#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