括号号提供了一种仅使用左括号，空格和右括号（[ ]）表示大整数的简单方法。

括号号定义为一串或多对匹配的括号，[...]称为块，每串与它的邻居之间用零个或多个空格隔开。

每个块之间的空格数定义了它们之间的超操作。没有空格表示加法，1个空格表示乘法，2个空格表示乘幂，3个空格表示四次运算，依此类推。高阶超算术具有较高的优先级，因此四度运算发生在指数运算之前，指数运算发生在乘法运算之前，等等。它们也是右向关联的，因此a^b^c计算为a^(b^c)。（但a^b*c仍然是(a^b)*c。）

每个块可以为空（[]），也可以包含另一个括号。空块的值为0。非空块的值为所包含的括号号加1。

实施例：（^^是迭代幂次，^^^是pentation）

• [[]]具有值1，因为它是0（[]）加1
• [[[]]]的值为2，但是[[]][[]]因为两个（[[]]）相加，所以也是如此
• [[[]]] [[[[]]] [[[[]]]]][[[]]] 值20 =（2 *（（（2 ^ 3）+1））+ 2
• [[[]]] [[[[]]]] 具有值65536 = 2 ^^^ 3 = 2 ^^（2 ^^ 2）= 2 ^^ 4 == 2 ^（2 ^（2 ^ 2））
• [[[[]]]] [[[]]] [[]] 具有值7625597484987 = 3 ^^^（2 ^^^ 1）= 3 ^^^ 2 = 3 ^^ 3 = 3 ^（3 ^ 3）

在有效的括号中：

• 永远不会有前导或尾随空格。
• 总是会有至少一对匹配的括号。
• 所有左括号将具有匹配的右括号。
• 空格永远不会直接出现在的右侧[或左侧]。
• 该值始终是非负整数。

挑战

请注意，括号编号可能有许多形式具有相同的值。[[[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]]]和[[[]]] [[[[]]]]都代表16，但后者是短得多。

您面临的挑战是编写一种算法，尝试找到给定值的最短括号数字表示形式。例如，我认为表示16的最短方法是使用17个字符[[[]]] [[[[]]]]。

得分（更新）

令S为1到256（含）之间的整数以及以下10个值：

8191 13071 524287 2147483647 1449565302 1746268229 126528612 778085967 1553783038 997599288

（前四个是梅森素数，其余是随机数。）

为S中的所有内容生成最短括号编号的提交将获胜。您的分数是S中所有值的括号数字长度的总和（越小越好）。

使用您的代码，请提交所有S的括号编号列表，确切顺序并不十分重要。例如：

1=[[]]
2=[[[]]]
3=[[[[]]]]
...
2147483647=[...]
...

（我知道这不是最佳评分方法，但我没有设置为每次提交都运行一堆随机启发式测试。对不起:(）

规则

• 除了平凡的增量解决方案（）外，您可能无法对任何括号编号进行硬编码[], [[]], [[[]]], ...。您的程序实际上必须在寻找最佳的简短表示形式。（尽管结果可能不是最佳的。）
• 您的算法应适用于所有低于2,147,483,648（2 ^ 31）的非负整数。 您可能没有特别关注S中的值。
• 对于任何特定的输入，您的算法应在一台像样的现代计算机（〜2.5Ghz处理器，〜6GB RAM）上最多运行10分钟。
• 在（看似）平局的罕见机会中，最高投票率的获胜者获胜。
• 如果您复制另一个解决方案或修改该解决方案但没有注明出处，则将失去参赛资格。

Python 11455b

该解决方案采用贪婪的方法来寻找分解质数的方法，而不是穷举的方法。对于1-256，我需要9875b，而在该空间中，Martin可能是最佳的解决方案，而我需要8875b。

较大的乘法和乘幂结果表在较大的测试用例中会稍有改善。下面的解决方案大约花费了7分钟。将运行时间增加到30分钟以上对输出的影响最小。

我和马丁一样，对优先权也有疑问。我在限制操作选择方面的解决方案可能不是最佳的。

#!/usr/bin/env python

# http://codegolf.stackexchange.com/questions/35480/find-the-shortest-bracket-numbers

import sys, math

reps = {}
forwards = {}
backwards = {}

MAX = 2**31

TABLE_SIZE = 2**12

def op_dec(op):
    if op>1:
        return op-1
    return op

def rep_op(a,op,b):
    return rep_num(a) +  (" "*op) + rep_num(b)
def min_rep_op(a,op,b,op_max):
    return min_rep(a,op_max) +  (" "*op) + min_rep(b,op_dec(op_max))

def rep_num(a):
    return ("["*(a+1)) + ("]"*(a+1))

def min_rep(n,op_max):
    if n < 9:
        return ("["*(n+1))+("]"*(n+1))
    for op in range(op_max,-1,-1):
        if (n, op) in reps:
            return reps[(n, op)]
    for op in range(op_max,-1,-1):
        if (n, op) in backwards:
            a,op,b = backwards[(n, op)]
            return min_rep_op(a,op,b,op_max)
    else:
        for m in rep_list:
            c = m[0]
            if c < n:
                r = n - c
                for op in range(op_max,-1,-1):
                    if (c, op) in backwards:
                        a,op,b = backwards[(c, op)]
                        if r<10:
                            return ("["*r) + min_rep_op(a,op,b,op_max) + ("]"*r)
                        else:
                            return "[" + min_rep(r-1,op_max) + min_rep_op(a,op,b,op_max) + "]"
                break

def expand(a,op,b):
    if op == 0:
        n = a+b
    elif op == 1:
        n = a*b
    elif op == 2:
        if b*math.log10(a) > math.log10(MAX):
            n = MAX
        else: 
            n = a**b
    elif (a,op,b) in forwards:
        n = forwards[(a,op,b)]
    else: # tetration and higher
        t = a
        for i in xrange(b-1):
            t = expand(a,op-1,t)
            if t>=MAX:
                break
        n = t

    if n > MAX-1:
        n = MAX
    forwards[(a,op,b)] = n

    if (n, op) in backwards:
        c = len(rep_op(*backwards[(n, op)]))
        if c > (a*2+op+b*2):
            backwards[(n, op)] = (a,op,b)
    else:
        backwards[(n, op)] = (a,op,b)

    return n

t = 0

# populate the multiplication, exponentiation, and tetration tables
for op in range(1,4):
    for a in range((1,2,2,2)[op],TABLE_SIZE):
        for b in range((1,2,2,2)[op],TABLE_SIZE):
            t = expand(a,op,b)
            if t == MAX:
                break
rep_list = sorted(backwards.keys(),key=lambda x: x[0]*4-x[1],reverse=True)

for i in list(range(1, 257))+[8191,13071,524287,2147483647,1449565302,1746268229,126528612,778085967,1553783038,997599288]:
    t = min_rep(i,3)
    reps[i] = t
    print i, t

输出：

1 [[]]
2 [[[]]]
3 [[[[]]]]
4 [[[[[]]]]]
5 [[[[[[]]]]]]
6 [[[[[[[]]]]]]]
7 [[[[[[[[]]]]]]]]
8 [[[[[[[[[]]]]]]]]]
9 [[[[]]]]  [[[]]]
10 [[[[[[]]]]]] [[[]]]
11 [[[[[[[]]]]]] [[[]]]]
12 [[[[[[[]]]]]]] [[[]]]
13 [[[[[[[[]]]]]]] [[[]]]]
14 [[[[[[[[]]]]]]]] [[[]]]
15 [[[[[[]]]]]] [[[[]]]]
16 [[[]]]   [[[[]]]]
17 [[[[]]]   [[[[]]]]]
18 [[[[[[[]]]]]]] [[[[]]]]
19 [[[[[[[[]]]]]]] [[[[]]]]]
20 [[[[[[]]]]]] [[[[[]]]]]
21 [[[[[[[[]]]]]]]] [[[[]]]]
22 [[[[[[[]]]]]] [[[]]]] [[[]]]
23 [[[[[[[[]]]]]] [[[]]]] [[[]]]]
24 [[[[[[[[[]]]]]]]]] [[[[]]]]
25 [[[[[[]]]]]]  [[[]]]
26 [[[[[[[[]]]]]]] [[[]]]] [[[]]]
27 [[[[]]]]   [[[]]]
28 [[[[[[[[]]]]]]]] [[[[[]]]]]
29 [[[[[[[[[]]]]]]]] [[[[[]]]]]]
30 [[[[[[[]]]]]]] [[[[[[]]]]]]
31 [[[[[[[[]]]]]]] [[[[[[]]]]]]]
32 [[[]]]  [[[[[[]]]]]]
33 [[[[[[[]]]]]] [[[]]]] [[[[]]]]
34 [[[[]]]   [[[[]]]]] [[[]]]
35 [[[[[[[[]]]]]]]] [[[[[[]]]]]]
36 [[[[[[[]]]]]]]  [[[]]]
37 [[[[[[[[]]]]]]]  [[[]]]]
38 [[[[[[[[]]]]]]] [[[[]]]]] [[[]]]
39 [[[[[[[[]]]]]]] [[[]]]] [[[[]]]]
40 [[[[[[]]]]]] [[[]]] [[[[[]]]]]
41 [[[[[[[]]]]]] [[[]]] [[[[[]]]]]]
42 [[[[[[[[]]]]]]]] [[[[[[[]]]]]]]
43 [[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]]
44 [[[[[[[]]]]]] [[[]]]] [[[[[]]]]]
45 [[[[]]]]  [[[]]] [[[[[[]]]]]]
46 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[]]]
47 [[[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[]]]]
48 [[[[[[[[[]]]]]]]]] [[[[[[[]]]]]]]
49 [[[[[[[[]]]]]]]]  [[[]]]
50 [[[[[[]]]]]] [[[]]] [[[[[[]]]]]]
51 [[[[]]]   [[[[]]]]] [[[[]]]]
52 [[[[[[[[]]]]]]] [[[]]]] [[[[[]]]]]
53 [[[[[[[[[]]]]]]] [[[]]]] [[[[[]]]]]]
54 [[[[]]]]  [[[]]] [[[[[[[]]]]]]]
55 [[[[[[[]]]]]] [[[]]]] [[[[[[]]]]]]
56 [[[[[[[[[]]]]]]]]] [[[[[[[[]]]]]]]]
57 [[[[[[[[]]]]]]] [[[[]]]]] [[[[]]]]
58 [[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[]]]
59 [[[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[]]]]
60 [[[[[[[]]]]]]] [[[]]] [[[[[[]]]]]]
61 [[[[[[[[]]]]]]] [[[]]] [[[[[[]]]]]]]
62 [[[[[[[[]]]]]]] [[[[[[]]]]]]] [[[]]]
63 [[[[]]]]  [[[]]] [[[[[[[[]]]]]]]]
64 [[[[[]]]]]  [[[[]]]]
65 [[[[[[[[]]]]]]] [[[]]]] [[[[[[]]]]]]
66 [[[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]]]
67 [[[[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]]]]
68 [[[[]]]   [[[[]]]]] [[[[[]]]]]
69 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[]]]]
70 [[[[[[]]]]]] [[[]]] [[[[[[[[]]]]]]]]
71 [[[[[[[]]]]]] [[[]]] [[[[[[[[]]]]]]]]]
72 [[[[[[[]]]]]]] [[[]]] [[[[[[[]]]]]]]
73 [[[[[[[[]]]]]]] [[[]]] [[[[[[[]]]]]]]]
74 [[[[[[[[]]]]]]]  [[[]]]] [[[]]]
75 [[[[[[]]]]]] [[[[]]]] [[[[[[]]]]]]
76 [[[[[[[[]]]]]]] [[[[]]]]] [[[[[]]]]]
77 [[[[[[[]]]]]] [[[]]]] [[[[[[[[]]]]]]]]
78 [[[[[[[[]]]]]]] [[[]]]] [[[[[[[]]]]]]]
79 [[[[[[[[[]]]]]]] [[[]]]] [[[[[[[]]]]]]]]
80 [[[[[[]]]]]] [[[]]] [[[[[[[[[]]]]]]]]]
81 [[[[]]]]  [[[[[]]]]]
82 [[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[]]]
83 [[[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[]]]]
84 [[[[[[[[]]]]]]]] [[[]]] [[[[[[[]]]]]]]
85 [[[[]]]   [[[[]]]]] [[[[[[]]]]]]
86 [[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[]]]
87 [[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[[]]]]
88 [[[[[[[]]]]]] [[[]]]] [[[[[[[[[]]]]]]]]]
89 [[[[[[[[]]]]]] [[[]]]] [[[[[[[[[]]]]]]]]]]
90 [[[[[[]]]]]] [[[]]] [[[[]]]]  [[[]]]
91 [[[[[[[[]]]]]]] [[[]]]] [[[[[[[[]]]]]]]]
92 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[[]]]]]
93 [[[[[[[[]]]]]]] [[[[[[]]]]]]] [[[[]]]]
94 [[[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[]]]] [[[]]]
95 [[[[[[[[]]]]]]] [[[[]]]]] [[[[[[]]]]]]
96 [[[[[[[]]]]]]] [[[]]] [[[[[[[[[]]]]]]]]]
97 [[[[[[[[]]]]]]] [[[]]] [[[[[[[[[]]]]]]]]]]
98 [[[[[[[[]]]]]]]] [[[]]] [[[[[[[[]]]]]]]]
99 [[[[[[[]]]]]] [[[]]]] [[[[]]]]  [[[]]]
100 [[[[[[]]]]]] [[[]]]  [[[]]]
101 [[[[[[[]]]]]] [[[]]]  [[[]]]]
102 [[[[]]]   [[[[]]]]] [[[[[[[]]]]]]]
103 [[[[[]]]   [[[[]]]]] [[[[[[[]]]]]]]]
104 [[[[[[[[]]]]]]] [[[]]]] [[[[[[[[[]]]]]]]]]
105 [[[[[[]]]]]] [[[[]]]] [[[[[[[[]]]]]]]]
106 [[[[[[[[[]]]]]]] [[[]]]] [[[[[]]]]]] [[[]]]
107 [[[[[[[[[[]]]]]]] [[[]]]] [[[[[]]]]]] [[[]]]]
108 [[[[[[[]]]]]]] [[[]]] [[[[]]]]  [[[]]]
109 [[[[[[[[]]]]]]] [[[]]] [[[[]]]]  [[[]]]]
110 [[[[[[[]]]]]] [[[]]]] [[[[[[]]]]]] [[[]]]
111 [[[[[[[[]]]]]]]  [[[]]]] [[[[]]]]
112 [[[]]]   [[[[]]]] [[[[[[[[]]]]]]]]
113 [[[[]]]   [[[[]]]] [[[[[[[[]]]]]]]]]
114 [[[[[[[[]]]]]]] [[[[]]]]] [[[[[[[]]]]]]]
115 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[[[]]]]]]
116 [[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[[[]]]]]
117 [[[[[[[[]]]]]]] [[[]]]] [[[[]]]]  [[[]]]
118 [[[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[]]]] [[[]]]
119 [[[[]]]   [[[[]]]]] [[[[[[[[]]]]]]]]
120 [[[[[[]]]]]] [[[[]]]] [[[[[[[[[]]]]]]]]]
121 [[[[[[[]]]]]] [[[]]]]  [[[]]]
122 [[[[[[[[]]]]]]] [[[]]] [[[[[[]]]]]]] [[[]]]
123 [[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[[]]]]
124 [[[[[[[[]]]]]]] [[[[[[]]]]]]] [[[[[]]]]]
125 [[[[[[]]]]]]  [[[[]]]]
126 [[[[[[[[]]]]]]]] [[[]]] [[[[]]]]  [[[]]]
127 [[[[[[[[[]]]]]]]] [[[]]] [[[[]]]]  [[[]]]]
128 [[[]]]  [[[[[[[[]]]]]]]]
129 [[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[[]]]]
130 [[[[[[[[]]]]]]] [[[]]]] [[[[[[]]]]]] [[[]]]
131 [[[[[[[[[]]]]]]] [[[]]]] [[[[[[]]]]]] [[[]]]]
132 [[[[[[[]]]]]]] [[[]]] [[[[[[[]]]]]] [[[]]]]
133 [[[[[[[[]]]]]]] [[[[]]]]] [[[[[[[[]]]]]]]]
134 [[[[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]]]] [[[]]]
135 [[[[[[]]]]]] [[[[]]]] [[[[]]]]  [[[]]]
136 [[[[]]]   [[[[]]]]] [[[[[[[[[]]]]]]]]]
137 [[[[[]]]   [[[[]]]]] [[[[[[[[[]]]]]]]]]]
138 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[[[[]]]]]]]
139 [[[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[[[[]]]]]]]]
140 [[[[[[[[]]]]]]]] [[[]]] [[[[[[]]]]]] [[[]]]
141 [[[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[]]]] [[[[]]]]
142 [[[[[[[]]]]]] [[[]]] [[[[[[[[]]]]]]]]] [[[]]]
143 [[[[[[[[]]]]]]] [[[]]]] [[[[[[[]]]]]] [[[]]]]
144 [[[[[[[]]]]]]] [[[]]]  [[[]]]
145 [[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[[[[]]]]]]
146 [[[[[[[[]]]]]]] [[[]]] [[[[[[[]]]]]]]] [[[]]]
147 [[[[[[[[]]]]]]]] [[[[]]]] [[[[[[[[]]]]]]]]
148 [[[[[[[[]]]]]]]  [[[]]]] [[[[[]]]]]
149 [[[[[[[[[]]]]]]]  [[[]]]] [[[[[]]]]]]
150 [[[[[[]]]]]] [[[[]]]] [[[[[[]]]]]] [[[]]]
151 [[[[[[[]]]]]] [[[[]]]] [[[[[[]]]]]] [[[]]]]
152 [[[[[[[[]]]]]]] [[[[]]]]] [[[[[[[[[]]]]]]]]]
153 [[[[]]]   [[[[]]]]] [[[[]]]]  [[[]]]
154 [[[[[[[[]]]]]]]] [[[]]] [[[[[[[]]]]]] [[[]]]]
155 [[[[[[[[]]]]]]] [[[[[[]]]]]]] [[[[[[]]]]]]
156 [[[[[[[[]]]]]]] [[[]]]] [[[[[[[]]]]]]] [[[]]]
157 [[[[[[[[[]]]]]]] [[[]]]] [[[[[[[]]]]]]] [[[]]]]
158 [[[[[[[[[]]]]]]] [[[]]]] [[[[[[[]]]]]]]] [[[]]]
159 [[[[[[[[[]]]]]]] [[[]]]] [[[[[]]]]]] [[[[]]]]
160 [[[]]]   [[[[]]]] [[[[[[]]]]]] [[[]]]
161 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[[[[[]]]]]]]]
162 [[[[[[[]]]]]]] [[[[]]]] [[[[]]]]  [[[]]]
163 [[[[[[[[]]]]]]] [[[[]]]] [[[[]]]]  [[[]]]]
164 [[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[[[]]]]]
165 [[[[[[]]]]]] [[[[]]]] [[[[[[[]]]]]] [[[]]]]
166 [[[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[]]]] [[[]]]
167 [[[[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[]]]] [[[]]]]
168 [[[[[[[[]]]]]]]] [[[]]] [[[[[[[]]]]]]] [[[]]]
169 [[[[[[[[]]]]]]] [[[]]]]  [[[]]]
170 [[[[]]]   [[[[]]]]] [[[[[[]]]]]] [[[]]]
171 [[[[[[[[]]]]]]] [[[[]]]]] [[[[]]]]  [[[]]]
172 [[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[[[]]]]]
173 [[[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[[[]]]]]]
174 [[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[[[[[]]]]]]]
175 [[[[[[]]]]]]  [[[]]] [[[[[[[[]]]]]]]]
176 [[[]]]   [[[[]]]] [[[[[[[]]]]]] [[[]]]]
177 [[[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[]]]] [[[[]]]]
178 [[[[[[[[]]]]]] [[[]]]] [[[[[[[[[]]]]]]]]]] [[[]]]
179 [[[[[[[[[]]]]]] [[[]]]] [[[[[[[[[]]]]]]]]]] [[[]]]]
180 [[[[[[]]]]]] [[[[[]]]]] [[[[]]]]  [[[]]]
181 [[[[[[[]]]]]] [[[[[]]]]] [[[[]]]]  [[[]]]]
182 [[[[[[[[]]]]]]]] [[[]]] [[[[[[[[]]]]]]] [[[]]]]
183 [[[[[[[[]]]]]]] [[[]]] [[[[[[]]]]]]] [[[[]]]]
184 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[[[[[[]]]]]]]]]
185 [[[[[[[[]]]]]]]  [[[]]]] [[[[[[]]]]]]
186 [[[[[[[[]]]]]]] [[[[[[]]]]]]] [[[[[[[]]]]]]]
187 [[[[]]]   [[[[]]]]] [[[[[[[]]]]]] [[[]]]]
188 [[[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[]]]] [[[[[]]]]]
189 [[[[[[[[]]]]]]]] [[[[]]]] [[[[]]]]  [[[]]]
190 [[[[[[[[]]]]]]] [[[[]]]]] [[[[[[]]]]]] [[[]]]
191 [[[[[[[[[]]]]]]] [[[[]]]]] [[[[[[]]]]]] [[[]]]]
192 [[[]]]   [[[[]]]] [[[[[[[]]]]]]] [[[]]]
193 [[[[]]]   [[[[]]]] [[[[[[[]]]]]]] [[[]]]]
194 [[[[[[[[]]]]]]] [[[]]] [[[[[[[[[]]]]]]]]]] [[[]]]
195 [[[[[[]]]]]] [[[[]]]] [[[[[[[[]]]]]]] [[[]]]]
196 [[[[[[[[]]]]]]]] [[[]]]  [[[]]]
197 [[[[[[[[[]]]]]]]] [[[]]]  [[[]]]]
198 [[[[[[[]]]]]]] [[[[]]]] [[[[[[[]]]]]] [[[]]]]
199 [[[[[[[[]]]]]]] [[[[]]]] [[[[[[[]]]]]] [[[]]]]]
200 [[[[[[]]]]]] [[[[[]]]]] [[[[[[]]]]]] [[[]]]
201 [[[[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]]]] [[[[]]]]
202 [[[[[[[]]]]]] [[[]]]  [[[]]]] [[[]]]
203 [[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[[[[[[]]]]]]]]
204 [[[[]]]   [[[[]]]]] [[[[[[[]]]]]]] [[[]]]
205 [[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[[[[]]]]]]
206 [[[[[]]]   [[[[]]]]] [[[[[[[]]]]]]]] [[[]]]
207 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[]]]]  [[[]]]
208 [[[]]]   [[[[]]]] [[[[[[[[]]]]]]] [[[]]]]
209 [[[[[[[[]]]]]]] [[[[]]]]] [[[[[[[]]]]]] [[[]]]]
210 [[[[[[]]]]]] [[[[]]]] [[[[[[[[]]]]]]]] [[[]]]
211 [[[[[[[]]]]]] [[[[]]]] [[[[[[[[]]]]]]]] [[[]]]]
212 [[[[[[[[[]]]]]]] [[[]]]] [[[[[]]]]]] [[[[[]]]]]
213 [[[[[[[]]]]]] [[[]]] [[[[[[[[]]]]]]]]] [[[[]]]]
214 [[[[[[[[[[]]]]]]] [[[]]]] [[[[[]]]]]] [[[]]]] [[[]]]
215 [[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[[[[]]]]]]
216 [[[[[[[]]]]]]]  [[[[]]]]
217 [[[[[[[[]]]]]]] [[[[[[]]]]]]] [[[[[[[[]]]]]]]]
218 [[[[[[[[]]]]]]] [[[]]] [[[[]]]]  [[[]]]] [[[]]]
219 [[[[[[[[]]]]]]] [[[]]] [[[[[[[]]]]]]]] [[[[]]]]
220 [[[[[[[]]]]]] [[[]]]] [[[]]] [[[[[[]]]]]] [[[]]]
221 [[[[]]]   [[[[]]]]] [[[[[[[[]]]]]]] [[[]]]]
222 [[[[[[[[]]]]]]]  [[[]]]] [[[[[[[]]]]]]]
223 [[[[[[[[[]]]]]]]  [[[]]]] [[[[[[[]]]]]]]]
224 [[[]]]   [[[[]]]] [[[[[[[[]]]]]]]] [[[]]]
225 [[[[[[]]]]]] [[[[]]]]  [[[]]]
226 [[[[]]]   [[[[]]]] [[[[[[[[]]]]]]]]] [[[]]]
227 [[[[[]]]   [[[[]]]] [[[[[[[[]]]]]]]]] [[[]]]]
228 [[[[[[[[]]]]]]] [[[[]]]]] [[[[[[[]]]]]]] [[[]]]
229 [[[[[[[[[]]]]]]] [[[[]]]]] [[[[[[[]]]]]]] [[[]]]]
230 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[[[]]]]]] [[[]]]
231 [[[[[[[[]]]]]]]] [[[[]]]] [[[[[[[]]]]]] [[[]]]]
232 [[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[[[[[[[]]]]]]]]]
233 [[[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[[[[[[[]]]]]]]]]]
234 [[[[[[[]]]]]]] [[[[]]]] [[[[[[[[]]]]]]] [[[]]]]
235 [[[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[]]]] [[[[[[]]]]]]
236 [[[[[[[[[[]]]]]]]] [[[[[]]]]]] [[[]]]] [[[[[]]]]]
237 [[[[[[[[[]]]]]]] [[[]]]] [[[[[[[]]]]]]]] [[[[]]]]
238 [[[[]]]   [[[[]]]]] [[[[[[[[]]]]]]]] [[[]]]
239 [[[[[]]]   [[[[]]]]] [[[[[[[[]]]]]]]] [[[]]]]
240 [[[[[[]]]]]] [[[[[]]]]] [[[[[[[]]]]]]] [[[]]]
241 [[[[[[[]]]]]] [[[[[]]]]] [[[[[[[]]]]]]] [[[]]]]
242 [[[[[[[]]]]]] [[[]]]] [[[]]] [[[[[[[]]]]]] [[[]]]]
243 [[[[]]]]  [[[[[[]]]]]]
244 [[[[[[[[]]]]]]] [[[]]] [[[[[[]]]]]]] [[[[[]]]]]
245 [[[[[[[[]]]]]]]] [[[[[[]]]]]] [[[[[[[[]]]]]]]]
246 [[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[[[[[]]]]]]]
247 [[[[[[[[]]]]]]] [[[[]]]]] [[[[[[[[]]]]]]] [[[]]]]
248 [[[[[[[[]]]]]]] [[[[[[]]]]]]] [[[[[[[[[]]]]]]]]]
249 [[[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[]]]] [[[[]]]]
250 [[[[[[]]]]]]  [[[]]] [[[[[[]]]]]] [[[]]]
251 [[[[[[[]]]]]]  [[[]]] [[[[[[]]]]]] [[[]]]]
252 [[[[[[[[]]]]]]]] [[[[]]]] [[[[[[[]]]]]]] [[[]]]
253 [[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[[[[]]]]]] [[[]]]]
254 [[[[[[[[[]]]]]]]] [[[]]] [[[[]]]]  [[[]]]] [[[]]]
255 [[[[]]]   [[[[]]]]] [[[[[[]]]]]] [[[[]]]]
256 [[[[[]]]]]   [[[]]]
8191 [[[[[[[[[]]]]]]] [[[]]]] [[[[[[[[]]]]]]]] [[[[[[]]]]]] [[[]]] [[[[]]]] [[[[]]]]]
13071 [[[[[[[[[[[]]]]]]] [[[[]]]] [[[[]]]]  [[[]]]] [[[[[]]]]]] [[[]]]] [[[[[[]]]]]] [[[]]]]
524287 [[[[[[[[[]]]]]]] [[[[]]]]] [[[]]] [[[[[[[[]]]]]]]] [[[[]]]] [[[[[[[[]]]]]]] [[[]]] [[[[[[[]]]]]]]] [[[[]]]] [[[[]]]]]
2147483647 [[[[[[[[[[[]]]]]]]]] [[[[]]]] [[[[[[[[]]]]]]]] [[[]]]] [[[[]]]] [[[[[[[[[]]]]]]] [[[]]]] [[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]]][[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[[[[[]]]]]]] [[[[[[]]]]]]  [[[[]]]]]
1449565302 [[[[[[[[[[[[[]]]]]]]] [[[]]] [[[[]]]]  [[[]]]] [[[[[]]]]]] [[[]]]] [[[]]]] [[[[[[[[[]]]]]] [[[]]]] [[[]]]] [[[[[[[]]]]]]]] [[[[[[]]]]]] [[[]]][[[[[[[[]]]]]]] [[[]]]] [[[[]]]] [[[[[[[[[]]]]]]]] [[[[[]]]]]]  [[[[]]]]]
1746268229 [[[[[[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]]]] [[[[]]]  [[[[[]]]]]] [[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[[[[[[]]]]]]] [[[[]]]]]][[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[[[[[[]]]]]]]] [[[[[]]]]]  [[[[]]]]]
126528612 [[[[[[[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]]]] [[[[[]]]]]] [[[[[[[]]]]]]] [[[]]]] [[[[[[[[]]]]]]]][[[[[[[]]]]]]  [[[]]] [[[[[[]]]]]] [[[]]]] [[[]]]  [[[[]]]]]
778085967 [[[[[[[[[[]]]]]]]] [[[[[[[]]]]]]] [[[[[[[[]]]]]]] [[[]]]] [[[]]]] [[[[[[[[[]]]]]]] [[[]]]] [[[[[]]]]]] [[[[[[]]]]]][[[[[[[[[]]]]]] [[[]]] [[[[[]]]]]] [[[]]]] [[[]]]]  [[[[[]]]]]]
1553783038 [[[[[[[[[]]]]]]] [[[]]]] [[[[]]]] [[[[[[]]]]]]  [[[]]] [[[[[[[[[]]]]]]] [[[]]] [[[[[[[[[]]]]]]]]]] [[[[[[]]]]]] [[[]]]][[[[]]]   [[[[]]]] [[[[[[[]]]]]]] [[[]]]] [[[[[[[]]]]]]]  [[[[]]]]]
997599288 [[[[[[[[]]]]]] [[[]]]] [[[[[[[[]]]]]]]] [[[[[[[]]]]]] [[[]]]] [[[]]]  [[[[[[]]]]]] [[[[[[[]]]]]] [[[]]]] [[[]]][[[[[[[[]]]]]]]  [[[]]]] [[[[]]]]  [[[[]]]]  [[[[]]]]]

Mathematica

注意：此算法永远无法在较大的测试数字附近获得任何结果。我需要一种完全不同的方法，因此我将其保留不变，以供其他人检查他们的较低数字。您可能认为此提交无效。

这是前256个数字的开始（其他数字是在我开始之后添加的，我可能需要为这些数字找到一个单独的解决方案）

1=[[]]
2=[[[]]]
3=[[[[]]]]
4=[[[[[]]]]]
5=[[[[[[]]]]]]
6=[[[[[[[]]]]]]]
7=[[[[[[[[]]]]]]]]
8=[[[]]]  [[[[]]]]
9=[[[[]]]]  [[[]]]
10=[[[[[]]]]  [[[]]]]
11=[[[[[[]]]]  [[[]]]]]
12=[[[[[]]]]] [[[[]]]]
13=[[[[[[]]]]] [[[[]]]]]
14=[[[[[[[]]]]] [[[[]]]]]]
15=[[[[[[]]]]]] [[[[]]]]
16=[[[]]]   [[[[]]]]
17=[[[[]]]   [[[[]]]]]
18=[[[[[]]]   [[[[]]]]]]
19=[[[[[[]]]   [[[[]]]]]]]
20=[[[[[[]]]]]] [[[[[]]]]]
21=[[[[[[[]]]]]] [[[[[]]]]]]
22=[[[[[[[[]]]]]] [[[[[]]]]]]]
23=[[[[[[[[[]]]]]] [[[[[]]]]]]]]
24=[[[[[[[]]]]]]] [[[[[]]]]]
25=[[[[[[]]]]]]  [[[]]]
26=[[[[[[[]]]]]]  [[[]]]]
27=[[[[]]]]   [[[]]]
28=[[[[[]]]]   [[[]]]]
29=[[[[[[]]]]   [[[]]]]]
30=[[[[[[[]]]]   [[[]]]]]]
31=[[[[[[[[]]]]   [[[]]]]]]]
32=[[[]]]  [[[[[[]]]]]]
33=[[[[]]]  [[[[[[]]]]]]]
34=[[[[[]]]  [[[[[[]]]]]]]]
35=[[[[[[]]]  [[[[[[]]]]]]]]]
36=[[[[[[[]]]]]]]  [[[]]]
37=[[[[[[[[]]]]]]]  [[[]]]]
38=[[[[[[[[[]]]]]]]  [[[]]]]]
39=[[[[[[[[[[]]]]]]]  [[[]]]]]]
40=[[[]]]  [[[[]]]] [[[[[[]]]]]]
41=[[[[]]]  [[[[]]]] [[[[[[]]]]]]]
42=[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]
43=[[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]]
44=[[[[[[]]]]  [[[]]]]] [[[[[]]]]]
45=[[[[]]]]  [[[]]] [[[[[[]]]]]]
46=[[[[[]]]]  [[[]]] [[[[[[]]]]]]]
47=[[[[[[]]]]  [[[]]] [[[[[[]]]]]]]]
48=[[[]]]   [[[[]]]] [[[[]]]]
49=[[[[[[[[]]]]]]]]  [[[]]]
50=[[[[[[[[[]]]]]]]]  [[[]]]]
51=[[[[[[[[[[]]]]]]]]  [[[]]]]]
52=[[[[[[[]]]]]]  [[[]]]] [[[]]]
53=[[[[[[[[]]]]]]  [[[]]]] [[[]]]]
54=[[[[]]]]   [[[]]] [[[]]]
55=[[[[[]]]]   [[[]]] [[[]]]]
56=[[[[[]]]]   [[[]]]] [[[]]]
57=[[[[[[]]]]   [[[]]]] [[[]]]]
58=[[[[[[]]]]   [[[]]]]] [[[]]]
59=[[[[[[[]]]]   [[[]]]]] [[[]]]]
60=[[[[[[[]]]]   [[[]]]]]] [[[]]]
61=[[[[[[[[]]]]   [[[]]]]]] [[[]]]]
62=[[[[[[[[]]]]   [[[]]]]]]] [[[]]]
63=[[[[]]]]  [[[]]] [[[[[[[[]]]]]]]]
64=[[[[[]]]]]  [[[[]]]]
65=[[[[[[]]]]]  [[[[]]]]]
66=[[[[[[[]]]]]  [[[[]]]]]]
67=[[[[[[[[]]]]]  [[[[]]]]]]]
68=[[[[[[[[[]]]]]  [[[[]]]]]]]]
69=[[[[[[[[[[]]]]]  [[[[]]]]]]]]]
70=[[[[[[[[[[[]]]]]  [[[[]]]]]]]]]]
71=[[[[[[[[[[[[]]]]]  [[[[]]]]]]]]]]]
72=[[[[[[[]]]]]]]  [[[]]] [[[]]]
73=[[[[[[[[]]]]]]]  [[[]]] [[[]]]]
74=[[[[[[[[]]]]]]]  [[[]]]] [[[]]]
75=[[[[[[]]]]]]  [[[]]] [[[[]]]]
76=[[[[[[[]]]]]]  [[[]]] [[[[]]]]]
77=[[[[[[[[]]]]]]  [[[]]] [[[[]]]]]]
78=[[[[[[[]]]]]]  [[[]]]] [[[[]]]]
79=[[[[[[[[]]]]]]  [[[]]]] [[[[]]]]]
80=[[[]]]   [[[[]]]] [[[[[[]]]]]]
81=[[[[]]]]  [[[[[]]]]]
82=[[[[[]]]]  [[[[[]]]]]]
83=[[[[[[]]]]  [[[[[]]]]]]]
84=[[[[[[[]]]]  [[[[[]]]]]]]]
85=[[[[[[[[]]]]  [[[[[]]]]]]]]]
86=[[[[[[[[[]]]]  [[[[[]]]]]]]]]]
87=[[[[[[]]]]   [[[]]]]] [[[[]]]]
88=[[[[[[[]]]]   [[[]]]]] [[[[]]]]]
89=[[[[[[[[]]]]   [[[]]]]] [[[[]]]]]]
90=[[[[[[[]]]]   [[[]]]]]] [[[[]]]]
91=[[[[[[[[]]]]   [[[]]]]]] [[[[]]]]]
92=[[[[[[[[[]]]]   [[[]]]]]] [[[[]]]]]]
93=[[[[[[[[]]]]   [[[]]]]]]] [[[[]]]]
94=[[[[[[[[[]]]]   [[[]]]]]]] [[[[]]]]]
95=[[[[[[]]]   [[[[]]]]]]] [[[[[[]]]]]]
96=[[[]]]  [[[[[[]]]]]] [[[[]]]]
97=[[[[]]]  [[[[[[]]]]]] [[[[]]]]]
98=[[[[[[[[]]]]]]]]  [[[]]] [[[]]]
99=[[[[]]]  [[[[[[]]]]]]] [[[[]]]]
100=[[[[[]]]]  [[[]]]]  [[[]]]
101=[[[[[[]]]]  [[[]]]]  [[[]]]]
102=[[[[[[[]]]]  [[[]]]]  [[[]]]]]
103=[[[[[[[[]]]]  [[[]]]]  [[[]]]]]]
104=[[[[[[[]]]]]]  [[[]]]] [[[[[]]]]]
105=[[[[[[[[]]]]]]  [[[]]]] [[[[[]]]]]]
106=[[[[[[[[[]]]]]]  [[[]]]] [[[[[]]]]]]]
107=[[[[[[[[[[]]]]]]  [[[]]]] [[[[[]]]]]]]]
108=[[[[]]]]   [[[]]] [[[[[]]]]]
109=[[[[[]]]]   [[[]]] [[[[[]]]]]]
110=[[[[[[]]]]   [[[]]] [[[[[]]]]]]]
111=[[[[[[[[]]]]]]]  [[[]]]] [[[[]]]]
112=[[[[[]]]]   [[[]]]] [[[[[]]]]]
113=[[[[[[]]]]   [[[]]]] [[[[[]]]]]]
114=[[[[[[[]]]]   [[[]]]] [[[[[]]]]]]]
115=[[[[[[[[]]]]   [[[]]]] [[[[[]]]]]]]]
116=[[[[[[]]]]   [[[]]]]] [[[[[]]]]]
117=[[[[[[[]]]]   [[[]]]]] [[[[[]]]]]]
118=[[[[[[[[]]]]   [[[]]]]] [[[[[]]]]]]]
119=[[[[]]]   [[[[]]]]] [[[[[[[[]]]]]]]]
120=[[[[[[[]]]]   [[[]]]]]] [[[[[]]]]]
121=[[[[[[]]]]  [[[]]]]]  [[[]]]
122=[[[[[[[]]]]  [[[]]]]]  [[[]]]]
123=[[[[[[[[]]]]  [[[]]]]]  [[[]]]]]
124=[[[[[[[[[]]]]  [[[]]]]]  [[[]]]]]]
125=[[[[[[]]]]]]  [[[[]]]]
126=[[[[[[[]]]]]]  [[[[]]]]]
127=[[[[[[[[]]]]]]  [[[[]]]]]]
128=[[[]]]  [[[[[[[[]]]]]]]]
129=[[[[]]]  [[[[[[[[]]]]]]]]]
130=[[[[[]]]  [[[[[[[[]]]]]]]]]]
131=[[[[[[]]]  [[[[[[[[]]]]]]]]]]]
132=[[[[[[[]]]]]  [[[[]]]]]] [[[]]]
133=[[[[[[[[]]]]]  [[[[]]]]]] [[[]]]]
134=[[[[[[[[]]]]]  [[[[]]]]]]] [[[]]]
135=[[[[]]]]   [[[]]] [[[[[[]]]]]]
136=[[[[[]]]]   [[[]]] [[[[[[]]]]]]]
137=[[[[[[]]]]   [[[]]] [[[[[[]]]]]]]]
138=[[[[[[[]]]]   [[[]]] [[[[[[]]]]]]]]]
139=[[[[[[[[]]]]   [[[]]] [[[[[[]]]]]]]]]]
140=[[[[[]]]]   [[[]]]] [[[[[[]]]]]]
141=[[[[[[]]]]   [[[]]]] [[[[[[]]]]]]]
142=[[[[[[[]]]]   [[[]]]] [[[[[[]]]]]]]]
143=[[[[[[[[]]]]   [[[]]]] [[[[[[]]]]]]]]]
144=[[[[[[[]]]]]]]  [[[]]] [[[[[]]]]]
145=[[[[[[]]]]   [[[]]]]] [[[[[[]]]]]]
146=[[[[[[[]]]]   [[[]]]]] [[[[[[]]]]]]]
147=[[[[[[[[]]]]]]]]  [[[]]] [[[[]]]]
148=[[[[[[[[[]]]]]]]]  [[[]]] [[[[]]]]]
149=[[[[[[[[[[]]]]]]]]  [[[]]] [[[[]]]]]]
150=[[[[[[]]]]]]  [[[]]] [[[[[[[]]]]]]]
151=[[[[[[[]]]]]]  [[[]]] [[[[[[[]]]]]]]]
152=[[[[[[[[[]]]]]]]  [[[]]]]] [[[[[]]]]]
153=[[[[]]]   [[[[]]]]] [[[[]]]]  [[[]]]
154=[[[[[]]]   [[[[]]]]] [[[[]]]]  [[[]]]]
155=[[[[[[[[]]]]   [[[]]]]]]] [[[[[[]]]]]]
156=[[[[[[[]]]]]]  [[[]]]] [[[[[[[]]]]]]]
157=[[[[[[[[]]]]]]  [[[]]]] [[[[[[[]]]]]]]]
158=[[[[[[[[]]]]]]  [[[]]]] [[[[]]]]] [[[]]]
159=[[[[[[[[]]]]]]  [[[]]]] [[[]]]] [[[[]]]]
160=[[[]]]  [[[[[[]]]]]] [[[[[[]]]]]]
161=[[[[]]]  [[[[[[]]]]]] [[[[[[]]]]]]]
162=[[[[]]]]  [[[[[]]]]] [[[]]]
163=[[[[[]]]]  [[[[[]]]]] [[[]]]]
164=[[[[[]]]]  [[[[[]]]]]] [[[]]]
165=[[[[[[]]]]  [[[[[]]]]]] [[[]]]]
166=[[[[[[]]]]  [[[[[]]]]]]] [[[]]]
167=[[[[[[[]]]]  [[[[[]]]]]]] [[[]]]]
168=[[[[[[[]]]]  [[[[[]]]]]]]] [[[]]]
169=[[[[[[]]]]] [[[[]]]]]  [[[]]]
170=[[[[[[[]]]]] [[[[]]]]]  [[[]]]]
171=[[[[[[[[]]]]] [[[[]]]]]  [[[]]]]]
172=[[[[[[[[[]]]]] [[[[]]]]]  [[[]]]]]]
173=[[[[[[[[[[]]]]] [[[[]]]]]  [[[]]]]]]]
174=[[[[[[]]]]   [[[]]]]] [[[[[[[]]]]]]]
175=[[[[[[]]]]]]  [[[]]] [[[[[[[[]]]]]]]]
176=[[[]]]   [[[[]]]] [[[[[[]]]]  [[[]]]]]
177=[[[[[[[]]]]   [[[]]]]] [[[]]]] [[[[]]]]
178=[[[[[[[[]]]]   [[[]]]]] [[[]]]] [[[[]]]]]
179=[[[[[[[[[]]]]   [[[]]]]] [[[]]]] [[[[]]]]]]
180=[[[[[[[]]]]]]]  [[[]]] [[[[[[]]]]]]
181=[[[[[[[[]]]]]]]  [[[]]] [[[[[[]]]]]]]
182=[[[[[[[[[]]]]]]]  [[[]]] [[[[[[]]]]]]]]
183=[[[[[[[[[[]]]]]]]  [[[]]] [[[[[[]]]]]]]]]
184=[[[[[]]]]  [[[]]] [[[[[[]]]]]]] [[[[[]]]]]
185=[[[[[[[[]]]]]]]  [[[]]]] [[[[[[]]]]]]
186=[[[[[[[[[]]]]]]]  [[[]]]] [[[[[[]]]]]]]
187=[[[[]]]   [[[[]]]]] [[[[[[]]]]  [[[]]]]]
188=[[[[[]]]   [[[[]]]]] [[[[[[]]]]  [[[]]]]]]
189=[[[[]]]]   [[[]]] [[[[[[[[]]]]]]]]
190=[[[[[]]]]   [[[]]] [[[[[[[[]]]]]]]]]
191=[[[[[[]]]]   [[[]]] [[[[[[[[]]]]]]]]]]
192=[[[[[]]]]]  [[[[]]]] [[[[]]]]
193=[[[[[[]]]]]  [[[[]]]] [[[[]]]]]
194=[[[[[[[]]]]]  [[[[]]]] [[[[]]]]]]
195=[[[[[[]]]]]  [[[[]]]]] [[[[]]]]
196=[[[[[[[]]]]] [[[[]]]]]]  [[[]]]
197=[[[[[[[[]]]]] [[[[]]]]]]  [[[]]]]
198=[[[[[[[]]]]]  [[[[]]]]]] [[[[]]]]
199=[[[[[[[[]]]]]  [[[[]]]]]] [[[[]]]]]
200=[[[[[]]]]  [[[]]]]  [[[]]] [[[]]]
201=[[[[[[]]]]  [[[]]]]  [[[]]] [[[]]]]
202=[[[[[[]]]]  [[[]]]]  [[[]]]] [[[]]]
203=[[[[[[[]]]]  [[[]]]]  [[[]]]] [[[]]]]
204=[[[[[[[[[]]]]]  [[[[]]]]]]]] [[[[]]]]
205=[[[[[[[[[[]]]]]  [[[[]]]]]]]] [[[[]]]]]
206=[[[[[[[[]]]]  [[[]]]]  [[[]]]]]] [[[]]]
207=[[[[[[[[[[]]]]]  [[[[]]]]]]]]] [[[[]]]]
208=[[[]]]   [[[[]]]] [[[[[[]]]]] [[[[]]]]]
209=[[[[]]]   [[[[]]]] [[[[[[]]]]] [[[[]]]]]]
210=[[[[[[[]]]]   [[[]]]]]] [[[[[[[[]]]]]]]]
211=[[[[[[[[]]]]   [[[]]]]]] [[[[[[[[]]]]]]]]]
212=[[[[[[[[]]]]]]  [[[]]]] [[[]]]] [[[[[]]]]]
213=[[[[[[[[[[[[]]]]]  [[[[]]]]]]]]]]] [[[[]]]]
214=[[[[[[[[[[[[[]]]]]  [[[[]]]]]]]]]]] [[[[]]]]]
215=[[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[[[[]]]]]]
216=[[[[[[[]]]]]]]  [[[[]]]]
217=[[[[[[[[]]]]]]]  [[[[]]]]]
218=[[[[[[[[[]]]]]]]  [[[[]]]]]]
219=[[[[[[[[[[]]]]]]]  [[[[]]]]]]]
220=[[[[[[[[[[[]]]]]]]  [[[[]]]]]]]]
221=[[[[[[[[[[[[]]]]]]]  [[[[]]]]]]]]]
222=[[[[[[[[[[[[[]]]]]]]  [[[[]]]]]]]]]]
223=[[[[[[[[[[[[[[]]]]]]]  [[[[]]]]]]]]]]]
224=[[[[[]]]]   [[[]]]] [[[]]]  [[[[]]]]
225=[[[[[[]]]]]]  [[[]]] [[[[]]]]  [[[]]]
226=[[[[[[[]]]]]]  [[[]]] [[[[]]]]  [[[]]]]
227=[[[[[[[[]]]]]]  [[[]]] [[[[]]]]  [[[]]]]]
228=[[[[[[]]]]   [[[]]]] [[[]]]] [[[[[]]]]]
229=[[[[[[[]]]]   [[[]]]] [[[]]]] [[[[[]]]]]]
230=[[[[[[[[]]]]   [[[]]]] [[[]]]] [[[[[]]]]]]]
231=[[[[]]]  [[[[[[]]]]]]] [[[[[[[[]]]]]]]]
232=[[[[[[]]]]   [[[]]]]] [[[]]]  [[[[]]]]
233=[[[[[[[]]]]   [[[]]]]] [[[]]]  [[[[]]]]]
234=[[[[[[[]]]]]]  [[[]]]] [[[[]]]]  [[[]]]
235=[[[[[[[[]]]]]]  [[[]]]] [[[[]]]]  [[[]]]]
236=[[[[[[[]]]]   [[[]]]]] [[[]]]] [[[[[]]]]]
237=[[[[[[[[]]]]]]  [[[]]]] [[[[]]]]] [[[[]]]]
238=[[[[[]]]  [[[[[[]]]]]]]] [[[[[[[[]]]]]]]]
239=[[[[[[]]]  [[[[[[]]]]]]]] [[[[[[[[]]]]]]]]]
240=[[[]]]   [[[[]]]] [[[[[[]]]]]] [[[[]]]]
241=[[[[]]]   [[[[]]]] [[[[[[]]]]]] [[[[]]]]]
242=[[[[[[]]]]  [[[]]]]]  [[[]]] [[[]]]
243=[[[[]]]]  [[[[[[]]]]]]
244=[[[[[]]]]  [[[[[[]]]]]]]
245=[[[[[[]]]]  [[[[[[]]]]]]]]
246=[[[[[[[]]]]  [[[[[[]]]]]]]]]
247=[[[[[[[[]]]]  [[[[[[]]]]]]]]]]
248=[[[[[[[[[]]]]  [[[[[[]]]]]]]]]]]
249=[[[[[[]]]]  [[[[[]]]]]]] [[[[]]]]
250=[[[[[[]]]]]]  [[[[]]]] [[[]]]
251=[[[[[[[]]]]]]  [[[[]]]] [[[]]]]
252=[[[[[[[]]]]]]  [[[[]]]]] [[[]]]
253=[[[[[[[[]]]]]]  [[[[]]]]] [[[]]]]
254=[[[[[[[[]]]]]]  [[[[]]]]]] [[[]]]
255=[[[[[[[[[]]]]]]  [[[[]]]]]] [[[]]]]
256=[[[[[]]]]]   [[[]]]

前256个数字的总长度为7963字符。我不知道这是否是最佳选择。

忽略加法，在几分钟内发现了8191和13071的结果，而在几分钟内发现了524387的结果，

8191=[[[[[[[[]]]]]]  [[[[]]]]] [[[[[[]]]]]  [[[[]]]]]]
13071=[[[[[[[[]]]]]  [[[[]]]]]]  [[[]]]] [[[[]]]]
524387=[[[[[[[[]]]]]  [[[[]]]]] [[[[[]]]]]  [[[[]]]]] [[[[[[[]]]]]]  [[[[]]]]]]

在164个字符在一起。

这是代码：

ClearAll[repr, sl, i, j, op, re, frontop, rearop, lastop];
repr[n_] = "";
repr[0] = "[]";
(*Hard-code higher-order solutions*)
repr[65536] = "[[[]]]    [[[[]]]]";
repr[16] = "[[[]]]   [[[[]]]]";
repr[27] = "[[[[]]]]   [[[]]]";
repr[256] = "[[[[[]]]]]   [[[]]]";
repr[3125] = "[[[[[[]]]]]]   [[[]]]";
repr[46656] = "[[[[[[[]]]]]]]   [[[]]]";
repr[823543] = "[[[[[[[[]]]]]]]]   [[[]]]";
repr[16777216] = "[[[[[[[[[]]]]]]]]]   [[[]]]";
repr[387420489] = "[[[[[[[[[[]]]]]]]]]]   [[[]]]";
frontop[n_] = 2;
rearop[n_] = 2;
sl[n_] := If[repr[n] == "", Infinity, StringLength@repr@n];
n = 256;
op[0] := (# + #2) &
op[1] := (#*#2) &
op[2] := (#^#2) &
re[0] := (repr@# <> repr@#2) &
re[1] := (repr@# <> " " <> repr@#2) &
re[2] := (repr@# <> "  " <> repr@#2) &
For[i = 0, i < n, ++i,
  If[sl[i + 1] >= sl[i] + 2,
   repr[i + 1] = "[" <> repr[i] <> "]";
   frontop[i + 1] = 2; rearop[i + 1] = 2
   ];
  For[m = 0, m < 3, ++m,
   If[rearop[i] >= m,
    For[j = 1, j <= i, ++j,
     If[frontop[j] < m || (res = op[m][i, j]) > n, Break[]];
     rep = re[m][i, j];
     If[sl[res] > StringLength@rep ||
       sl[res] == StringLength@rep && m > frontop[res],
      repr[res] = rep;
      If[m == 2,
       frontop[res] = 2; rearop[res] = 1,
       frontop[res] = m;
       rearop[res] = m
       ]
      ]
     ]
    ];
   If[frontop[i] >= m,
    For[j = 1, j <= i, ++j,
     If[rearop[j] < m || (res = op[m][j, i]) > n, Break[]];
     rep = re[m][j, i];
     If[sl[res] > StringLength@rep ||
       sl[res] == StringLength@rep && m > frontop[res],
      repr[res] = rep;
      If[m == 2,
       frontop[res] = 2; rearop[res] = 1,
       frontop[res] = m;
       rearop[res] = m
       ]
      ]
     ]
    ]
   ];
  ];

我进行了详尽的搜索以求幂。没有四边或更高阶的运算。我只是手动尝试了高阶运算，只有极少数组合实际上产生的数字低于2 ³¹，因此我只是对有效的了硬编码。

编辑：我以前的解决方案并不关心优先级，它只是把事情放在一起。现在，我认为我的新代码已解决此问题，但前256个数字均未更改，也未更改8191（我检查过之前是有效的）...现在我要告诉我我的代码是否已实际修复该问题已为时已晚。我明天再看一眼，并添加一个解释，因为现在优先级检查有点麻烦（希望它可以减少搜索时间）。

编辑：好的，有一些预期的错误。我想我现在已经解决了，将总长度从1到256增加到7963。我不确定这是否是最佳选择，因为如果允许次优运算，则有可能从次优部分中找到更短的解决方案。当我设法稍微整理一下代码时，将进行解释。

Python 9219b

这是我的第二篇文章。我从头开始，尝试了一种新的数据排列方式，包括使用blist包进行排序的列表和字典，以及一些用于查找大型解决方案的新方法。我认为我有一个最佳的1-256。运行时间从30s增加到4m，将大型测试用例缩短了大约30个字节。

# https://pypi.python.org/pypi/blist/
# provides sorteddict
from blist import *

import math, sys

TABLE_SIZE=2**8
MAX_INT = 2**31

repr = sorteddict()

for i in range(12):
    repr[i] = sorteddict({(i*2+2,-1,-1):("["*(i+1)+"]"*(i+1), str(i))});

repr    [65536] = sorteddict({(18, 4, 4):("[[[]]]    [[[[]]]]", "2^^^3")}); # 2^^^3 = 2^^(2^^2) = 2^(2^(2^2))
repr       [16] = sorteddict({(17, 3, 3):("[[[]]]   [[[[]]]]", "2^^3")}); # 2^^3 = 2^(2^2)
repr       [27] = sorteddict({(17, 3, 3):("[[[[]]]]   [[[]]]", "3^^2")}); # 3^^2 = 3^3
repr      [256] = sorteddict({(19, 3, 3):("[[[[[]]]]]   [[[]]]", "4^^2")}); # 4^^2 = 4^4
repr     [3125] = sorteddict({(21, 3, 3):("[[[[[[]]]]]]   [[[]]]", "5^^2")}); # 5^^2 = 5^5
repr    [46656] = sorteddict({(23, 3, 3):("[[[[[[[]]]]]]]   [[[]]]", "6^^2")}); # 6^^2 = 6^6
repr   [823543] = sorteddict({(25, 3, 3):("[[[[[[[[]]]]]]]]   [[[]]]", "7^^2")}); # 7^^2 = 7^7
repr [16777216] = sorteddict({(27, 3, 3):("[[[[[[[[[]]]]]]]]]   [[[]]]", "8^^2")}); # 8^^2 = 8^8
repr[387420489] = sorteddict({(29, 3, 3):("[[[[[[[[[[]]]]]]]]]]   [[[]]]", "9^^2")}); # 9^^2 = 9^9

def expr_to_repr(a,op,b):
    rep_a = None
    for d,r in repr[a].iteritems():
        op_min, op_max = ((0,9),(1,9),(3,9))[op]
        if (d[1]==-1 or d[1]>=op_min) and d[2]<=op_max:
            rep_a = (d,r)
            break
    if not rep_a:
        rep_a = ((a*2+2,-1,-1),("["*(a+1)+"]"*(a+1), str(a)));

    rep_b = None
    for d,r in repr[b].iteritems():
        op_min, op_max = ((0,9),(1,9),(3,9))[op]
        if (d[1]==-1 or d[1]>=op_min) and d[2]<=op_max:
            rep_b = (d,r)
            break
    if not rep_b:
        rep_b = ((b*2+2,-1,-1),("["*(b+1)+"]"*(b+1), str(b)));

    r = rep_a[1][0] + " "*op + rep_b[1][0]

    return (
            (
                len(r),
                min(op, rep_a[0][1] if rep_a[0][1]!=-1 else op, rep_b[0][1] if rep_b[0][1]!=-1 else op), 
                max(op, rep_a[0][2], rep_b[0][2])
            ),
            ( 
                r, 
                expr_to_string(rep_a[1][1],op,rep_b[1][1])
            )
        );

def opsym(op):
    return ("+","*","^","^^")[op]

def expr_to_string(a,op,b):
    return str(a) + opsym(op) + str(b)

def calc(a,op,b):
    if op == 0:
        return min(a+b,MAX_INT)
    elif op == 1:
        return min(a*b,MAX_INT)
    elif op == 2:
        if (b*math.log10(a)>math.log10(MAX_INT)):
            return MAX_INT
        return min(a**b,MAX_INT)
    else:
        t = a
        for h in range(b):
            t = calc(a,op-1,t)
            if t>=MAX_INT:
                t = MAX_INT
                break
        return t

def populate_repr(a,op,b):
    o = (a,op,b)
    n = calc(*o)
    if n == MAX_INT:
        return n
    if n not in repr:
        repr[n] = sorteddict()
    r = expr_to_repr(*o)
    if conditional_replace_repr(n,r):
        for i in range(1,11):
            conditional_replace_repr(n+i,
                (
                    (
                        r[0][0]+i*2,
                        -1,
                        -1
                    ),
                    (
                        "["*i + r[1][0] + "]"*i,
                        "(" + r[1][1] + "+" + str(i) + ")"
                    )
                )
            )
    return n

def conditional_replace_repr(n,new_rep):
    if n not in repr:
        repr[n] = sorteddict()
        repr[n][new_rep[0]] = new_rep[1]
        return True
    found = None
    repl = False
    for d, r in repr[n].iteritems():
        if d[1] == new_rep[0][1] and d[2] == new_rep[0][2]:
            found = d
            if d[0] > new_rep[0][0]:
                repl = True
            break
    if (not found) or (found and repl):
        repr[n][new_rep[0]] = new_rep[1]
        if found:
            del repr[n][found]
        return True
    return False

def vaguely_decent_repr(n):
    if n <= TABLE_SIZE:
        return repr[n].iteritems().next()[1][0]
    if n in repr:
        return repr[n].iteritems().next()[1][0]
    else:
        keys = sorted(repr.keys(),reverse=True)
        best_rep = None
        tested = 0
        for i in keys:
            if i>n:
                continue
            if tested > 10:
                break
            tested += 1
            cand_rep = vaguely_decent_repr(n-i) + repr[i].iteritems().next()[1][0]
            if (not best_rep) or len(cand_rep) < len(best_rep):
                best_rep = cand_rep
        return best_rep



keys = repr.keys()
for k in keys:
    for d,r in repr[k].iteritems():
        for i in range(1,11):
            conditional_replace_repr(k+i,
                (
                    (
                        d[0]+i*2,
                        -1,
                        -1
                    ),
                    (
                        "["*i + r[0] + "]"*i,
                        "(" + r[1] + "+" + str(i) + ")"
                    )
                )
            )

# initialize the repr array with results of 1..256, 2+2 up to TABLE_SIZE^TABLE_SIZE
for row in range(2,TABLE_SIZE+1):
    for col in range(2,row):
        for op in range(1,3):
            populate_repr(row,op,col)
            if op > 1:
                populate_repr(col,op,row)
    for op in range(1,3):
        populate_repr(row,op,row)
    if row > 10:
        for frac in range(1,10):
            rep_a = repr[row-frac].iteritems().next()
            conditional_replace_repr(row,
                (
                    (
                        rep_a[0][0] + frac*2,
                        -1,
                        -1
                    ),
                    (
                        "["*frac + rep_a[1][0] + "]"*frac,
                        "(" + rep_a[1][1] + "+" + str(frac) + ")"
                    )
                )
            )
        for frac in range(10,row/2):
            rep_a = repr[frac].iteritems().next()
            rep_b = repr[row-frac].iteritems().next()
            conditional_replace_repr(row,
                (
                    (
                        rep_a[0][0]+rep_b[0][0],
                        min(rep_a[0][1],rep_b[0][1]),
                        max(rep_a[0][2],rep_b[0][2])
                    ),
                    (
                        rep_a[1][0] + rep_b[1][0],
                        rep_a[1][1] + "+" + rep_b[1][1]
                    )
                )
            )



# for n,reps in repr.iteritems():
#   for d,r in reps.iteritems():

for n in range(1,257):
    print str(n)+"="+repr[n].iteritems().next()[1][0]

for n in (8191,13071,524287,2147483647,1449565302,1746268229,126528612,778085967,1553783038,997599288):
    print str(n)+"="+vaguely_decent_repr(n)

输出：

1=[[]]
2=[[[]]]
3=[[[[]]]]
4=[[[[[]]]]]
5=[[[[[[]]]]]]
6=[[[[[[[]]]]]]]
7=[[[[[[[[]]]]]]]]
8=[[[]]]  [[[[]]]]
9=[[[[]]]]  [[[]]]
10=[[[[[]]]]  [[[]]]]
11=[[[[[[]]]]  [[[]]]]]
12=[[[[[]]]]] [[[[]]]]
13=[[[[[[]]]]] [[[[]]]]]
14=[[[[[[[]]]]] [[[[]]]]]]
15=[[[[[[]]]]]] [[[[]]]]
16=[[[]]]   [[[[]]]]
17=[[[[]]]   [[[[]]]]]
18=[[[[[]]]   [[[[]]]]]]
19=[[[[[[]]]   [[[[]]]]]]]
20=[[[[[[]]]]]] [[[[[]]]]]
21=[[[[[[[]]]]]] [[[[[]]]]]]
22=[[[[[[[[]]]]]] [[[[[]]]]]]]
23=[[[[[[[[[]]]]]] [[[[[]]]]]]]]
24=[[[[[[[]]]]]]] [[[[[]]]]]
25=[[[[[[]]]]]]  [[[]]]
26=[[[[[[[]]]]]]  [[[]]]]
27=[[[[]]]]   [[[]]]
28=[[[[[]]]]   [[[]]]]
29=[[[[[[]]]]   [[[]]]]]
30=[[[[[[[]]]]   [[[]]]]]]
31=[[[[[[[[]]]]   [[[]]]]]]]
32=[[[]]]  [[[[[[]]]]]]
33=[[[[]]]  [[[[[[]]]]]]]
34=[[[[[]]]  [[[[[[]]]]]]]]
35=[[[[[[]]]  [[[[[[]]]]]]]]]
36=[[[[[[[]]]]]]]  [[[]]]
37=[[[[[[[[]]]]]]]  [[[]]]]
38=[[[[[[[[[]]]]]]]  [[[]]]]]
39=[[[[[[[[[[]]]]]]]  [[[]]]]]]
40=[[[[[]]]]  [[[]]]] [[[[[]]]]]
41=[[[[]]]  [[[[]]]] [[[[[[]]]]]]]
42=[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]
43=[[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]]
44=[[[[[[]]]]  [[[]]]]] [[[[[]]]]]
45=[[[[]]]]  [[[]]] [[[[[[]]]]]]
46=[[[[[]]]]  [[[]]] [[[[[[]]]]]]]
47=[[[[[[]]]]  [[[]]] [[[[[[]]]]]]]]
48=[[[]]]   [[[[]]]] [[[[]]]]
49=[[[[[[[[]]]]]]]]  [[[]]]
50=[[[[[[[[[]]]]]]]]  [[[]]]]
51=[[[[[[[[[[]]]]]]]]  [[[]]]]]
52=[[[[[[[]]]]]]  [[[]]]] [[[]]]
53=[[[[[[[[]]]]]]  [[[]]]] [[[]]]]
54=[[[[]]]]   [[[]]] [[[]]]
55=[[[[[]]]]   [[[]]] [[[]]]]
56=[[[[[]]]]   [[[]]]] [[[]]]
57=[[[[[[]]]]   [[[]]]] [[[]]]]
58=[[[[[[]]]]   [[[]]]]] [[[]]]
59=[[[[[[[]]]]   [[[]]]]] [[[]]]]
60=[[[[[[[]]]]   [[[]]]]]] [[[]]]
61=[[[[[[[[]]]]   [[[]]]]]] [[[]]]]
62=[[[[[[[[]]]]   [[[]]]]]]] [[[]]]
63=[[[[]]]]  [[[]]] [[[[[[[[]]]]]]]]
64=[[[[[]]]]]  [[[[]]]]
65=[[[[[[]]]]]  [[[[]]]]]
66=[[[[[[[]]]]]  [[[[]]]]]]
67=[[[[[[[[]]]]]  [[[[]]]]]]]
68=[[[[[[[[[]]]]]  [[[[]]]]]]]]
69=[[[[[[[[[[]]]]]  [[[[]]]]]]]]]
70=[[[[[[[[[[[]]]]]  [[[[]]]]]]]]]]
71=[[[[[[[[[[[[]]]]]  [[[[]]]]]]]]]]]
72=[[[[[[[]]]]]]]  [[[]]] [[[]]]
73=[[[[[[[[]]]]]]]  [[[]]] [[[]]]]
74=[[[[[[[[]]]]]]]  [[[]]]] [[[]]]
75=[[[[[[]]]]]]  [[[]]] [[[[]]]]
76=[[[[[[[]]]]]]  [[[]]] [[[[]]]]]
77=[[[[[[[[]]]]]]  [[[]]] [[[[]]]]]]
78=[[[[[[[]]]]]]  [[[]]]] [[[[]]]]
79=[[[[[[[[]]]]]]  [[[]]]] [[[[]]]]]
80=[[[]]]   [[[[]]]] [[[[[[]]]]]]
81=[[[[]]]]  [[[[[]]]]]
82=[[[[[]]]]  [[[[[]]]]]]
83=[[[[[[]]]]  [[[[[]]]]]]]
84=[[[[[[[]]]]  [[[[[]]]]]]]]
85=[[[[[[[[]]]]  [[[[[]]]]]]]]]
86=[[[[[[[[[]]]]  [[[[[]]]]]]]]]]
87=[[[[[[]]]]   [[[]]]]] [[[[]]]]
88=[[[[[[[]]]]   [[[]]]]] [[[[]]]]]
89=[[[[[[[[]]]]   [[[]]]]] [[[[]]]]]]
90=[[[[[[[]]]]   [[[]]]]]] [[[[]]]]
91=[[[[[[[[]]]]   [[[]]]]]] [[[[]]]]]
92=[[[[[[[[[]]]]   [[[]]]]]] [[[[]]]]]]
93=[[[[[[[[]]]]   [[[]]]]]]] [[[[]]]]
94=[[[[[[[[[]]]]   [[[]]]]]]] [[[[]]]]]
95=[[[[[[]]]   [[[[]]]]]]] [[[[[[]]]]]]
96=[[[]]]  [[[[[[]]]]]] [[[[]]]]
97=[[[[]]]  [[[[[[]]]]]] [[[[]]]]]
98=[[[[[[[[]]]]]]]]  [[[]]] [[[]]]
99=[[[[]]]  [[[[[[]]]]]]] [[[[]]]]
100=[[[[[]]]]  [[[]]]]  [[[]]]
101=[[[[[[]]]]  [[[]]]]  [[[]]]]
102=[[[[[[[]]]]  [[[]]]]  [[[]]]]]
103=[[[[[[[[]]]]  [[[]]]]  [[[]]]]]]
104=[[[[[[[]]]]]]  [[[]]]] [[[[[]]]]]
105=[[[[[[[[]]]]]]  [[[]]]] [[[[[]]]]]]
106=[[[[[[[[[]]]]]]  [[[]]]] [[[[[]]]]]]]
107=[[[[[[[[[[]]]]]]  [[[]]]] [[[[[]]]]]]]]
108=[[[[]]]]   [[[]]] [[[[[]]]]]
109=[[[[[]]]]   [[[]]] [[[[[]]]]]]
110=[[[[[[]]]]   [[[]]] [[[[[]]]]]]]
111=[[[[[[[[]]]]]]]  [[[]]]] [[[[]]]]
112=[[[[[]]]]   [[[]]]] [[[[[]]]]]
113=[[[[[[]]]]   [[[]]]] [[[[[]]]]]]
114=[[[[[[[]]]]   [[[]]]] [[[[[]]]]]]]
115=[[[[[[[[]]]]   [[[]]]] [[[[[]]]]]]]]
116=[[[[[[]]]]   [[[]]]]] [[[[[]]]]]
117=[[[[[[[]]]]   [[[]]]]] [[[[[]]]]]]
118=[[[[[[[[]]]]   [[[]]]]] [[[[[]]]]]]]
119=[[[[]]]   [[[[]]]]] [[[[[[[[]]]]]]]]
120=[[[[[[[]]]]   [[[]]]]]] [[[[[]]]]]
121=[[[[[[]]]]  [[[]]]]]  [[[]]]
122=[[[[[[[]]]]  [[[]]]]]  [[[]]]]
123=[[[[[[[[]]]]  [[[]]]]]  [[[]]]]]
124=[[[[[[[[[]]]]  [[[]]]]]  [[[]]]]]]
125=[[[[[[]]]]]]  [[[[]]]]
126=[[[[[[[]]]]]]  [[[[]]]]]
127=[[[[[[[[]]]]]]  [[[[]]]]]]
128=[[[]]]  [[[[[[[[]]]]]]]]
129=[[[[]]]  [[[[[[[[]]]]]]]]]
130=[[[[[]]]  [[[[[[[[]]]]]]]]]]
131=[[[[[[]]]  [[[[[[[[]]]]]]]]]]]
132=[[[[[[[]]]]]  [[[[]]]]]] [[[]]]
133=[[[[[[[[]]]]]  [[[[]]]]]] [[[]]]]
134=[[[[[[[[]]]]]  [[[[]]]]]]] [[[]]]
135=[[[[]]]]   [[[]]] [[[[[[]]]]]]
136=[[[[[]]]]   [[[]]] [[[[[[]]]]]]]
137=[[[[[[]]]]   [[[]]] [[[[[[]]]]]]]]
138=[[[[[[[]]]]   [[[]]] [[[[[[]]]]]]]]]
139=[[[[[[[[]]]]   [[[]]] [[[[[[]]]]]]]]]]
140=[[[[[]]]]   [[[]]]] [[[[[[]]]]]]
141=[[[[[[]]]]   [[[]]]] [[[[[[]]]]]]]
142=[[[[[[[]]]]   [[[]]]] [[[[[[]]]]]]]]
143=[[[[[[[[]]]]   [[[]]]] [[[[[[]]]]]]]]]
144=[[[[[[[]]]]  [[[]]]]]]  [[[]]]
145=[[[[[[[[]]]]  [[[]]]]]]  [[[]]]]
146=[[[[[[[[[]]]]  [[[]]]]]]  [[[]]]]]
147=[[[[[[[[]]]]]]]]  [[[]]] [[[[]]]]
148=[[[[[[[[[]]]]]]]]  [[[]]] [[[[]]]]]
149=[[[[[[[[[]]]]]]]  [[[]]]] [[[[[]]]]]]
150=[[[[[[[[[]]]]]]]]  [[[]]]] [[[[]]]]
151=[[[[[[[]]]]]]  [[[]]] [[[[[[[]]]]]]]]
152=[[[[[[[[[]]]]]]]  [[[]]]]] [[[[[]]]]]
153=[[[[]]]   [[[[]]]]] [[[[]]]]  [[[]]]
154=[[[[[]]]   [[[[]]]]] [[[[]]]]  [[[]]]]
155=[[[[[[[[]]]]   [[[]]]]]]] [[[[[[]]]]]]
156=[[[[[[[]]]]]]  [[[]]]] [[[[[[[]]]]]]]
157=[[[[[[[[]]]]]]  [[[]]]] [[[[[[[]]]]]]]]
158=[[[[[[[[]]]]]]  [[[]]]] [[[[]]]]] [[[]]]
159=[[[[[[[[]]]]]]  [[[]]]] [[[]]]] [[[[]]]]
160=[[[]]]  [[[[[[]]]]]] [[[[[[]]]]]]
161=[[[[]]]  [[[[[[]]]]]] [[[[[[]]]]]]]
162=[[[[]]]]  [[[[[]]]]] [[[]]]
163=[[[[[]]]]  [[[[[]]]]] [[[]]]]
164=[[[[[]]]]  [[[[[]]]]]] [[[]]]
165=[[[[[[]]]]  [[[[[]]]]]] [[[]]]]
166=[[[[[[]]]]  [[[[[]]]]]]] [[[]]]
167=[[[[[[[]]]]  [[[[[]]]]]]] [[[]]]]
168=[[[[[[[]]]]  [[[[[]]]]]]]] [[[]]]
169=[[[[[[]]]]] [[[[]]]]]  [[[]]]
170=[[[[[[[]]]]] [[[[]]]]]  [[[]]]]
171=[[[[[[[[]]]]] [[[[]]]]]  [[[]]]]]
172=[[[[[[[[[]]]]] [[[[]]]]]  [[[]]]]]]
173=[[[[[[[[[[]]]]] [[[[]]]]]  [[[]]]]]]]
174=[[[[[[]]]]   [[[]]]]] [[[[[[[]]]]]]]
175=[[[[[[]]]]]]  [[[]]] [[[[[[[[]]]]]]]]
176=[[[]]]   [[[[]]]] [[[[[[]]]]  [[[]]]]]
177=[[[[[[[]]]]   [[[]]]]] [[[]]]] [[[[]]]]
178=[[[[[[[[]]]]   [[[]]]]] [[[]]]] [[[[]]]]]
179=[[[[[[[[[]]]]   [[[]]]]] [[[]]]] [[[[]]]]]]
180=[[[[[[[]]]]]]]  [[[]]] [[[[[[]]]]]]
181=[[[[[[[[]]]]]]]  [[[]]] [[[[[[]]]]]]]
182=[[[[[[[[[]]]]]]]  [[[]]] [[[[[[]]]]]]]]
183=[[[[[[[[]]]]]]  [[[]]]] [[[[[[[[]]]]]]]]]
184=[[[[[]]]]  [[[]]] [[[[[[]]]]]]] [[[[[]]]]]
185=[[[[[[[[]]]]]]]  [[[]]]] [[[[[[]]]]]]
186=[[[[[[[[[]]]]]]]  [[[]]]] [[[[[[]]]]]]]
187=[[[[]]]   [[[[]]]]] [[[[[[]]]]  [[[]]]]]
188=[[[[[]]]   [[[[]]]]] [[[[[[]]]]  [[[]]]]]]
189=[[[[]]]]   [[[]]] [[[[[[[[]]]]]]]]
190=[[[[[]]]]   [[[]]] [[[[[[[[]]]]]]]]]
191=[[[[[[]]]]   [[[]]] [[[[[[[[]]]]]]]]]]
192=[[[[[]]]]]  [[[[]]]] [[[[]]]]
193=[[[[[[]]]]]  [[[[]]]] [[[[]]]]]
194=[[[[[[[]]]]]  [[[[]]]] [[[[]]]]]]
195=[[[[[[]]]]]  [[[[]]]]] [[[[]]]]
196=[[[[[[[]]]]] [[[[]]]]]]  [[[]]]
197=[[[[[[[[]]]]] [[[[]]]]]]  [[[]]]]
198=[[[[[[[]]]]]  [[[[]]]]]] [[[[]]]]
199=[[[[[[[[]]]]]  [[[[]]]]]] [[[[]]]]]
200=[[[[[]]]]  [[[]]]]  [[[]]] [[[]]]
201=[[[[[[]]]]  [[[]]]]  [[[]]] [[[]]]]
202=[[[[[[]]]]  [[[]]]]  [[[]]]] [[[]]]
203=[[[[[[[]]]]  [[[]]]]  [[[]]]] [[[]]]]
204=[[[[[[[[[]]]]]  [[[[]]]]]]]] [[[[]]]]
205=[[[[[[[[[[]]]]]  [[[[]]]]]]]] [[[[]]]]]
206=[[[[[[[[]]]]  [[[]]]]  [[[]]]]]] [[[]]]
207=[[[[[[[[[[]]]]]  [[[[]]]]]]]]] [[[[]]]]
208=[[[[[[[]]]]]]  [[[]]]] [[[]]]  [[[[]]]]
209=[[[[]]]   [[[[]]]] [[[[[[]]]]] [[[[]]]]]]
210=[[[[[[[]]]]   [[[]]]]]] [[[[[[[[]]]]]]]]
211=[[[[[[[[]]]]   [[[]]]]]] [[[[[[[[]]]]]]]]]
212=[[[[[[[[]]]]]]  [[[]]]] [[[]]]] [[[[[]]]]]
213=[[[[[[[[[[[[]]]]]  [[[[]]]]]]]]]]] [[[[]]]]
214=[[[[[[[[[[[[[]]]]]  [[[[]]]]]]]]]]] [[[[]]]]]
215=[[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]] [[[[[[]]]]]]
216=[[[[[[[]]]]]]]  [[[[]]]]
217=[[[[[[[[]]]]]]]  [[[[]]]]]
218=[[[[[[[[[]]]]]]]  [[[[]]]]]]
219=[[[[[[[[[[]]]]]]]  [[[[]]]]]]]
220=[[[[[[[[[[[]]]]]]]  [[[[]]]]]]]]
221=[[[[[[[[[[[[]]]]]]]  [[[[]]]]]]]]]
222=[[[[[[[[[[[[[]]]]]]]  [[[[]]]]]]]]]]
223=[[[[[[[[[[[[[[]]]]]]]  [[[[]]]]]]]]]]]
224=[[[[[]]]]   [[[]]]] [[[]]]  [[[[]]]]
225=[[[[[[[[]]]]] [[[[]]]]]]]  [[[]]]
226=[[[[[[[[[]]]]] [[[[]]]]]]]  [[[]]]]
227=[[[[[[[[[[]]]]] [[[[]]]]]]]  [[[]]]]]
228=[[[[[[[[[[[]]]]] [[[[]]]]]]]  [[[]]]]]]
229=[[[[[[[[[[[[]]]]] [[[[]]]]]]]  [[[]]]]]]]
230=[[[[[[[[[[[[[]]]]] [[[[]]]]]]]  [[[]]]]]]]]
231=[[[[]]]  [[[[[[]]]]]]] [[[[[[[[]]]]]]]]
232=[[[[[[]]]]   [[[]]]]] [[[]]]  [[[[]]]]
233=[[[[[[[]]]]   [[[]]]]] [[[]]]  [[[[]]]]]
234=[[[[[[[]]]]]]  [[[]]]] [[[[]]]]  [[[]]]
235=[[[[[[[[]]]]]]  [[[]]]] [[[[]]]]  [[[]]]]
236=[[[[[[[]]]]   [[[]]]]] [[[]]]] [[[[[]]]]]
237=[[[[[[[[]]]]]]  [[[]]]] [[[[]]]]] [[[[]]]]
238=[[[[[]]]  [[[[[[]]]]]]]] [[[[[[[[]]]]]]]]
239=[[[[[[]]]  [[[[[[]]]]]]]] [[[[[[[[]]]]]]]]]
240=[[[]]]   [[[[]]]] [[[[[[]]]]]] [[[[]]]]
241=[[[[]]]   [[[[]]]] [[[[[[]]]]]] [[[[]]]]]
242=[[[[[[]]]]  [[[]]]]]  [[[]]] [[[]]]
243=[[[[]]]]  [[[[[[]]]]]]
244=[[[[[]]]]  [[[[[[]]]]]]]
245=[[[[[[]]]]  [[[[[[]]]]]]]]
246=[[[[[[[]]]]  [[[[[[]]]]]]]]]
247=[[[[[[[[]]]]  [[[[[[]]]]]]]]]]
248=[[[[[[[[[]]]]  [[[[[[]]]]]]]]]]]
249=[[[[[[]]]]  [[[[[]]]]]]] [[[[]]]]
250=[[[[[[]]]]]]  [[[[]]]] [[[]]]
251=[[[[[[[]]]]]]  [[[[]]]] [[[]]]]
252=[[[[[[[]]]]]]  [[[[]]]]] [[[]]]
253=[[[[[[[[]]]]]]  [[[[]]]]] [[[]]]]
254=[[[[[[[[]]]]]]  [[[[]]]]]] [[[]]]
255=[[[[[[[[[]]]]]]  [[[[]]]]]] [[[]]]]
256=[[[[[]]]]]   [[[]]]
8191=[[[[[[[[]]]]]]  [[[[]]]]] [[[[[[]]]]]  [[[[]]]]]]
13071=[[[[[[[[[]]]]  [[[]]]]]  [[[]]] [[[[]]]]   [[[]]] [[[[[]]]]]]]]
524287=[[[[]]]]   [[[]]] [[[[[[[[]]]]]]]] [[[[[[]]]]]  [[[[]]]]][[[[[[[[[[[]]]]]]  [[[]]]] [[[[]]]]]]  [[[[]]]]]]
2147483647=[[[[[[]]]]]]  [[[[]]]] [[[[[]]]]] [[[[]]]][[[[]]]   [[[[]]]]]  [[[[[]]]]][[[[[[[[[[[]]]]]]]  [[[[]]]]]]]]  [[[[]]]][[[[[[[[[[[[[[[]]]]]  [[[[]]]]]]]]]]] [[[[]]]]]]  [[[[[]]]]]]
1449565302=[[[[[[[[[]]]]  [[[]]]]]]  [[[]]]]] [[[[[[[[]]]]  [[[[[]]]]]]]]][[[[[]]]   [[[[]]]]] [[[[]]]]  [[[]]]]  [[[[]]]][[[[[[[[[[[]]]]]  [[[[]]]] [[[[]]]]]]]  [[[[[]]]]]]]]
1746268229=[[[[[[[]]]]]]]  [[[[]]]] [[[[]]]  [[[[[[[[]]]]]]]]][[[[]]]]   [[[]]]  [[[[[[]]]]]][[[[[[[[[[]]]]  [[[]]]]  [[[]]]] [[[]]]]]  [[[[[]]]]]]]
126528612=[[[[[[]]]]  [[[[[[]]]]]]]] [[[[[]]]]][[[[[[[]]]]]]]  [[[[[[[[]]]]]]]][[[[[[[[[]]]]]]  [[[]]]] [[[[[]]]]]]]  [[[[[]]]]]
778085967=[[[[[[[[[]]]]  [[[[[]]]]]]]]]] [[[[[[]]]]]]  [[[]]][[[[[[[]]]]]  [[[[]]]]]]  [[[[]]]][[[[[[[]]]]  [[[[[]]]]]]] [[[]]]]  [[[[[]]]]]
1553783038=[[[[[]]]  [[[[[[[[]]]]]]]]]] [[[[[[[]]]]   [[[]]]]]][[[[[]]]   [[[[]]]]]]  [[[[[]]]]][[[[[[[[[]]]]  [[[]]]]  [[[]]]]]] [[[]]]]  [[[[]]]][[[[[[[[]]]  [[[[[[]]]]]]]]  [[[[[[[]]]]]]]]]]
997599288=[[[[[]]]]   [[[]]] [[[[[[]]]]]]] [[[[[[[[]]]]]  [[[[]]]]]]][[[[[[[[]]]]]] [[[[[]]]]]]]  [[[[[[]]]]]][[[[[[[[[[]]]]   [[[]]]]]]] [[[]]]]  [[[[[[]]]]]]]

7944b适用于1-256

1275b适用于大型案例