10003 - Cutting Sticks

[ayon]

you used O(L^2*n), L can be 1000 at most, and n only 50
L*L*n = 1000*1000*50 = 50000000 and
n*n*n = 50 * 50 * 50 = 125000
the original matrix chain multiplication algorithm takes only O(n^3) time, that should be used for this problem

[shihabrc]

Thanx a lt. I took too much redaundant states. Now, i've changed my soln. and got AC. Thanx again.

-Shihab

[MAK]

I am using a straightforward recursion+memoization based attack at this problem. Worked for all DP problems I've tried before, but I'm getting TLE on this one. My recurrrence relation is

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cost(start, end)=min(cost(start,k)+cost(k,end)+(end-start))

where k is a cut. Is there a better/faster way?

[debajyoti]

i was looking for a solution.
amazingl thing is that i have tried as the same method like you and found wrong answer.
if you get any help would u please forward me?

debajyoti
debajyoti_mondal_cse@yahoo.com

[IRA]

I use DP method to solve the problem,but still got WA.
Who can give me test data to test my program?
Thanks in advance!

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#include <stdio.h>
#include <limits.h>

int table[100][100]={0};
int profit[100][100]={0};
int data[100];
int n;
int len;

void process(){
   int i,j,k,min=INT_MAX;
   for(i=n-1;i>=1;i--)
      for(j=i+1;j<=n;j++){
         min=INT_MAX;
         for(k=1;k<=j-i;k++){
            if( table[i][j-k]+table[j+1-k][j]<min )
               min=table[i][j-k]+table[j+1-k][j];
         }
         table[i][j]=min;
      }

}

void profit_process(){
   int i,j,k,min=INT_MAX;
   for(i=n-1;i>=1;i--)
      for(j=i+1;j<=n;j++){
         min=INT_MAX;
         for(k=1;k<=j-i;k++){
            if( i==j-k && j+1-k==j ){
               if( table[i][j-k]+table[j+1-k][j]<min )
                  min=table[i][j-k]+table[j+1-k][j];
            }else{
               if( i==j-k ){
                  if( profit[j+1-k][j]+table[i][j]<min )
                     min=profit[j+1-k][j]+table[i][j];

               }else if( j+1-k==j ){
                  if( profit[i][j-k]+table[i][j]<min )
                     min=profit[i][j-k]+table[i][j];
               }else{
                  if( profit[i][j-k]+profit[j+1-k][j]+table[i][j]<min )
                     min=profit[i][j-k]+profit[j+1-k][j]+table[i][j];
               }
            }
         }
         profit[i][j]=min;
      }
      printf("The minimum cutting is %d.\n",profit[1][n]);
}

int main(){

   int i,pre,temp;
   while( scanf("%d",&len)==1 && len ){
      scanf("%d",&n);
      n=n+1;
      pre=0;
      for(i=1;i<n;i++){
         scanf("%d",&temp);
         profit[i][i]=table[i][i]=temp-pre;
         pre=temp;
      }
      profit[i][i]=table[i][i]=len-pre;
      process();
      profit_process();
   }
   return 0;
}

[sumantbhardvaj]

This problem is based upon Matrix Multiplication .
I wrote a top down DP solution to it .which is being timed out. Can't we have top down solution to this problem get accepted ??

Or if there is any mistake in optimization in solution then plz point it out. My code goes as follows.

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#include<string>
#include<iostream>
#include<vector>
#include<algorithm>

using namespace std;

int a[1001];
int data[1001][1001];


class sumant
{
public:
       int count;
       int input()
       {
           int l,x,n;
           cin>>l;
           while(l!=0)
           {
                count=0;
                for(int i=0;i<=l;i++)
                for(int j=0;j<=l;j++)
                data[i][j]=-1;
               
               cin>>n;
               for(int i=0;i<=l;i++)
               a[i]=0;
               
               for(int i=0;i<n;i++)
               {
                   cin>>x;
                   a[x]=1;
               }
               int z=memo(0,l);
               cout<<"The minimum cutting is "<<z<<".\n";
               //cout<<count<<"\n";
               cin>>l;
           }
       }
       int memo(int p,int q)
       {
           if(data[p][q]==-1)
           {
               int z=doit(p,q);
               data[p][q]=z;
               return z;
           }
           else
           {
               return data[p][q];
           }
       }
               
       int doit(int p,int q)
       {
           int min=100000000,m;
           bool flag=false;
           
           for(int i=p+1;i<q;i++)
           {
               if(a[i]!=0)
               {
                          flag=true;break;
               }
           } 
           if(!flag)
           return 0; 
           
           for(int i=p+1;i<q;i++)
           {
                 if(a[i]==1)
                 {
                     //cout<<"madar";       
                     m=q-p+memo(p,i)+memo(i,q);
                     if(min>m)
                     min=m;
                     flag=true;
                 }
           }
                     
           return min;
       }
};
int main()
{
    sumant s;
    s.input();
    return 0;
}


[rio]

Top - down DP is enough to solve this problem.
Your implementation has too waste.

Instead of

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int a[1001];
int data[1001][1001];


Find a way with

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int a[51];
int data[51][51];


ADD : Don't open a new thread if it already exists for the problem.

[andmej]

Hello all,

I'm a dynamic programming newbie.

I'm trying to solve this problem with a recursive function with memoization. However, I'm getting Time limit exceeded. I calculate the cost of cutting stick which starts at position i and ends and position j by finding the minimum cost of summing (j-i) plus the cost of cutting the stick from i to P[k] and from P[k] to j, where P[k] is a given partition point.

I read there's a faster algorithm, but I can't understand it.

Any advice?
Thanks for helping a newbie!

If you are interested, here's my (slow) code:

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I got accepted thanks to the help of emotional blind.


Thanks again!

[emotional blind]

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memset(cache, -1, sizeof(cache));

This part is costly. Try using O(n^2) memory. Here n<50, which is much smaller.

[emotional blind]

Another approach:

remove memset part
and
insert

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   for(int i=0;i<=n+1;++i){
      for(int j=i;j<=n+1;++j){
         cache[p[i]][p[j]]=-1;
      }
   }

after this block

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for (int i=1; i<=n; ++i){
      cin >> p[i];
    }

[andmej]

Thanks a lot, emotional blind. That made the trick and got my program accepted.

I thought memset was the fastest way to initialize a block of memory. However, you made my notice that I'm wasting a lot of space when using a matrix of 1001 * 1001 integers. I think it's possible to solve it using a 52 * 52 integers matrix, I will try to do it.

Thanks again, emotional blind!

[BUET]

why Runtime error?

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#include<iostream>

using namespace std;

#define INF 4294967295
int num,l;
int length;
bool cut[100000];

unsigned long s[2005][2005] = {0};

// will print the ordering of cutting
//this part is optional to UVA 10003 problem

void print(int i,int j)
{
     if( s[i][j] != 0)
     printf("%d ",s[i][j]);
     else return;
     print(i,s[i][j]);
     print(s[i][j],j);
         
     
}


void matrix_chain()
{
     unsigned long m[500][500] = {0};
     //int **m;
     unsigned int q;
     
     int l,j,i,k;
     int check = 0;
     
   
     
     memset(s,0,sizeof(s));
     //memset(m,0,sizeof(m));
     
     for( l = 2; l <= length; l++)
     {
          for( i = 0; i <= length-l; i++)
          {
               j = i+l;
               m[i][j] = INF;
               for( k = i + 1; k < j;k++)
               {
                    if( cut[k] == true )
                    {
                        check = 1;
                        q = m[i][k] + m[k][j] + (j - i);
                   
                        if( q < m[i][j])
                        {
                            m[i][j] = q;
                            s[i][j] = k;
                           
                        }
                    }
                   
               }
               
               if( check == 0)
               {
                   m[i][j] = 0;
               }
               check = 0;
          }
     }
     
     cout << m[0][length] << ".\n" ;
     
     print(0,length);
     
     cout << endl;
     
   
     
}

int main(void)
{
   
    int size,i,k,m,n,c = 1;
    int p[2010] = {0};
   
   
     while(1)
     {
             cin >> l;
             length = l;
             if(!l) break;
             cin >> n;
             
             memset(cut,false,sizeof(cut));
             
             for(i = 1; i <= n; i++)
             {
                   cin >> m;
                   cut[m] = true;

             }
             
              cout << "The minimum cutting is ";
              matrix_chain();
             
     }


   
   
    return 0;
}


[sir. manuel]

libreiries...you need "string.h" to memset,,,too "stdio.h"

[plamplam]

Try to find a O(n*n) algorithm...O(n*n*l) fails.

[bazocc4]

HELPPP... i really don't get to understand the meaning of this problem +_+
can someone please give a short explanation please?
i'm already see http://www.algorithmist.com/index.php/U ... xplanation
but still don't get the problem meaning, very stressed +_+

Thanks in advande