307 - Sticks

[wsarzynski]

By the way, this is not NP-complete problem.
(Parts lenghts are bounded by 50).

[uzioriluzan]

Hi all! What's the idea behind the dynamic programming?
Thanx a lot!

My solution worked with an array with 100000 elements. So there are no more than 100000 parts in the input.
But how do you store the used solutions? I think this is your problem. I used another array of 100000 elements to memorize, which parts I had used and reset it after every step (that means after I had not found a solution with length n and had to look for a solution with length n+1).

[zerosean]

these are test data I have:

9
12 12 12 11 11 11 10 10 10
48
3 7 8 4 1 1 6 3 6 1 5 5 8 4 8 2 7 6 3 3 8 5 6 7 4 8 6 6 8 5 8 3 3 5 5 4 1 8 3 1 2 7 1 6 2 6 8 8
38
2 6 6 8 7 4 1 8 4 1 4 4 3 3 2 3 3 4 6 8 8 7 2 4 1 1 5 8 4 7 6 5 1 3 3 3 1 6
9
5 2 1 5 2 1 5 2 1
4
1 2 3 4
9
2 2 2 2 2 2 2 3 3
40
1 1 2 2 2 2 2 2 3 3 3 4 4 4 4 5 6 7 7 7 8 8 8 9 9 11 11 11 12 12 12 13 14 14 15 16 21 22 35 40
10
21 14 13 11 9 6 4 3 2 1

and these are my output:
33
47
18
6
5
10
62
21

However, I had Wrong Answer judge after 6 sec of running.
I just worn out..
What's wrong?
Can you show me other test data?

below is my algorithm sketch:
1) read input
2) guess target stick length : a number can divide sum of input
3) verify target length : first fit and backtrack
a. number of subset = sum of input / target stick length
b. make all subset size = target stick length
use first fit: that is, blindly select first item of array
c. if fail, backtrack
. erase failed subset from item list
. generate subset of failed(size mismatch) subset
. add subset to the item list and retry until all subset tried

[hank]

Does anybody know how to solve this problem without TLE....?

[turuthok]

This problem is really interesting and hard at the same time. It slowly leads me to bin-packing or integer-partioning problem ... which is NP-hard ... Most likely, my approach is not right ... could somebody give me a hint on this ...

Thanks a lot,

-turuthok-

[anupam]

i used dp but getting wa...
is there any tricky case????

[turuthok]

Just an update, ... I've been trying to solve this problem using "backtracking". It sure involves a lot of optimization. But, so far, mine still got TLE.

Still can't think of any DP approach for this ... I definitely need some words of wisdom here ...

BTW, ...
I noticed that as of today, the time-limit for this problem is 10 seconds. I saw lots of AC-ed solutions took more than 10 seconds.

-turuthok-

[Dominik Michniewski]

If judge don't rejudge this problem yet, it's possible, that in ranklist are solutions which took more then 10 sec of time. But after rejudgement they disappear

Dominik

[turuthok]

Could somebody please confirm these input/outputs:

Input

Code: Select all

100
49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49
49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49
49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49
49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49
49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 1 1 1 1 3
100
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 47
100
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 49
100
49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49
49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49
49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49
49 49 47 47 47 47 49 49 49 49 49 49 49 49 49 49 49 49 49 49
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 49
9
5 2 1 5 2 1 5 2 1 
4 
1 2 3 4 
0 

Output

Code: Select all

4662
54
74
4911
6
5

Is there any critical-input with at most 100 parts ... I know I got TLE >= 10 secs with inputs <= 100 from the judge. For above inputs, my solution gives the outputs pretty quick.

Thanks for any inputs/suggestions ...

-turuthok-

[Per]

turuthok: your output is correct (or at least my accepted solution outputs the same).

Here are the test cases I used.

Code: Select all

57
50 49 48 43 32 29 28 17 14 13 12 12 9 8 6 28 29 12 32 48 40 8 13 9 49 12 43 17 14 50 2 3 3 2 1 2 37 30 19 2 31 3 12 31 31 23 9 5 49 4 23 49 43 50 25 24 8 8
10
21 14 13 11 9 6 4 3 2 1
48
3 7 8 4 1 1 6 3 6 1 5 5 8 4 8 2 7 6 3 3 8 5 6 7 4 8 6 6 8 5 8 3 3 5 5 4 1 8 3 1 2 7 1 6 2 6 8 8
38
2 6 6 8 7 4 1 8 4 1 4 4 3 3 2 3 3 4 6 8 8 7 2 4 1 1 5 8 4 7 6 5 1 3 3 3 1 6

Output should be

Code: Select all

82
21
47
18

[hank]

The problem must be solved by Backtracking.

[hank]

How did you solve it? Can you share your method with us?

Thanks a lot!!

[hank]

i used dp but getting wa...
is there any tricky case????

The problem can be solved by DP? That's interesting!!
What's your method?

[hank]

Hello Adrian Kuegel!!
What is your method to solve this problem?
Can you share your method with us?

[hank]

Hi, I still can't figure out the problem.
My method is using recursion. and I always get TLE...
(but I think it is fast enough)
The following is my code. I hope you can give me some tips.
Thanks in advance.
[c]#include "stdio.h"
#include "stdlib.h"
#include "string.h"
#define MAX 200
int n,stick[MAX],howmany[MAX],target,yes,count,sum;
int newc,pp;
void sort_stick()
{
int i,j,p;
do{
p=0;
for(i=1;i<=count;i++)
if(stick[i-1]<stick){
stick[i-1]^=stick^=stick[i-1]^=stick;
howmany[i-1]^=howmany^=howmany[i-1]^=howmany;
p=1;
}
}while(p);
}
void recursive(int extra,int finishedstick,int total)
{
int i,j,k,tmp,restart=0;
if(total==target){
finishedstick++;
newc=finishedstick;
restart=1;
if( finishedstick>=pp-1 ) yes=1;
}else if( total>target )
return;
if( yes ) return;
j=total;
for(i=extra;i<=count;i++)
if(howmany>0){
j+=stick*howmany;
if(j>=target) break;
}
if(j<target) return;
for(i=extra;i<=count;i++){
if(howmany<=0) continue;
if( (j=restart?stick:total+stick[i])>target ) continue;
tmp=howmany[i];
howmany[i]--;
recursive(restart?0:i,finishedstick,restart?stick[i]:total+stick[i]);
if( yes ) return;
howmany[i]=tmp;
if(restart||total+stick[i]==target)
return;
}
}
void main()
{
int N,i,tmp,j,k,minlen;
for( ; ; ){
scanf(" %d ", &n );
if(!n) break;
count=-1;
memset(howmany,0,sizeof(howmany));
minlen=0;
for( i=sum=0 ; i<n ; i++ ){
scanf("%d",&tmp);
if(tmp>minlen) minlen=tmp;
sum+=tmp;
k=0;
for(j=k=0;j<=count;j++)
if( stick[j]==tmp ){
howmany[j]++;
k=1;
break;
}
if(!k){
count++;
stick[count]=tmp;
howmany[count]=1;
}
}
sort_stick();
for(i=minlen;i<=sum;i++){
if(sum%i) continue;
target=i;
pp=sum/i;
yes=0;
recursive(0,0,0);
if(yes) {
printf("\n");
break;
}
}
}
}[/c]