## 10827 - Maximum sum on a torus

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Sedefcho
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Posts: 374
Joined: Sun Jan 16, 2005 10:18 pm
Location: Bulgaria

### more test data ?

Can someone post more test data ?
I first had one O(N^4) solution which was getting TLE.

I rewrote everything so that I use now an O(N^3) algorithm.
The problem is that this algorithm now gets WA and I don't
find any bugs in my code. My code produces same output
as the one posted by liulike.

I also tried the strategy where we do not allow empty subrectangles
( that is we allow only subrectangles with both sizes >= 1).
If this strategy is followed I have the following output:

Code: Select all

``````1
15
9
-2
-10
-2
-10
1000
15
15
10
15
45``````
Now the point is ... Are there some critical cases or not really ?
Is somewhere on the web some test data posted ?

Sedefcho
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Posts: 374
Joined: Sun Jan 16, 2005 10:18 pm
Location: Bulgaria

### A variation of the "Maximum Contiguous Subarray Problem

I fixed my solution but in such a way that it makes my time complexity
O(N^4) in some special cases. With that fix I managed to get ACC
but of course my runtime is bad ( about 4 secs ).

Now I have the following question which arised from
the problem I had and from the way I fixed that problem.

1) The so-called "Maximum Contiguous Subarray Problem" is quite
well known and it is also well known that there is an O(N) solution
for it ( where N is the size ot the array ).

2) Suppose we change slightly the classical problem in the following
way: a) we treat our array as cyclic ; b) we are interested in the
"Maximum Contiguous Subarray" BUT we allow that subarray to
have a lenght of at most N. That means we do not want in our
subarray some elements of the original array to be included twice.

3) Now my question is : how do we decently modify the original
linear time algorithm so that it solves the changed problem and
so that it still remains a linear time algorithm.

Does anyone know some sources on the web on that particular
problem ( on that variation of the original "Maximum Contiguous Subarray Problem" ) ?

misof
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Posts: 430
Joined: Wed Jun 09, 2004 1:31 pm

### Re: A variation of the "Maximum Contiguous Subarray Pro

Sedefcho wrote:3) Now my question is : how do we decently modify the original
linear time algorithm so that it solves the changed problem and
so that it still remains a linear time algorithm.
Either the sequence you seek or the rest of the numbers form a contiguous part of the original sequence.
I.e. the situation looks either this way

Code: Select all

``BBBGGGGGGBB``
or this way:

Code: Select all

``GGGBBBBBGGG``
(G are the good numbers forming the maximum-sum subsequence).

The first case is exactly the original problem, the best solution for the second case is (sum of all numbers) minus (subsequence with the smallest sum, found using the same algorithm)

Sedefcho
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Posts: 374
Joined: Sun Jan 16, 2005 10:18 pm
Location: Bulgaria
Pretty simple ! Although not so obvious at first sight.

Thank you.

I implemented that idea and it made my running time 4 times
faster which is normal as now my whole algorithm really
has a O(N^3) time complexity. Now I get ACC in about
0.900 secs which is pretty good for me.

Thanks once again for the nice idea.

Chok
New poster
Posts: 48
Joined: Mon Jun 27, 2005 4:18 pm
Location: Hong Kong
Hi all,
There is lots of input in this thread, but i'm confuced abt the ouput. Please anyone provide the output for those case or other input. Another thing, if i got neg value then what should i print -(neg) or 0 (zero). My idea for this problem is generate all of the combination sum by row then generate circular/coloum-wise best sum. is it ok ? thankx in advance.

Sedefcho
A great helper
Posts: 374
Joined: Sun Jan 16, 2005 10:18 pm
Location: Bulgaria
Chok,

Right now I do not remember a lot of details about
that problem. I just remember it was difficult for me
to get ACC on it. Here is some sample I/O from
my ACC program.

INPUT

Code: Select all

``````13
2
-1 1
1 -1
5
1 2 4 3 -3
-1 3 1 -2 2
0 -2 -1 1 4
0 -3 5 -3 1
-4 2 0 2 -4
4
1 0 0 1
0 -1 -1 0
0 4 -1 0
1 0 0 2
2
-2 -5
-4 -3
1
-10
2
-2 -3
-4 -5
1
-10
1
1000

5
1 -1 0 0 -4
2 3 -2 -3 2
4 1 -1 5 0
3 -2 1 -3 2
-3 2 4 1 -4
5
1 2 4 3 -3
-1 3 1 -2 2
0 -2 -1 1 4
0 -3 5 -3 1
-4 2 0 2 -4
2
1 2
3 4
5
1 -1 0 0 -4
2 3 -2 -3 2
4 1 -1 5 0
3 -2 1 -3 2
-3 2 4 1 -4
3
1 2 3
4 5 6
7 8 9
``````

OUTPUT

Code: Select all

``````1
15
9
-2
-10
-2
-10
1000
15
15
10
15
45
``````
Try these test cases.

Moha
Experienced poster
Posts: 216
Joined: Tue Aug 31, 2004 1:02 am
Location: Tehran
Contact:

### WA again

My code passed all of these test cases, but still WA? can anybody help me?
My code is above and I think I have a misunderstanding in this problem, because my source code seemes to be correct.
this is my algorithm:
i double the input array, then i preform a simple 2d maximum sum in rectangle.
Oh my God, Where is the BUG??

shamim
A great helper
Posts: 498
Joined: Mon Dec 30, 2002 10:10 am
Location: Bozeman, Montana, USA
Another thing, if i got neg value then what should i print -(neg) or 0 (zero).
It should be 0.

Moha
Experienced poster
Posts: 216
Joined: Tue Aug 31, 2004 1:02 am
Location: Tehran
Contact:

Due to Shamim and Sedefcho posts, I think there is no test case in judge test data, which all the board filled by negative numbers. we shouldn`t envolve us with such these test cases. But this problem has a very nasty point, which i don`t find it out yet. i really want to know judge test case, because I believe( some how) my solution is ok!!

But the question is Where is the problem with my code?

Chok
New poster
Posts: 48
Joined: Mon Jun 27, 2005 4:18 pm
Location: Hong Kong
Hi all,
Thanks Sedefcho and Shamim. I've got accepted with O(n^4). now i'll try it for O(n^3). Thanks again.

Moha
Experienced poster
Posts: 216
Joined: Tue Aug 31, 2004 1:02 am
Location: Tehran
Contact:

### Please test these test case with a accepted code

Can anybody test these testcases with a accepted code?
Input
• 10
59
54 -52 -8 44 -44 -65 -51 1 89 25 20 -38 30 -20 -51 43 97 -26 57 65 -75 -86 -87 64 88 100 40 -38 44 -46 -43 -32 -15 -77 -95 -38 -37 -27 77 31 80 37 33 -21 -100 37 22 81 94 -76 65 89 -4 24 7 78 17 -39 -22
-93 -94 -97 -65 -20 -67 78 -42 -32 -49 60 -44 -75 -17 11 -40 -95 0 -82 0 -56 30 64 66 18 19 2 81 -91 -91 70 -73 97 -21 -70 -46 -54 -92 47 -46 -38 75 -61 84 86 19 37 -86 97 -44 -60 -58 -31 63 -73 76 73 83 -4
51 -7 77 -95 10 0 23 -9 39 -97 84 44 -11 8 83 -27 34 35 -10 39 -53 -40 66 90 -55 -39 88 -97 32 -60 83 80 53 94 -77 16 3 71 4 -6 13 -30 -27 66 -64 -5 44 -29 -65 59 87 36 29 -92 -34 59 76 13 -48
-27 37 -25 83 77 -9 55 -76 18 -64 4 -74 77 18 -84 -36 -10 75 -87 22 37 -65 59 -14 79 54 8 12 -9 42 95 70 -83 40 -34 66 -59 -95 3 -62 19 98 -8 80 -72 43 -65 71 89 -49 -5 59 -11 -49 28 -29 92 41 -1
-50 7 -4 -37 86 -19 -14 15 -55 93 73 80 -100 94 3 -27 -33 -78 -73 -80 5 59 -22 59 32 47 3 39 97 -9 60 85 38 -63 -8 35 -6 100 -66 -39 41 -34 -11 80 4 74 -92 89 -19 -6 26 -8 67 -95 -99 96 51 -83 -35
71 16 -69 -35 3 -41 -49 -83 67 -97 13 60 -33 -71 -39 -43 -77 -53 33 34 -8 79 9 -46 43 2 -70 31 -4 -84 39 -52 -52 93 -59 21 35 -57 -28 -86 78 -94 48 83 59 28 25 46 51 -62 -32 43 -15 -77 -68 -47 82 -26 -98
-13 -7 55 -55 76 5 -15 53 36 -23 -10 -6 -69 29 -49 36 -84 71 8 -71 -97 88 -46 35 7 27 -82 40 -88 44 62 32 -55 49 94 14 63 -68 75 -23 27 65 85 -57 39 7 46 -12 -41 -31 14 91 -12 -17 -26 0 92 60 1
46 -84 -8 -93 64 14 0 72 -71 81 -70 -96 -26 -1 95 -70 -9 94 -15 -71 -87 -5 -13 -10 -94 -38 98 -99 86 -43 -35 20 -98 -61 66 -24 -82 72 39 11 -38 27 49 -59 58 81 -80 -70 46 56 -27 63 -77 -36 -48 81 -62 55 100
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96 93 81 13 90 46 32 -75 -8 -97 99 -61 -46 -89 -34 -78 24 -34 -96 73 -72 50 36 67 -82 51 43 35 39 0 -86 34 46 80 -48 -92 36 -55 -31 49 -51 59 44 -48 85 -21 58 -45 -90 -11 43 -89 77 -84 66 88 -66 77 6
59 39 26 -68 0 -28 -27 -48 82 60 -32 65 -74 -32 -72 -41 96 43 42 25 34 -88 -56 -44 -25 69 27 -9 -96 -84 12 -30 -36 -95 16 53 -71 -44 -7 -30 23 -23 -65 -17 -73 60 57 92 96 36 -4 -61 96 -68 -25 -69 28 -31 -56
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7 59 26 -5 26 -79 52 11 -83 95 -1 27 -25 4 24 -8 -73 89 25 77 -24 -16 -58 -53 -55 -78 -38 -88 -8 48 -48 97 89 18 78 99 48 44 -42 11 -10 19 25 77 30 99 -13 98 -12 -82 -8 93 61 28 -66 65 -61 -90 22
52 -22 -96 -10 -70 40 80 -98 37 40 60 -2 -47 -7 -15 34 -48 83 24 -69 48 11 90 31 32 -90 -9 48 -55 -25 51 69 83 -74 -76 67 17 -17 -18 -65 -87 -7 11 85 -77 68 70 24 53 24 6 -86 67 62 -17 34 -46 32 63
-56 -26 -65 -26 -80 -52 -6 27 -47 -61 -45 -67 -14 53 -36 28 -87 47 83 72 -85 -33 -48 49 53 -36 53 -10 -82 79 45 -41 95 82 27 5 77 -69 -98 -53 -93 81 58 12 -54 90 64 -62 86 -1 -63 91 -44 30 8 -23 -38 -45 -61
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14 -58 -33 61 92 -48 79 6 76 98 -87 14 1 7 81 -92 -16 3 54 57 55 -93 100 70 69 39 5 -2 51 40 78 60 -79 -75 59 -10 2 80 67 10 -16 -23 -68 95 68 -84 -64 -71 -72 -40 -42 76 -86 80 -4 -88 -4 -75 69
-23 -35 80 -15 6 -61 -49 -29 80 47 -34 14 -38 98 -57 13 0 53 -12 -29 -54 30 -25 94 41 -30 -58 62 96 40 58 -64 67 -4 17 -63 56 -39 18 -51 -5 100 58 24 87 -37 83 -34 -50 27 4 70 15 -6 -40 59 -4 -75 86
81 -29 48 84 -27 87 -32 77 16 -9 92 79 95 -40 -10 -35 -29 74 -8 -92 23 -23 0 56 -58 4 -14 -31 32 10 63 100 42 -1 -97 -18 36 75 -7 18 -96 -12 71 -50 -80 78 -72 0 -15 30 60 31 -56 98 1 26 -3 -72 -81
76 -15 -35 96 -67 69 -21 10 90 23 -61 -34 -88 91 9 81 64 3 -82 100 42 -10 -62 -48 19 70 28 100 73 8 -94 33 84 -21 1 -46 -20 4 -9 99 -56 8 3 66 64 24 -28 81 59 -9 -55 1 -77 -23 24 82 22 30 -63
-34 -36 -51 47 -8 -100 99 -72 -97 73 34 -74 -43 -37 -55 34 -94 80 -67 7 65 -92 95 30 77 -42 -65 -59 45 46 63 20 -83 32 -59 90 12 -53 -9 -29 17 64 -54 -90 -85 -30 -83 35 -83 14 73 97 51 -24 -65 -79 -91 65 98
-41 -22 62 -54 -36 30 9 -86 53 88 -29 97 -1 83 -30 52 94 -42 45 85 -98 97 83 44 85 45 85 -54 -60 84 48 61 -42 96 30 0 26 -32 -46 42 -7 -43 94 9 99 -43 61 -19 -4 -22 -26 -60 -53 -93 -68 61 88 33 66
35 68 8 81 63 -8 -86 -41 53 3 -58 13 -11 55 -82 19 84 27 -81 -86 -58 -27 -62 21 61 93 -61 70 73 -16 -77 3 88 -18 3 -9 30 37 4 73 -48 83 3 -80 8 62 63 -78 27 50 32 24 63 -20 51 65 -90 73 -66
0 47 -26 94 59 -66 -17 0 25 -68 97 70 -49 -8 18 -6 15 48 -61 -10 -62 95 5 53 -58 8 5 81 4 -8 -97 74 -100 18 -29 -46 37 -2 -1 -5 43 79 -59 -35 -81 84 24 20 -45 -17 100 31 -3 -44 55 -96 -30 12 -65
50 57 55 -91 38 -46 76 17 81 6 57 41 25 92 -92 16 -35 40 21 98 -100 80 89 -82 50 -27 14 -25 -4 -8 5 69 -65 63 -72 10 -70 -12 -52 -95 13 -41 -55 100 -48 -53 -99 60 -62 14 -49 71 -46 77 42 -32 -24 -15 4
36 -21 39 -76 49 -88 -4 54 20 -24 31 0 -54 69 -36 83 58 27 -56 -28 74 -35 17 18 88 0 41 14 59 -63 54 66 -81 -41 29 75 50 -46 30 71 -39 -2 4 -40 -98 -57 13 30 -82 -29 -6 -79 -79 -56 21 -94 63 72 45
29 13 -94 75 -18 -27 -33 -17 55 -69 38 2 48 93 32 30 -46 -13 -1 -96 9 100 -21 20 -80 19 10 -14 19 77 -77 79 15 94 45 68 -43 63 -51 -39 -3 -13 -45 -3 100 -48 52 64 50 82 -45 82 -49 85 59 -96 81 7 -68
90 -56 76 97 73 -30 40 35 29 -64 50 -37 -16 87 77 -100 55 -35 -95 -2 -10 -53 74 -70 -38 83 55 -67 71 60 40 45 -46 58 78 39 -93 70 11 0 72 -71 36 -29 -56 19 -80 -23 -43 -98 -41 40 60 -31 -14 -53 -47 -44 26
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60 -85 81 78 16 34 38 75 9 -59 62 6 -43 72 62 40 79 -49 90 84 3 -70 11 -89 46 53 -80 -38 83 15 -38 -31 45 8 73 73 -75 -51 -54 -40 86 -39 -17 19 -19 77 22 39 20 -35 -5 2 -16 -66 -91 -68 30 -40 83
-79 27 24 96 -83 -78 41 -92 62 28 77 99 -95 -84 -41 60 -34 -41 -36 89 85 2 47 35 67 2 81 54 96 9 -36 23 -22 -62 33 8 48 -8 -70 -70 5 46 74 27 -70 -72 -37 42 -25 49 19 7 0 28 -92 -74 70 -14 -52
-45 -43 -93 44 -72 4 -59 11 57 13 48 49 33 -40 -61 55 79 -54 -11 -72 32 70 -33 89 25 7 39 -27 -6 -53 -24 38 38 -73 56 99 54 11 48 -42 35 -11 -71 -45 -71 10 -38 63 41 -92 -47 51 -56 -53 -29 -76 -44 70 -58
-58 45 -56 84 -59 21 87 -72 0 33 -31 47 -58 -26 -38 -75 -80 97 69 -20 -3 -43 -75 -27 8 27 88 78 -98 -71 55 -64 -99 1 -40 -61 -63 32 -51 79 18 -30 13 -49 78 79 99 -65 68 -96 -55 84 93 -88 -75 -34 72 -98 -37
27 -99 80 -13 -92 -44 -55 9 -48 20 10 -1 86 -74 23 62 -93 -22 90 -15 49 -34 -23 -75 11 -40 -21 -32 13 -56 84 -52 44 -80 42 46 -20 27 -91 -48 29 -90 -95 -58 95 -9 -31 -19 1 -40 26 100 -32 23 -62 -91 -58 -41 68
-25 79 5 27 83 56 37 -74 95 -97 95 -54 14 -31 -96 20 -27 -87 6 -23 -8 -77 26 82 -23 71 -68 -69 -2 3 64 -85 -21 -90 52 -83 -23 -38 10 -2 29 -16 65 -45 16 31 4 37 20 -20 -71 -64 62 9 -54 71 -51 -80 -4
-83 39 68 -62 -35 -64 -19 -58 -95 -18 -58 81 55 -14 -47 92 6 76 40 -77 -19 30 -7 88 73 -71 78 58 -49 66 57 -58 54 -69 -37 1 18 60 51 59 -19 -87 -47 -28 -82 -58 17 68 15 -64 15 74 -62 92 14 2 -46 63 65
20 50 -51 61 -72 89 -95 -67 -69 68 41 -77 -82 -98 47 0 74 -11 -84 77 -14 23 34 -42 -84 -63 58 -33 -94 15 -24 -6 -32 -56 56 70 97 -78 -48 99 -97 22 -32 -93 -52 31 90 6 -89 -35 60 -81 -63 -52 10 -8 44 94 -51
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-99 -87 -85 45 -53 26 10 -99 85 -62 -68 -11 -69 -92 96 39 -74 -87 -9 -100 -30 94 -62 90 17 -29 -55 -63 94 -92 -53 14 -23 17 98 26 7 34 -78 -13 41 -46 49 51 -97 -63 40 8 43 -61 -7 -68 -38 82 57 -43 37 93 -30
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-44 -55 96 9 28 -50 -45 -11 86 53 73 -48 -29 22 34 -92 -25 -55 -64 68 -48 -93 -13 -2 -76 32 13 12 89 -89 -13 1 -59 -92 53 12 44 -92 -74 55 -15 -30 -99 71 75 -77 -4 -93 -66 -17 10 17 100 -77 -2 -89 50 -46 -93
35 7 54 21 7 64 -38 87 -94 -64 -25 67 50 64 -30 10 -89 9 -95 -21 18 59 -24 78 97 -19 40 -67 68 -17 -52 30 -44 -49 -36 73 -21 -43 -42 -96 -28 -93 67 24 56 99 -35 -14 0 -51 -66 -57 -21 98 86 0 74 -15 -86
40 47 -82 -100 95 -92 2 0 9 91 -17 -32 22 -43 -78 77 36 90 38 -46 -21 9 27 -14 98 77 46 99 -47 72 70 8 4 -55 53 -7 72 -63 26 1 13 -4 -19 -60 10 -22 -46 -17 95 -59 -5 -87 -48 -42 -58 31 -54 -97 4
-37 -88 60 56 -50 81 -30 -6 -29 -99 96 47 -94 -27 5 -12 -11 67 66 -80 -6 23 47 -86 -51 80 74 -38 -59 -23 -29 38 -33 -44 -60 -48 -50 1 67 -5 -3 29 -77 10 -65 -65 0 32 -73 99 32 31 -84 -11 86 34 33 -32 -97
-77 7 53 -76 -73 -27 -13 50 -73 9 -50 -32 -16 -12 6 89 1 -56 -35 39 46 -45 -57 -36 95 -80 73 -94 9 69 -47 -31 -18 69 18 -27 -5 55 -33 -58 -3 4 14 -31 37 -5 -23 99 -22 -61 -7 -2 -92 -41 -15 86 1 -60 87
-5 -23 40 12 -19 -72 -7 -33 -59 34 16 31 -33 -23 47 -16 100 -29 -17 -44 43 -49 27 93 73 -18 -75 89 -13 -33 -55 80 20 -60 83 -5 17 8 -2 30 -27 63 -29 -42 96 -70 90 71 90 -79 66 64 4 -27 39 -80 4 100 60
43 82 -5 27 46 38 89 -41 -52 57 -84 36 -27 -72 40 0 -18 95 -53 -31 -71 56 38 44 -7 2 97 87 -10 84 -21 -33 66 -96 82 -51 96 78 -70 90 -89 0 -28 42 10 -56 75 -2 49 59 -24 -15 48 18 81 61 -99 20 -13
32 53 87 42 1 53 55 -1 28 29 33 53 -10 -87 45 -25 -89 97 -73 96 62 66 -91 -53 82 -98 90 -74 68 63 25 -55 33 20 -22 -11 -30 -67 -9 -72 -33 72 -86 -54 38 32 -72 76 71 -42 44 76 62 28 -27 27 -1 14 -10
5 52 43 -91 -60 81 19 -87 -31 -3 18 -92 90 10 -45 -4 34 -54 11 62 -37 -4 99 -83 4 -55 49 0 38 74 97 -66 0 5 -62 15 41 87 9 -2 21 69 3 -40 -11 -23 92 -36 -40 -37 -75 32 -71 -89 19 -61 -13 8 -65
-91 -62 -16 -34 78 -94 7 -33 -17 -56 -84 62 -48 -40 -58 71 12 94 -17 -81 67 -76 8 -45 79 -97 41 -39 -100 11 15 37 -46 -56 -90 -24 76 96 -41 -9 6 -14 -30 -2 -64 18 -27 -72 17 -1 96 -28 -59 56 96 -86 -3 15 -85
96 63 59 1 -28 57 -92 -54 -23 -76 79 -43 -39 29 -12 37 60 -89 -55 -47 -75 -45 56 -19 -78 91 -99 86 45 -58 60 -32 -61 70 42 65 -20 83 -41 87 -28 40 76 98 -5 -11 16 -16 -29 -60 1 20 -67 29 -36 -25 -59 24 56
-89 -42 58 -8 69 25 -40 85 81 96 58 -25 -63 -80 -52 -74 62 5 -73 -59 -16 1 -77 49 -3 66 43 -77 -8 -58 -92 66 -79 -39 84 59 -48 21 -80 47 82 10 -37 62 -10 71 -83 -88 6 -79 58 55 -98 -63 12 -25 -89 -50 56
2 97 -100 75 73 47 -2 21 -42 -66 61 81 71 -89 27 32 -42 -69 -40 -95 -23 29 11 15 1 -24 -57 49 -40 48 13 -95 40 96 39 -58 98 53 71 29 -81 34 -24 -65 -52 29 -24 86 53 -77 -4 19 -55 -9 6 -63 -58 24 -79
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65 78 31 84 10 -11 -57 -70 20 -24 39 4 -5 1 33 66 16 81 49 -74 -97 -42 89 24 28 -13 70 -64 -86 -19 100 83 -61 -95 -95 -70 85 76 -55 -47 -80 -16 9 92 10 14 -28 91 -93 -32 -18 43 -45 42 85 48 82 -47 9
-87 -81 96 29 -31 37 -75 -97 -92 -70 73 55 51 17 28 -68 79 -47 -91 27 30 16 52 56 -19 43 45 78 0 26 54 -75 76 73 -30 -86 -97 98 -80 92 -10 -56 -64 -85 95 -59 3 -46 88 77 51 10 -29 -96 94 73 53 25 62
-47 53 -70 -73 68 0 -44 73 65 94 77 -79 23 -44 -14 -91 94 100 -31 -44 -32 9 -29 -96 -15 20 8 40 97 45 55 3 44 43 75 40 64 14 29 53 -31 69 -37 70 58 76 -16 -93 -49 68 89 -63 -56 11 -53 97 2 -89 6
5 4 -43 -26 -13 -3 65 -88 -9 -70 29 16 72 56 -57 -50 93 8 7 2 42 -34 -63 66 -31 25 -91 51 -59 -55 -1 77 26 -95 -19 20 35 0 41 37 -34 99 -2 20 -23 77 -46 85 38 72 75 84 11 75 83 -91 -72 74 72
36 -1 -85 -99 19 47 59 -48 -31 -59 -77 49 -91 56 96 -57 -88 76 4 74 -43 46 -7 -11 -18 -77 78 -62 47 30 -10 -72 -44 1 -54 4 -61 100 10 74 46 -23 -42 -23 -68 29 40 41 -14 66 -84 31 -53 45 6 25 1 42 65
34
32 -94 25 -83 -8 -74 -40 74 63 62 77 50 -48 3 28 -21 -20 -68 -9 54 74 92 4 -30 1 93 -5 -39 73 9 -78 -94 12 76
44 37 -24 -97 60 61 -86 -4 62 9 -17 0 82 -25 -21 13 -30 -48 45 -48 37 -98 -62 -45 -43 -23 -5 -21 -17 -13 12 69 43 -29
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85 94 -4 -99 -33 100 58 -33 -20 -49 -91 -14 25 -79 76 -89 22 -94 54 79 -54 -31 -12 62 -84 -94 28 37 -41 70 31 -43 -5 -12
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-35 -4 62 -43 17 86 -65 42 -63 -26 -88 -64 -96 -72 -42 -64 -18 31 9 -84 21 -22 83 14 4 -61 -46 10 0 12 42 -86 -77 -5
-22 79 -92 96 65 52 15 -94 3 -36 -17 -79 -90 -51 47 18 -79 -79 -98 76 -15 63 40 -25 -25 13 75 34 -22 97 75 72 77 -55
-23 68 24 1 53 40 19 88 -78 -91 39 -1 -33 -32 22 16 -16 15 -81 37 76 -79 -63 21 86 -73 -30 -4 -46 5 56 79 -71 79
-77 52 -25 -14 -95 61 13 4 74 39 -12 53 98 73 57 -52 -99 19 -66 79 34 -40 39 23 19 -64 38 32 -80 -69 88 -2 -91 -76
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67 17 22 -52 -81 74 45 32 -89 42 -31 -30 26 64 -17 76 -35 14 -88 57 -55 92 27 -36 -91 90 55 -37 11 -76 74 -79 -45 -32 59 -66 -52
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92 3 -30 49 62 -1 24 -80 -43 10 56 -39 -23 -72 41 60 57 8 -23 62 45 -56 27 26 5 -88 -100 -22 -22 -68 -47 63 -23 22 61 -97 46
8 53 -42 -70 -18 89 -24 -66 40 -51 -48 -6 86 87 -39 66 38 47 10 -75 -18 1 74 -66 46 83 -57 97 -21 91 -47 40 -7 -30 -36 -79 34
28 -12 88 77 18 -24 41 63 -38 20 -61 99 -78 28 -55 1 -36 9 -72 -59 -85 -70 61 -23 -74 43 -2 58 42 -35 81 11 -16 -6 72 43 14
48 -77 -40 46 -17 -57 -28 -93 -61 32 57 -59 -1 28 53 -89 50 -37 -13 5 -30 -71 -26 -20 -3 -91 66 -89 -12 -43 -93 -31 28 31 -16 -38 -30
13
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-26 -69 100 -41 77 21 30 8 44 -62 100 -16 91
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-48 -72 -54 11 96 -99 70 -69 -65 -10 -60 15 79
83 -78 39 -67 -96 98 51 13 -92 77 -68 98 -32
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40 -23 -31 -59 71 -59 -78 -40 12 -14 83 40 88
7 62 -60 51 -86 -97 18 -33 -40 -18 -46 -58 -72
40 52 -16 -81 -7 -80 -89 7 -75 -85 -2 -51 -37
-17 -55 68 68 22 45 28 8 77 -4 -81 76 -18
23 30 98 88 70 -47 41 53 -37 71 -54 -41 64
40
5 88 76 11 -20 -90 61 -86 -19 -17 24 41 -18 43 -18 -11 -17 38 87 61 41 11 -95 -32 51 -85 -79 -9 46 5 83 53 47 58 6 73 -69 -81 -13 -77
94 -38 18 1 66 95 -55 13 4 -1 -22 90 -90 -20 49 -100 -56 82 51 -4 22 -30 80 45 -80 27 -86 -25 -19 -10 -74 78 80 -70 -74 -12 5 73 -51 1
29 32 43 -88 35 -31 -75 -4 -33 -17 13 69 -4 36 -24 -18 98 66 -40 -3 -17 49 -75 12 -26 46 24 92 -21 -50 31 97 51 35 -82 31 38 57 -66 -86
30 98 -12 -15 -83 11 65 7 -36 38 47 83 -82 -64 74 -4 -14 -23 -23 -26 -69 85 12 82 1 32 55 100 -19 49 -46 62 55 18 -90 50 -15 24 59 -41
26 -8 -53 50 37 30 -85 -75 -43 -84 71 56 -100 -79 -53 -85 -25 92 33 -83 -6 86 71 63 86 -78 45 -74 -46 35 71 43 -79 5 -42 48 -33 72 -92 49
80 -66 25 0 -91 36 22 -22 81 -79 48 -37 58 50 -42 93 -24 44 31 88 46 83 69 1 99 -38 -38 -94 -49 -44 -42 44 -62 -83 98 80 59 -10 33 -43
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58 73 -1 -82 -73 -51 -51 15 4 -92 -18 68 -88 -61 -34 -19 34 96 35 85 -63 78 -94 -65 23 -4 -75 -46 -61 14 -48 -52 -58 49 -90 34 0 32 -70 58
86 -67 68 88 19 -90 34 -82 55 -17 30 -63 62 -92 -90 57 -10 -1 -2 -39 90 21 -35 48 0 0 83 61 56 -75 68 -20 -21 -22 44 -78 55 -23 68 12
68 65 7 -27 -44 7 -100 -21 49 -77 36 -92 -53 13 84 55 3 68 10 -73 29 98 -6 82 -95 13 79 54 18 -18 -58 54 -24 -37 -15 21 -89 -71 70 50
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39 75 -35 56 24 98 -41 59 45 -20 69 -11 84 33 -78 -3 13 -52 19 -80 91 81 79 -99 12 -40 -23 16 80 55 92 -6 2 52 65 98 -74 -19 83 -76
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51 -13 -89 -15 46 20 -29 -47 66 18 -40 56 81 86 65 92 -20 -50 -11 99 39 53 -34 -53 92 -28 13 -43 34 -7 -69 -80 -36 -65 28 -2 -47 67 -22 14
57 77 -93 97 -13 -92 -34 -38 -67 15 -98 27 40 -58 -81 7 47 -74 -69 31 5 -30 -60 -42 -2 21 41 -10 8 75 -39 26 31 91 1 -48 -77 78 79 -28
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-96 88 -90 -4 -91 81 -5 20 -13 12 50 66 56 -97 -32 60 67 -5 0 -22 -62 52 83 3 81 -91 72 67 46 51 -29 38 91 -18 86 49 9 -47 -4 -54
31 48 -100 -29 -78 -55 -91 35 -70 39 -60 69 -20 -95 31 -76 92 97 -3 -1 -5 20 82 9 -8 6 -68 -70 -22 79 11 -81 43 -59 69 -94 48 1 69 47
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99 11 -7 -2 -20 -15 -7 -20 58 1 69 -87 -26 54 100 40 -56 40 50 -8 58 -24 79 -32 51 -16 -98 -23 44 33 17 -6 57 -1 -20 -76 66 -42 76 46
73 79 -64 25 11 -16 -64 -67 0 -27 44 98 -69 20 79 3 -28 87 51 -32 1 -57 -3 -19 -58 57 14 -43 59 -60 -96 -88 -11 13 -17 91 -60 16 -2 -32
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36
14 -11 6 -22 21 26 -75 -36 60 25 -28 98 19 -95 68 5 -24 -1 41 88 62 59 92 72 61 99 -72 -95 -6 -1 25 21 90 45 11 92
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18 -62 -75 -69 65 37 -65 61 -59 48 54 -67 -78 -84 -65 42 -42 58 59 -24 37 -16 40 75 -40 5 -69 -89 53 -46 100 -66 -23 -58 15 71
75 -87 -96 14 -50 -28 24 31 20 60 -31 -28 -48 -2 34 48 -26 90 -95 56 -56 -63 -66 22 -37 -73 6 90 52 49 -65 -27 97 -12 53 -1
85 -20 91 69 90 -28 -7 -48 -76 -11 60 -30 88 -13 -43 81 11 9 -8 62 -19 25 -40 -19 35 54 -35 -17 -59 28 -78 -61 41 57 -15 -79
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36 96 -2 7 -41 -40 0 40 46 83 75 42 -100 -86 47 28 41 -97 -62 -30 99 32 1 43 -26 72 10 -92 -14 -62 -76 10 80 25 -76 11
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98 -5 1 -19 45 -75 -18 -74 -47 86 39 -41 -26 -70 60 3 54 -11 -52 -93 -72 -50 73 -33 -98 -12 -70 47 -72 -72 -6 88 17 -13 -29 98
38 -22 70 -98 39 71 -62 -38 0 -64 51 -66 16 35 51 11 13 32 -54 -16 -4 34 71 99 -48 76 -13 100 -87 -40 100 -24 16 -62 18 -95
31 22 67 71 83 46 -88 57 11 -43 -80 90 -56 -31 62 64 -20 93 -72 68 -8 -48 -91 68 -33 -80 -10 -40 -19 -6 63 -5 21 36 26 -80
84 29 99 -43 74 -10 -23 15 -88 89 -92 66 -23 -39 72 83 -46 -63 -74 43 -26 97 -36 -58 0 6 39 -37 -6 10 -61 -66 -70 -17 32 -91
46 40 65 -72 42 23 49 76 2 100 44 35 -93 22 -45 -15 -32 39 -18 28 21 -7 43 -25 34 40 22 57 -95 71 -58 30 40 -52 -45 -51
63 -3 6 84 -52 -84 100 54 -18 -99 77 -65 29 74 63 74 48 99 -3 26 -72 -95 15 97 -5 42 22 64 90 59 27 11 -7 27 23 32
28 -32 7 9 57 94 -90 63 -27 -65 -52 -62 -17 -36 -8 35 -26 79 -29 45 71 -63 95 -5 -80 41 11 -57 24 -69 -93 0 -70 18 -32 16
0 -29 -72 82 71 -49 58 77 -31 -80 -81 -76 25 15 56 -93 44 -17 22 65 -89 -40 -53 95 94 -40 87 -58 8 -36 3 87 16 61 3 -97
-6 3 -86 -75 4 -52 -63 69 82 -1 66 -65 58 -52 -17 -18 16 -48 18 -80 -4 -13 74 4 53 5 25 -32 -62 44 -98 -69 84 -48 39 24
91 -43 -51 85 -85 54 -26 -93 69 -33 99 12 84 83 19 99 -42 -40 -20 29 -81 81 35 -27 -42 2 94 88 40 -67 9 35 -39 -11 -65 30
90 86 15 62 5 30 -79 -42 -21 -44 -6 48 19 70 66 62 -42 12 93 82 38 28 96 -67 -11 -13 21 -95 53 57 -97 -5 -32 97 -58 -54
-55 44 -85 -33 54 -46 40 -48 -72 -77 -23 73 -99 -11 -12 -85 79 85 -39 -26 -97 -34 79 95 -53 -85 51 -63 93 -73 -37 -4 18 80 39 16
-43 -3 65 38 -34 60 12 0 -96 -41 -63 49 67 71 66 -73 -35 30 39 -85 -57 91 -66 39 97 -61 -59 72 -36 98 61 -76 12 -29 41 -57
-90 33 -3 -50 85 24 -18 -35 4 -21 -68 -95 69 -64 2 -7 -67 -80 -44 -2 -72 -38 -89 -9 71 -92 -94 51 -75 38 -34 34 17 -3 -76 56
98 -70 33 -12 -42 -76 -21 -64 7 -72 -12 -75 18 56 -15 75 -73 31 -90 -42 12 33 -77 95 98 91 71 -4 75 49 -39 35 -34 49 76 -21
41 54 -17 -67 81 -57 55 -5 89 52 -44 4 -53 34 -10 48 -42 -1 -50 7 -93 -13 -92 -43 -5 -73 48 94 97 -61 49 -57 10 16 -27 89
-20 -66 53 91 71 74 6 86 61 41 -21 67 23 -91 5 35 13 -35 76 91 89 -98 64 29 -61 0 0 47 49 -39 16 -45 -41 62 5 96
49 87 -41 70 17 -50 -70 7 -34 72 -87 -46 63 10 -59 60 64 -53 27 72 -59 -28 -18 47 -15 69 -1 -96 -21 -64 9 -54 -35 9 -96 -39
69 -49 35 72 -82 85 -54 -80 -84 -55 -100 31 -48 -63 -53 30 -34 -42 -7 52 -87 -38 -48 14 26 23 78 -26 26 -1 -22 68 8 -24 -89 71
45 -81 92 91 -98 76 0 -32 89 73 -97 -100 15 -88 -66 -11 -33 -71 19 -75 -41 -23 -85 1 -55 50 -13 90 -39 98 -67 82 67 -91 -13 69
82 28 13 73 -2 -53 -4 -9 51 -13 48 84 -13 67 4 47 59 52 -71 -74 -79 21 0 -58 70 34 100 -65 -57 5 99 -14 -93 97 56 69
-62 -50 -86 79 -45 -6 97 57 69 81 -80 24 93 68 -22 -49 92 -11 72 65 35 27 -8 50 78 43 -58 62 -20 -65 -98 -93 44 -31 26 100
-33 58 -43 84 -38 -10 27 -12 -33 56 23 85 86 50 10 39 -41 17 -37 37 95 37 85 34 -93 13 5 -84 -45 68 48 -66 70 -5 50 -48
37
-85 73 32 -93 69 -94 -58 -77 -17 4 30 -60 -64 29 80 -60 -37 -64 -88 -23 30 -54 -32 44 -96 -40 6 -5 31 -42 -6 41 0 45 93 -77 -17
76 -28 66 33 -15 71 -77 -88 45 -87 -70 57 -75 -16 4 48 -49 32 -66 -86 -38 68 -91 65 14 21 -38 -32 27 29 13 -78 19 -43 8 32 -51
-93 20 -77 41 51 -75 -57 -63 33 30 -72 53 -67 43 -39 64 -1 -21 -84 8 -74 -50 -51 49 -22 93 61 -7 39 -92 -78 -42 -71 -90 -92 -21 12
-27 -51 -12 -21 -66 84 41 -56 -67 19 -79 38 -10 31 26 2 6 97 25 56 32 -97 -28 72 -52 -36 -81 -98 36 21 37 83 43 -61 28 58 89
-33 -73 -43 -61 -20 87 31 -78 -17 9 -57 -10 19 100 65 98 70 -34 60 59 36 -29 -100 19 54 -49 12 94 65 42 47 -60 76 96 -55 -48 -31
58 -16 81 71 46 -55 47 98 -82 -95 27 67 37 -9 -46 61 3 -80 79 -46 -65 -96 53 0 -70 41 -97 -51 96 -51 33 -10 -20 19 -72 -89 31
-15 43 -17 77 41 99 73 85 68 68 -52 67 -53 -1 41 -92 -16 38 -12 -91 -19 -11 15 49 -79 -59 -37 68 -30 -32 -68 60 24 51 -10 22 63
-54 95 93 -52 -35 -43 -79 38 -76 -67 56 -65 25 -81 -71 -46 53 -94 11 -28 -66 -15 -42 -88 -59 86 77 54 92 15 -9 19 34 -5 90 -59 37
-66 27 63 40 -32 32 -86 86 -18 28 55 -82 75 -26 92 -6 -74 44 -51 -18 -67 -35 -39 19 -14 26 -76 96 44 -49 -50 26 21 -27 -19 -22 95
71 -10 23 -3 61 57 -96 78 -69 -66 -17 97 26 -55 -35 -37 49 62 39 87 -9 -21 -77 -15 -59 73 0 -53 -51 6 -23 24 -92 -76 -16 -62 -38
63 -48 92 -57 -14 -33 16 -7 -2 -67 0 -78 -20 -70 51 -30 -88 23 -16 9 -4 -97 -59 43 100 -53 -66 -41 56 -100 85 -87 -40 -85 -56 20 69
-47 -20 20 -99 52 69 -16 -70 -97 -78 -60 25 41 70 -74 43 -98 42 82 -56 -71 -25 -81 -34 83 -59 97 52 98 64 93 -57 2 74 72 -83 87
-27 -35 -77 39 -59 -86 38 31 19 41 -79 7 -59 14 -19 81 -100 -73 -33 -79 80 -1 80 -52 21 7 34 18 25 100 65 56 63 -7 6 -20 -15
-71 20 -60 82 -8 47 -75 -92 48 87 20 -31 -78 79 91 -86 21 83 14 -80 12 14 -30 -93 28 47 27 8 -49 2 -13 -100 -60 48 -79 -62 20
-43 -14 61 13 90 19 -11 16 -73 -68 98 86 -34 39 -20 4 -43 -98 94 78 84 12 97 -75 -92 73 69 66 -89 30 -98 -4 -87 76 -45 96 -83
-90 -2 -14 39 14 46 76 18 76 7 21 -14 39 -16 20 -75 45 6 3 -12 -86 30 -25 0 29 47 33 -80 -87 -39 -27 83 56 -98 -33 -9 34
13 -54 25 -53 100 -34 -23 -40 94 -41 -5 -63 89 -79 -82 3 3 74 39 0 -78 -83 -21 -96 23 22 -66 -98 47 18 -20 -89 -44 -17 -20 54 85
-31 93 18 28 -9 92 -15 -48 -67 -88 57 50 81 -25 0 -4 14 -23 78 73 78 -60 68 -59 -42 -22 -43 5 -74 -92 -39 71 -24 -85 44 -20 19
47 -54 -88 -17 26 -13 16 95 -94 1 -52 91 -59 26 -22 -25 100 -40 40 -29 -49 -65 -62 5 -59 87 99 13 -78 70 18 -34 -40 -70 -63 12 74
-43 -69 91 -22 3 20 -10 90 -96 7 91 35 59 -92 8 -81 -100 -67 -42 -100 75 96 -15 64 58 -39 -84 -40 -37 47 62 64 9 85 85 29 36
-43 -75 62 -78 46 -7 37 50 -56 43 -6 -82 -36 6 58 56 60 -7 96 54 -80 60 -38 66 -89 -46 27 17 -94 94 32 -17 -12 -45 43 -14 93
-4 -51 -90 -44 -66 -63 100 -72 73 -75 -27 47 -94 -37 44 -49 59 50 71 84 98 85 34 57 93 -28 85 58 31 -52 -90 -90 32 -28 67 38 90
61 -45 96 -82 -22 66 -76 40 -4 61 -9 67 -96 -82 -97 89 61 74 -36 47 -53 -71 -41 -23 -73 6 43 19 -72 5 38 -24 94 -22 -19 -20 13
-1 -35 -66 -40 22 77 55 -8 -15 -19 11 37 75 -34 96 -52 68 -53 -61 72 8 57 -29 89 77 -49 -19 54 -76 -55 1 -100 -60 -2 10 -1 54
-14 -89 59 -44 87 27 -23 -95 5 -16 -65 22 -28 -73 -84 54 -42 68 -41 8 -6 -100 70 -39 -91 79 98 55 -65 89 -20 13 17 -97 -24 17 -72
-93 -78 82 53 55 -93 43 -3 5 -39 18 -65 47 51 -86 -81 63 8 58 -36 79 55 86 85 13 42 -12 79 62 23 -52 -91 27 -92 -93 -63 22
58 -41 65 99 -53 45 2 27 -19 28 27 -41 5 79 71 -18 -75 -37 81 -78 78 -97 96 -5 -70 91 -21 -13 31 -28 -26 96 72 73 100 17 -39
-24 -71 16 -62 -69 71 -77 -73 69 16 66 29 6 88 -38 71 28 58 -47 -16 -69 -29 -54 -82 67 19 87 36 8 -83 84 -8 60 -21 52 -88 91
99 -52 -100 44 -84 -99 -90 -76 -19 -92 36 26 24 61 31 -61 -27 -41 64 77 -82 99 -48 -9 -66 61 84 -92 -31 52 35 23 58 88 16 0 -72
-35 5 19 -77 -40 33 0 16 59 -30 46 80 41 65 -59 39 89 -3 -82 53 -6 -86 -84 -24 -18 -23 75 -99 64 56 -98 -16 -4 59 -100 -40 -31
-44 -93 -55 -55 76 -47 -77 -35 0 -93 -85 -2 -50 88 6 48 31 85 51 98 34 -32 -88 9 66 -37 -66 -59 40 -37 -64 64 -25 14 20 -35 88
98 0 96 -76 -82 -71 89 86 -23 -10 11 -68 -77 69 7 45 98 45 -43 -24 -94 -63 -72 -73 -65 48 84 -33 -69 -38 -57 13 -60 -47 -10 59 32
51 37 64 -73 -9 93 84 -9 3 37 53 -7 -99 3 -88 11 4 95 -82 -46 91 -99 66 -27 40 -84 -94 25 75 -81 29 -32 -6 -67 -27 -45 -17
23 84 -50 -47 49 91 64 34 -93 36 62 17 -64 -7 27 85 -5 33 58 54 52 -12 75 -59 -41 58 71 -64 -86 -8 -94 96 -28 53 -74 -59 84
6 16 -58 -59 93 -56 96 25 87 30 -16 76 9 -74 -6 72 -48 76 -10 20 -30 57 84 63 -66 84 -16 -49 -6 -60 -46 -57 51 99 33 97 61
-22 1 12 9 -82 20 -16 19 4 5 -25 59 84 75 -89 -65 78 61 66 85 -61 -9 -63 -52 61 -94 -80 -42 -78 8 -18 8 -5 -52 71 -50 -74
-6 54 70 -82 67 15 90 92 -91 2 73 33 10 27 -67 86 -4 -31 20 3 5 -61 -43 -24 29 -98 0 -92 66 3 87 -5 60 64 -81 -99 18
this is my output:
• 10073
2682
3632
2626
1549
4356
1277
5474
3815
2789

angga888
Experienced poster
Posts: 143
Joined: Sat Dec 21, 2002 11:41 am
Location: Indonesia
My AC program outputs:

Code: Select all

``````10126
2682
3632
2626
1549
4379
1277
5474
3887
2789``````
Good luck

Moha
Experienced poster
Posts: 216
Joined: Tue Aug 31, 2004 1:02 am
Location: Tehran
Contact:

### At last I Got Accepted !!

I did a very nasty bug in this problem, now I got Accepted with O(n^4). special thanks to angga888.

emotional blind
A great helper
Posts: 383
Joined: Mon Oct 18, 2004 8:25 am
Contact:
i solved this problem using O(n^4) DP algorithm
and get TLE
but the people in forum says that it should be get accepted

where is my algorithm should be checked
my code says my algorithm and it is very easy to read..
C++

Code: Select all

``````ACCEPTED
}``````
plz chek a bit