All Expressions

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Problem

Given a sequence of integers, generate all expressions that can be
made from the integers, addition (+), subtraction (-), multiplication
(*), and parentheses, without changing the order of integers.
Calculate the expressions and print the values in ascending order,
removing duplicates.

For example, if the sequence is "1, 9, 13", then possible expressions are:
(1 + (9 + 13))
(1 - (9 + 13))
(1 * (9 + 13))
(1 + (9 - 13))
(1 - (9 - 13))
(1 * (9 - 13))
(1 + (9 * 13))
(1 - (9 * 13))
(1 * (9 * 13))
((1 + 9) + 13)
((1 + 9) - 13)
((1 + 9) * 13)
((1 - 9) + 13)
((1 - 9) - 13)
((1 - 9) * 13)
((1 * 9) + 13)
((1 * 9) - 13)
((1 * 9) * 13)
plus those with redundant parentheses. And the output should be:
-116
-104
-21
-4
-3
5
22
23
117
118
130

Options

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Sample input:_

1 9 13

Sample output:

-116
-104
-21
-4
-3
5
22
23
117
118
130

Sample input:_

101 3 19 17

Sample output:

-32320
-27472
-3333
-1633
-1599
-868
-273
-225
-219
-171
-20
-7
27
61
62
68
95
96
100
101
102
106
107
134
140
141
175
196
208
209
267
301
305
339
373
421
427
475
505
606
626
748
1070
1343
1445
1845
1879
1959
1989
1993
2091
2205
2239
2686
3528
3744
3939
4040
4828
5474
5740
5774
7474
10908
31654
32926
33592
37774
97869

Sample input:_

3 3 3 1 1 1

Sample output:

-27
-24
-21
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
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
42
44
45
46
48
51
52
53
54
55
56
57
60
63
72
81

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Referer

Note that, they may contain spoilers.

• http://www.nmt.ne.jp/~ysas/diary/?200703a&to=200703081
• http://www.nmt.ne.jp/~ysas/diary/
• http://aolsearch.aol.com/aol/search?invocationType=wscreen-searchboxhtml&query=golf%20expressions
• http://mono.kmc.gr.jp/~yhara/files/anagol.html
• http://www.nmt.ne.jp/~ysas/diary/?20070531S1
• http://www.nmt.ne.jp/~ysas/diary/?200705
• http://aolsearch.aol.co.uk/aol/search?query=golf%20expressions&invocationType=sb_uk
• http://www.nmt.ne.jp/~ysas/diary/?200703
• http://www.nmt.ne.jp/~ysas/diary/?06150027
• http://shinh.skr.jp/m/?date=20070219
• http://www.nmt.ne.jp/~ysas/diary/?200705c
• http://shinh.skr.jp/m/?date=200702
• http://d.hatena.ne.jp/kstn/20070218
• http://d.hatena.ne.jp/kstn/20070218/1171779156
• http://shinh.skr.jp/m/?date=20070215
• http://72.14.235.104/search?q=cache:z41CbKUdWN8J:shinh.skr.jp/m/%3Fdate%3D20070305%252523c01+%E9%80%86%E3%83%9D%E3%83%BC%E3%83%A9%E3%83%B3%E3%83%89%E3%80%80infix+%E3%80%80%E5%A4%89%E6%8F%9B+postfix+%E9%96%A2%E6%95%B0%E3%80%80%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%A0&hl=ja&ct=clnk&cd=12&gl=jp
• http://shinh.skr.jp/m/

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