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Calculate the index sum and the value sum for for the first index.
Compute the difference between the sums - if its zero then the first number is not missing.
Increment the index and recalculate the index sum and the value sum.
Again compute the difference between the sums and also the 2nd difference - if this value is zero then the first missing number has not been found, if the second difference is 1 then the current index is the first missing number.
Continue until the second difference is 2 then the index at this point is the second missing number. etc.
Only 3 variables required (index, index sum, value sum) differences are temporary storage and it works for any number of missing values in a single pass!!
Apathy Rules - I suppose...
Its not the things you fear that come to get you but all the things that you don't expect
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There are 100 unrepeated numbers, the sum of which will be (1 + 2 + 3 + ... + 100). The summation equivalent to factorial - not sure if there is a proper mathematical name for it. If you then add up all the numbers in your array, the difference between these two answers must be the "rogue" number. I've not tried it but I think that's it.
Edit: Ah! ... just realised there were loads of other answers on the next page ... so this is history not news 
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Papadimitriou and Steiglitz wrote the following [see citation, section 15.2]:
"A combinatorial optimization problem is thus the following form of computational problem.
"Given representations of the parameters... find the optimal feasible solution.
"We call this the optimization version of the problem. However, a combinatorial optimization problem can also be posed in the following, more relaxed, form.
"Given [the parameters]... find the cost of the optimal solution.
"This will be referred to as the evaluation version of a combinatorial optimization problem. It is immediate that, under the assumption that... [the cost] is not too hard to compute--the evaluation version of a combinatorial optimization problem cannot be much harder that the optimization version."
I omitted some notation and terms, the definitions of which were earlier in the chapter. As I understand it, they are saying that these two versions are pretty much the same, though the evaluation version may be a bit harder. I don't see how that could be. The evaluation version only seeks the cost of the optimal solution, whereas the optimization version seeks the optimal solution itself. In order to find that optimal solution, certainly you must need to compute the cost of it. Am I missing something?
Thanks,
Alex
Citation: Papadimitriou & Steiglitz, Combinatorial Optimization, Dover, 1982.
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There may be a shortcut that lets you calculate the cost of an optimal solution (or at least prove some bounds on it) without actually calculating it.
This is similar to an existence proof in mathematics, where it's shown that a solution exists without actually finding it.
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Hi,
I need to find some way to get the LCS for some special strings.
Imagine we have two CSV files (tables where , column delimiter)
1)
a b c,d e f
One row with 2 columns
2)
a,d
b,e
c,f
Three rows with 2 columns
When i'm trying to get the regular LCS i'm missing a lot of data:
a b c,d e f
a, d b,e c,f
LCS:
a b c f
But it must be totally equal, because three rows can be fitted in one.
Can someone suggest some algorithm, or some preprocessing method?
The main pain that there can be adds and deletes, so i need to find some longest path.
Thank you.
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follow this algorithm ; What is there bigO
int sum = 0;
for(int i = 0 ; i < n ; i++){
for(int j = 0 ; j < n*n; j++){
sum += j;
}
}
Thank you for Answer 
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Hi,
you really should be able to figure it out yourself.
Just imagine you were to execute the code for some value of n and estimate the
number of important operations; and then for a value twice as large.
The ratio between those two "measures of complexity" should be visible in the big O.
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bosszy wrote: What is there bigO
You should really do your own homework. What do you think it is? You should really try it rather than waiting for an answer. The answer is really easy, and if you can't figure it out, then, well, don't know what to tell you.
"The clue train passed his station without stopping." - John Simmons / outlaw programmer
"Real programmers just throw a bunch of 1s and 0s at the computer to see what sticks" - Pete O'Hanlon
"Not only do you continue to babble nonsense, you can't even correctly remember the nonsense you babbled just minutes ago." - Rob Graham
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Paul Conrad wrote: don't know what to tell you
you don't know either? 
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Luc Pattyn wrote: you don't know either?
Heck yeah, I know the answer to it (it is a polynomial), but not going to announce it for him to cheat on his assignment.
"The clue train passed his station without stopping." - John Simmons / outlaw programmer
"Real programmers just throw a bunch of 1s and 0s at the computer to see what sticks" - Pete O'Hanlon
"Not only do you continue to babble nonsense, you can't even correctly remember the nonsense you babbled just minutes ago." - Rob Graham
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Assuming n>0, if you want to know how often "sum += j;" is executed, it's n cubed exactly -- never mind the big O.
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I am trying to implement Choleski's algorithm for a 5 by 5 matrix. When I run compare the results to Sci Lab, I find that my answer is different. Therefore, I am assuming that I am wrong. The code below is based on an algorithm given in the book "Numerical Analysis" by Burden, Faires
and Reynolds. Here is code:
void
Cholesky(double a[5][5], double l[5][5] )
{
const int n = 5;
l[0][0] = sqrt(a[0][0]);
for( int j=2; j<=n; j++ )
l[j-1][0] = a[j-1][0]/l[0][0];
for( int i = 2 ; i<=(n-1); i++ ) {
double sum = a[i-1][i-1];
for( int k=1; k<=i-1; k++ )
sum -= (l[i-1][k-1])*(l[i-1][k-1]);
l[i-1][i-1] = sqrt(sum);
for( int j = i+1; j<=n; j++ ) {
double sum = a[j-1][i-1];
for( int k = 1; k <= (i-1); k ++ )
sum -= l[j-1][k-1] * l[i-1][k-1];
l[j][i] = sum/l[i-1][i-1];
}
}
double sum = a[n-1][n-1];
for( int k = 1; k<=(n-1); k++ )
sum -= l[n-1][k-1] * l[n-1][k-1];
l[n-1][n-1] = sqrt(sum);
}
I am hoping that somebody can tell me where my problem is. Thanks.
Bob
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Hi Bob,
I think you should check your indices. I prefer the Numerical Recipes in C[^] version. See Chapter 2 Solution of Linear Algebraic Equations for other code. The Cholesky code for the Numerical Recipes routine is:
#include <math.h>
void choldc(float **a, int n, float p[])
{
void nrerror(char error_text[]);
int i,j,k;
float sum;
for (i=1;i<=n;i++) {
for (j=i;j<=n;j++) {
for (sum=a[i][j],k=i-1;k>=1;k--) sum -= a[i][k]*a[j][k];
if (i == j) {
if (sum <= 0.0)
nrerror("choldc failed");
p[i]=sqrt(sum);
} else a[j][i]=sum/p[i];
}
}
}
</math.h>
Try the NR code and see how it works.
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Thanks for the response, it was very helpful.
Bob
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BobInNJ wrote: Thanks for the response, it was very helpful.
No problem!
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Hi,
BobInNJ wrote: l[j][i] = sum/l[i-1][i-1];
IMO this is where the problem is.
Some more comments:
1.
the first few lines are not really useful
l[0][0] = sqrt(a[0][0]);
for( int j=2; j<=n; j++ )l[j-1][0] = a[j-1][0]/l[0][0];
you could get them for free by starting the next for loop with i=1 instead of i=2
2.
you are aware you could do the same thing in place? i.e. you can store l in a, you don't really need a separate array for input and output.
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Has anyone implemented clarke and wright algorithm with multiple truck capacities.If yes please help me with implementing the same. Thanks
Hemanth
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Try this: Single-Depot VRP[^].
They don't give you the code but there's more than enough information to show you how to implement it.
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plz help me in writing an algorithm of the following problem
Problem:
"Let S be a set of n disjoint line segments in the plane, and let p be a point not on any of the line segments of S. We wish to determine all line segments of S that p can see, that is, all line segments of S that contains some points q so that the open segment pq does not intersect any line segment of S. Give an O(nlogn) time algorithm for this problem that uses a rotating half line with its endpoint at p."
regards,
Irfan
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Sounds like homework to me.
What have you done to solve this yourself? Any code that doesn't work? Google is your friend!
Dave.
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you are a good algorithm writer as I think.
please help me in this regard. I could not find anything relevent to this problem.
kindly do this for me please.
I am waiting for your positive response.
regards,
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Here is an algorithm that solves your particular problem and many others as well:
1. formulate your problem (you did very well at that)
2. open the Google search page and enter the entire problem description into the textbox
3. click the "Search" button
4. wait a few seconds to see a small number of hits out of an often huge number of hits.
5. scan the list, open the ones that look most promising.
6. if necessary, click for the next page of hits.
7. repeat steps 4,5,6 if no solution found yet.
For your particular problem, there are over 50,000 hits. Now only two possibilities remain:
A. some of those contain a decent answer; problem solved.
B. they all repeat the problem without offering the solution; it is therefore safe to assume nobody knows the answer, so don't waste your time and ours, go do something completely different instead.
Good luck.
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Sorry, but this is the worst advice I can imagine. 
Do NOT search google! SOLVE the problem! And don't crib...
Greetings - Gajatko
Portable.NET is part of DotGNU, a project to build a complete Free Software replacement for .NET - a system that truly belongs to the developers.
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gajatko wrote: Do NOT search google! SOLVE the problem!
I agree. But there is nothing wrong with researching the problem on google for the sake of better clarity or understanding of the problem, but using google just to find an answer to the problem is a whole different matter.
"The clue train passed his station without stopping." - John Simmons / outlaw programmer
"Real programmers just throw a bunch of 1s and 0s at the computer to see what sticks" - Pete O'Hanlon
"Not only do you continue to babble nonsense, you can't even correctly remember the nonsense you babbled just minutes ago." - Rob Graham
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