10003 - Cutting Sticks

[bnbolo]

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

THX!

[Algoritmo]

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]

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]

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

[sohel]

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]

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.

[angga888]

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]

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 ]

[I LIKE GN]

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?

[pigwoley]

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]

Problem solved. Used arrays rather than vectors.

[jambon]

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]

Check this link:
http://online-judge.uva.es/board/viewtopic.php?t=7429

Online judge uses Java 1.1 sans useful stuff.

Darko

[chunyi81]

As Darko said, check out the HowTOs. BufferedReader, for some reason is now allowed in this online judge.

[shihabrc]

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