10987 - Antifloyd

[rushel]

Can this problem be solved using MST?

[Abednego]

I don't think so, but if you find a solution, I would love to hear about it.

[rushel]

Sorry for bothering u guys. I misunderstood the problem. Pardon me.

[rushel]

I tried many time but i failed to attack the problem. Its driving me crazy. Can anybody give some hint.

[Abednego]

There is a hint in the problem's name.

[rushel]

Did i have to run floyd warshall while maximizing path lenght between (u,v)

[Abednego]

My next hint is this.

The Floyd-Warshall algorithm takes an adjacency matrix and returns a shortest path matrix. In this problem, you get an shortest path matrix and have to produce the original adjacency matrix. Since there are multiple possible answers, I am asking you for the matrix with as many 0 entries as possible (as few edges as posssible).

[rushel]

So, I will try to remove the edges descending order from the matrix and check whether shortes paths holds

[Abednego]

My last hint is:

Figure out all the cases when the answer is "impossible". Then you should have a good idea how to solve the "possible" cases.

[rushel]

I am getting WA:
Algo: Invalid Case: C[k]+C[k][v] <C[v] where k != u && k!= v

if not invalid
if(C[k]+C[k][v]==C[v]) then cancel edge(u,v);
where k!=u and k!=v

Can anyone give me some test cases?

[rushel]

Thanks Abednego I got AC. I did mistake in reading input. Thanks Once Again For ur Help.

[Darko]

I don't know much about graphs so I thought about MST first, too (go me). As in - find MST of the shortest path matrix then do the Floyd's on it and compare it with the original one. If they are the same, print the tree. That doesn't work (well, works for the sample input, heh). I have no idea why it should or shouldn't work, though

Anyway - I just wanted to mention that input contains blank lines.

[kbr_iut]

I am getting WA. I tried with many inputs but failed to get the bugs.Can anyone help?
i just consider invalid where m[k]+m[k][j]<m[j]
and if not invalid then i just print the value of i i+1 value (where i is from 1 to n-1 )
is my algo correct?
here is my code.

Code: Select all

#include<iostream>
#include<algorithm>
using namespace std;
long n,e,m[200][200],sum;
bool antifloyed(){
	int i,j,k;
	for(k=1;k<=n;k++){
		for(i=1;i<=n;i++){
			for(j=1;j<=n;j++){
				if(k==i||k==j||i==j)continue;
				if(m[i][k]+m[k][j]<m[i][j])return true;
			}
		}
	}
	return false;
}
int main(){
	long t,x=0,i,j;
	//freopen("1.txt","r",stdin);
	cin>>t;
	while(t--){
		cout<<"Case #"<<++x<<":\n";
		cin>>n;
		fill(m[0],m[n+1],0);
		for(i=2;i<=n;i++){
			for(j=1;j<i;j++){
				cin>>m[i][j];
				m[j][i]=m[i][j];
			}
		}
		if(antifloyed()){cout<<"Need better measurements.\n\n";continue;}
		cout<<n-1<<endl;
		for(i=1;i<n;i++)cout<<i<<" "<<i+1<<" "<<m[i][i+1]<<endl;	
		cout<<endl;
	}
	return 0;
}

if possible pliz anyone give me some more test cases.
thanx in advance.

[calicratis19]

I tried it with floyd and mst together. But got wa.
my approach:
1) First run a floyd with the given floyd matrix and see if there is a better path.If there is a shorter path then its impossilbe. else i run a kruskel with the given floyd matrix . And then i print the edges. I am not sure if its the correct approach.Can anyone please clarify this for me. Thanks in advance

Code: Select all

#include<stdio.h>
#include<stdlib.h>
int node,rank[1001],parent[1001],i,j,k,u,v,pos[1002][3],edge,test,mat[102][102],kase;
bool flg;

typedef struct{
    int x,y,z;
}Ind;
Ind ar[10011],ans[10011];
int cmp(const void *a,const void *b)
{
   Ind *X = (Ind *) a;
   Ind *Y = (Ind *) b;
   if(X->y == Y->y)return X->z - Y->z;
   return X->y - Y->y;
}
int cmp1(const void *a,const void *b)
{
   Ind *X = (Ind *) a;
   Ind *Y = (Ind *) b;

   return X->x - Y->x;
}
int Find_Set(int x)
{
   if(x != parent[x] )
      parent[x]=Find_Set(parent[x]);
   return parent[x];
}
void Link(int x,int y)
{
    if(rank[x]>rank[y])
        parent[y]=x;
    else
    {
        parent[x]=y;
        if(rank[x]==rank[y])
            rank[y]=rank[y]+1;
    }
}
int main()
{

    scanf("%d",&test);
    while(test--)
    {
        scanf("%d",&node);
        k=0;
        for(i=0;i<node;i++) parent[i] = i,rank[i] = 0;
        for(i=1;i<node;i++)
        {
            for(j=0;j<i;j++)
            {
                scanf("%d",&u);
                ar[k].x = u ;
                ar[k].y = j ;
                ar[k++].z = i ;
                mat[j][i] = mat[i][j] = u;
            }
            mat[i][i]=0;
        }
        edge = k;
        flg = 0;
        for(k=0;k<node && !flg;k++)
            for(i=0;i<node && !flg;i++)
                for(j=0;j<node;j++)
                    if(mat[i][j] > mat[i][k]+mat[k][j])
                    {
                        flg = 1;
                        break;
                    }
        printf("Case #%d:\n",++kase);
        if(!flg)
        {
           qsort(ar,edge,sizeof(Ind),cmp1);
          /* for(i=0;i<edge;i++)
                    printf("%d %d %d\n",ar[i].x,ar[i].y+1,ar[i].z+1);*/
            k=0;

            for( i=0 ; i<edge ; i++ )
            {
                u=Find_Set(ar[i].y);
                v=Find_Set(ar[i].z);
                if(u!=v)
                {
                    Link(u,v);
                    ans[k].x = ar[i].y;
                    ans[k].y = ar[i].z;
                    ans[k++].z = ar[i].x;
                }
            }
            qsort(ans,k,sizeof(Ind),cmp);
            if(k!=node-1)
            {
                flg = 1;break;
            }
            for(i=0;i<k;i++)
                printf("%d %d %d\n",ans[i].x+1,ans[i].y+1,ans[i].z);

        }
        if(flg) printf("Need better measurements.\n");
        printf("\n");
    }
    return 0;
}