc_entropy(target, nums):
ab_counts = calc_ab_counts(target, nums)
total = sum(ab_counts)
hs = []
for abc in ab_counts:
h = 0
if abc:
p = float(abc) / total
h = p * math.log(p, 2)
hs.append(h)
return sum(hs)
#使用信息量作为衡量标准
def next_guess4(nums):
min_sd = 0
min_set = ()
touched = False
for num_set in nums:
sd = calc_entropy(num_set, nums)
if not touched or min_sd > sd:
touched = True
min_set = num_set
min_sd = sd
return min_set
def make_decision_tree():
from Queue import Queue
result = ((0, 1, 2, 3), {})
queue = Queue()
rest_nums = init_set()
queue.put((rest_nums, result))
#all xAyB set
abs = [(a, b) for a in range(5) for b in range(5 - a)]
while not queue.empty():
(rest_nums, (guess, mapping)) = queue.get()
for (a, b) in abs:
new_rest_nums = check_and_remove(rest_nums, guess, a, b)
length = len(new_rest_nums)
if length == 1:
if a != 4: #b can't be other than 0 when a == 4
mapping[a * 10 + b] = new_rest_nums[0]
elif length > 1:
new_guess = next_guess4(new_rest_nums) #TODO: 替换guess函数调整算法
new_result = (new_guess, {})
mapping[a * 10 + b] = new_result
queue.put((new_rest_nums, new_result))
return result
max_level = 0
level7_plus_tups = []
def pprint_result(result, level = 0):
global max_level, max_level_tup
(tup, mapping) = result
print tup
level += 1
if level > max_level:
max_level = level
if len(mapping) == 0:
print
else:
for key in mapping:
val = mapping[key]
#打印前缀
print u"%d|t" * level % tuple(range(1, level + 1)),
print u"%d:" % (level + 1),
#打印xAyB
print u"%dA%dB" % (key / 10, key % 10),
if len(val) == 4: #direct result
#打印结果
print val
if level >= 7:
level7_plus_tups.append((level, val))
else:
pprint_result(val, level)
#来玩玩www.iplaypy.com
print u"Notice: 4A0B is NOT included, since it result to Game Over"
pprint_result(make_decision_tree())
print
print u"max level is:", max_level + 1
print u"level7 plus tuples:"
for (level, tup) in level7_plus_tups:
print u"level:", level + 1, u"ttup:", tup
print