## 10003 - Cutting Sticks

All about problems in Volume 100. If there is a thread about your problem, please use it. If not, create one with its number in the subject.

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bnbolo
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Joined: Mon Nov 03, 2003 9:21 am

### I don't really understand your mean.

could you please paste your code out , or give your algorithm in pseudocode?

THX!

Algoritmo
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### Re: I don't really understand your mean.

bnbolo wrote: could you please paste your code out , or give your algorithm in pseudocode?

THX!
Bad news: No, I can't paste or post my code here
Good news: I have made a page explaining my solution

It was hard for me to think about a complete solution untill I wrote this in a piece of paper:

For more images and my complete explanation, have a look at:
http://200.167.46.219/ACM/10003.htm
Fell free to correct me if I wrote something wrong.

czar
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Joined: Tue Jun 10, 2003 7:30 pm

### 10003 Cutting Sticks

I was wondering if anyone had any suggestions on speeding this program up keeping the top down structure of the solution (It gets accepted but takes 9 secs on the test cases).

[cpp]
#include<iostream>
#include<vector>
#include<string>
#include<algorithm>

using namespace std;

typedef vector<int> VI; typedef vector<vector<int> > VVI;
typedef vector<string> VS; typedef vector<vector<string> > VVS;
typedef pair<int, int> PII;

VVI memo;

int doit(int len, const VI &cuts, int bin, int ein, int sl, int el) {

int ret = INT_MAX;

if(memo[bin][ein]) return memo[bin][ein];

if(bin >= ein) return 0;

for(int i = bin; i < ein; i++) {

int l = doit(cuts-sl, cuts, bin, i, 0, cuts);
int r = doit(el-cuts, cuts, i+1, ein, cuts, el);
ret = min( ret, l+r+len );

}

return memo[bin][ein] = ret;

}

int main() {

int len;

while(cin>>len) {

if(len == 0) break;

cin.ignore();

int ncuts, cut;
VI cuts;

cin>>ncuts; cin.ignore();
memo = VVI(ncuts+1, VI(ncuts+1));

for(int i = 0; i < ncuts; i++) {

cin>>cut; cin.ignore();
cuts.push_back(cut);

}

cout<<"The minimum cutting is "<<doit(len, cuts, 0, ncuts, 0, len)<<"."<<endl;

}

return 0;

}
[/cpp]

Faiz_Buet
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Joined: Mon Apr 19, 2004 9:20 am

### 10003

can we give me a way of solving the prob. 10003 'CUTTING STICK PROBLEM'

sohel
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Joined: Thu Jan 30, 2003 5:50 am
Location: New York

### MCM

This problem is very similar to matrix chain multiplication.

Maintain an array m[][] and update it dynamically.

Suppose you are given a stick of length N and c cuts are to be made. Then, at first a cut is to be made at k ( k<c+1) such that
m[1][k] + m[k+1][c+1] is minimum. And by the prinicple of optimality
m[1][k] and m[k+1][c] has got to be optimal.

and finally m[1][c+1] is the reqd answer.

Hackson
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### 10003 Cutting Sticks TLE, shouldn't it be O(n^3)?

Hi there, I have written 10003 using nearly the same algo as Matrix Chain Multiplication and submit it, but it gives me TLE.
I wonder if I have made anything wrong or there exists a better Algorithm.
Here comes my Code:

Code: Select all

``````Accepted, NO SPOILING!
``````
I hope someone can answer my question...

btw, DP is very difficult too...

Thanks a lot.
Last edited by Hackson on Tue Jul 19, 2005 5:37 pm, edited 1 time in total.
Solving problem is a no easy task...

angga888
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Posts: 143
Joined: Sat Dec 21, 2002 11:41 am
Location: Indonesia

Code: Select all

``````for i := 0 to 2000 do
for j := 0 to 2000 do
dp[i, j] := 99999;``````
You only need to initialize the variable as needed. No need to always perform 2000*2000 loop as above.

Hackson
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Posts: 35
Joined: Sun Nov 10, 2002 5:36 am
angga888 wrote:

Code: Select all

``````for i := 0 to 2000 do
for j := 0 to 2000 do
dp[i, j] := 99999;``````
You only need to initialize the variable as needed. No need to always perform 2000*2000 loop as above.
I 've got AC, thank you!!! [I have declared too large array size ]
Solving problem is a no easy task...

I LIKE GN
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hello all......
i amm not sure how DP logic works here...
please help me understand...
let's say we to cut at 2,4,7 and the stick is up to 10.
when considering the calculation of 0 to 7
we have the following sub-chains...
0 2, 2 7,
0 4, 4 7,
0 7, 0 2, 2 7
0 7, 0 4,
for the first two rows the calculations are fine(using previous values)
for the 3rd and 4th 0 7, and 0 2, are easy to know but what abot 2 7 and 0 4 ???
since while i calculated 2 7 the stick was up to 8(10-2 = but now it's up to 5
(7-2 = 5). so how to get the value with pre-calculation?
There are two tragedies in life one is to lose your hearts' desire and another is to gain it --- GBS.

pigwoley
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Posts: 3
Joined: Sat Jun 25, 2005 2:06 am

### 10003 - Cutting Sticks (TLE)

Hey, I implemented a solution similar to matrix-chain multiplication. Because it is an O(n^3) algorithm, and n is at most 51, I shouldn't have to worry about anything else, right? I have no idea what is wrong. Here is my code:

Code: Select all

``````// Headers, etc...

#define in cin

using namespace std;

vector<int> CutSpots;
int length, cuts;
vector< vector<int> > memo;
int MV = 1<<15;

int BestWay(int a, int b)
{
if(memo[a][b] != -1)
return memo[a][b];

if(b-a == 1)
return memo[a][b] = 0;

int minv = MV;
for(int i = a+1; i < b; ++i)
{
//cut here
minv = min(minv, (CutSpots[i]-CutSpots[a]) + (CutSpots[b]-CutSpots[i])
+ BestWay(a,i) + BestWay(i, b) );

}
return memo[a][b] = minv;
}

int main()
{
//ifstream in("in.txt");
while(1)
{
in >> length;
if(length == 0)
break;

in >> cuts;

CutSpots = vector<int>(cuts);

CutSpots.push_back(0);

//given in increasing order
for(int i = 0; i < cuts; ++i)
in >> CutSpots[i+1];

CutSpots.push_back(length);

memo = vector< vector<int> >(cuts+2, vector<int>(cuts+2,-1));

cout << "The minimum cutting is " << BestWay(0, cuts+1) << "." << endl;
}
return 0;
}

``````
What did I do wrong?

pigwoley
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Joined: Sat Jun 25, 2005 2:06 am
Problem solved. Used arrays rather than vectors.

jambon
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Posts: 1
Joined: Tue Oct 08, 2002 7:31 pm

### 10003 - Java code - Need help

Hi all,

I am new in Java and this is one of my first Java programs. I submited and got "Compile Error". Please help me. I tested in my computer and it worked fine. At least it compiled.

Here is my code. Please take a look.

Code: Select all

``````import java.io.*;
import java.util.*;

class p10003
{
public static void main(String args[]) throws IOException
{
BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
int m = Integer.parseInt(stdin.readLine());

while (m != 0)
{
int n = Integer.parseInt(stdin.readLine());
String[] sp = stdin.readLine().split(" ");
a = new int[n];
for (int i = 0; i < n; i++) a[i] = Integer.parseInt(sp[i]);

d = new int[m + 1][m + 1];
for (int i = 0; i <= m; i++)
for (int j = 0; j <= m; j++) d[i][j] = -1;

System.out.println("The minimum cutting is " + C(0, m) + ".");

m = Integer.parseInt(stdin.readLine());
}
}

static int[][] d;
static int[] a;

static int C(int left, int right)
{
if (d[left][right] != -1) return d[left][right];

int ret = 10000;
for (int i = 0; i < a.length; i++)
if (a[i] > left && a[i] < right)
{
ret = Math.min(ret, C(left, a[i]) + C(a[i], right));
}
if (ret == 10000) ret = 0;
else ret += right - left;
d[left][right] = ret;
return ret;
}
}
``````

Darko
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Posts: 580
Joined: Fri Nov 11, 2005 9:34 am
Location: Calgary, Canada
Check this link:
http://online-judge.uva.es/board/viewtopic.php?t=7429

Online judge uses Java 1.1 sans useful stuff.

Darko

chunyi81
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Joined: Sat Jun 21, 2003 4:19 am
Location: Singapore
As Darko said, check out the HowTOs. BufferedReader, for some reason is now allowed in this online judge.

shihabrc
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Location: CSE,BUET
Contact:

### 10003 TLE

I've solved this problems with a simillar approach to matrix chain multiplication. i think its complexity is O(L^2*n) where L is the length of the stick and n is the number of cut points. Since n is small this should run in time. But, i'm gettin TLE. Can someone help me plz

Code: Select all

``````
//removed after AC

``````
Plz hlp.

-Shihab
Last edited by shihabrc on Fri Jun 23, 2006 5:31 pm, edited 1 time in total.
Shihab
CSE,BUET