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### 10913 - Walking on a Grid

Posted: Sat Sep 24, 2005 5:13 am
dp?

### dp

Posted: Sat Sep 24, 2005 5:21 am
yes, it's DP

time complexity is about o(k * n^2)

Hint :

think when there is no rule that :
You can step on at most k negative integers from source to destination.

then you'll get DP algorithm,

it will be not difficult.

Posted: Sat Sep 24, 2005 5:13 pm
ac now
Thank you

Posted: Sun Sep 25, 2005 2:40 pm
Previous post is mine.

### Re: dp

Posted: Sun Sep 25, 2005 10:58 pm
Anonymous wrote:
wook wrote:yes, it's DP

time complexity is about o(k * n^2)
Are you sure about o(k * n^2) ?

My algo takes o(k * n^3). And work fast enough.
My time complexity is O(kn^2), too. And the memory complexity is O(kn).

Posted: Mon Sep 26, 2005 1:05 am
Thx, I optimized my algo. Now it's O(k * n^2) too.

However running time didn't improved much.

Posted: Mon Sep 26, 2005 2:16 am
kp wrote:Thx, I optimized my algo. Now it's O(k * n^2) too.

However running time didn't improved much.
It would have been more significiant if n would be much bigger than 75.

Posted: Tue Oct 04, 2005 10:14 am
Can someone post some example cases? Thanks!

Posted: Sat Dec 10, 2005 10:43 pm
Larry wrote:Can someone post some example cases? Thanks!
I'm lazy to generate any inputs , but if you post some here I can generate the correct answers for you.

Posted: Tue Jan 03, 2006 8:52 pm
hi,
i cannot make a way to use DP in this problem. if you anyone describe how to implement DP here, i will be greatly helped. btw, can this problem be solved within time limit using dfs?

Posted: Wed Jan 04, 2006 11:57 am
ayon wrote:hi,
i cannot make a way to use DP in this problem. if you anyone describe how to implement DP here, i will be greatly helped. btw, can this problem be solved within time limit using dfs?
I used following DP-algorithm:
In cell t[i,j,g] save the maximum sum of integers of the path to cell(i,j), g is a count negative integer in the sum.
1.) As we start at cell (1,1), in all cells of first row we can arrive from left only. So, t[1,i,g] = t[1,i-1,g]+m[1,i] if m[1,i] >= 0 else t[1,i,g+1] = t[1,i-1,g]+m[1,i].
2.) Then for all row from 2 to n do:
- move down from row (i-1) to row i
if m[i,j] >= 0 then t[i,j,g] = t[i-1,j,g]+m[i,j]
else t[i,j,g] = t[i-1,j,g-1]+m[i,j]
- buf1[j,g] = buf2[j,g] = t[i,j,g]
- move from cell(i,1) to cell (i,n) try to maximize the result in buf1:
if (m[i,j] >= 0) then buf1[j,g] = max(buf1[j,g],buf1[j-1,g]+m[i,j]) else buf1[j,g] = max(buf1[j,g],buf1[j-1,g-1]+m[i,j])
- also move from cell(i,n) to cell (1,n) correct buf2
- t[i,j,g] = max(t[i,j,g],buf1[j,g],buf2[j,g]);
3.) the maximum sum of integers of the path is max(t[n,n,g]) where 0<=g<=k.

Posted: Wed Jan 04, 2006 2:34 pm
thank you very much Andrey, now i understand clearly how to use DP here. your explaination is very clear and fine. thanks again for the help

Posted: Wed Jan 04, 2006 10:18 pm
Someone pls send some critical data, i m getting WA again and again. i use DP.

L I M O N

Posted: Wed Jan 04, 2006 11:31 pm
L I M O N wrote:Someone pls send some critical data, i m getting WA again and again. i use DP.

L I M O N
Try this input:

Code: Select all

``````1 0
1
1 0
-1
1 1
-1
3 0
1 1 1
1 1 1
1 1 1
4 0
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
4 1
1 -1 1 1
-1 1 1 1
10 -1 5 1
1 1 1 1
3 5
-1 -1 -1
-1 -1 -1
-1 -1 -1
3 4
-1 -1 -1
-1 -1 -1
-1 -1 -1
5 2
2 -1 10 3 13
5 -4 3 -2 1
-100 2 3 43 17
24 92 40 14 40
100 100 -1 -1 1
0 0
``````
Output:

Code: Select all

``````Case 1: 1
Case 2: impossible
Case 3: -1
Case 4: 9
Case 5: 13
Case 6: 14
Case 7: -5
Case 8: impossible
Case 9: 280
``````

Posted: Wed Jan 04, 2006 11:45 pm
my outputs :

Case 1: 1
Case 2: impossible
Case 3: -1
Case 4: 9
Case 5: 13
Case 6: 14
Case 7: -5
Case 8: impossible
Case 9: 280

but Same result, WA.
do u use "long long" data type ? i also use this type.

pls send more data

L I M O N