Problem Link : http://www.lightoj.com/volume_showproblem.php?problem=1257

/*
         +-+ +-+ +-+
         |R| |.| |S|
         +-+ +-+ +-+
 */

#include <bits/stdc++.h>

#define pii             pair <int,int>
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout<<#x " = "<<(x)<<endl
#define VI              vector <int>
#define DBG             pf("Hi\n")
#define MOD             100007
#define MAX             30001
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf("%d",&a)
#define sff(a,b)        scanf("%d%d",&a,&b)
#define sfff(a,b,c)     scanf("%d%d%d",&a,&b,&c)
#define loop(i,n)       for(int i=0;i<n;i++)
#define REP(i,a,b)      for(int i=a;i<b;i++)
#define TEST_CASE(t)    for(int z=1;z<=t;z++)
#define PRINT_CASE      printf("Case %d:\n",z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long


using namespace std;

vector<int> graph[MAX],cost[MAX];

int dis[MAX];
int dis1[MAX];
int a,b,max_dis,n;

void BFS(int src)
{
    dis[src]=0;
    queue<int>Q;
    Q.push(src);
    while(!Q.empty())
    {
        int u= Q.front();
        Q.pop();
        if(dis[u]>max_dis)
        {
            max_dis=dis[u];
            a=u;
        }
        loop(i,SZ(graph[u]))
        {
            int v=graph[u][i];
            if(dis[v]==-1)
            {
                dis[v]=dis[u]+cost[u][i];
                Q.push(v);
            }
        }
    }
}

void BFS1(int src)
{
    dis1[src]=0;
    queue<int>Q;
    Q.push(src);
    while(!Q.empty())
    {
        int u= Q.front();
        Q.pop();
        loop(i,SZ(graph[u]))
        {
            int v=graph[u][i];
            if(dis1[v]==-1)
            {
                dis1[v]=dis1[u]+cost[u][i];
                Q.push(v);
            }
        }
    }
}

void allclear()
{
    loop(i,n+1)
    {
        graph[i].clear();
        cost[i].clear();
        dis[i]=-1;
        dis1[i]=-1;
    }
    max_dis=-1;
    a=b=-1;
}

int main()
{
    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);
    int t,x,y,w;
    sf(t);

    TEST_CASE(t)
    {
        sf(n);
        allclear();
        loop(i,n-1)
        {
            sfff(x,y,w);
            graph[x].pb(y);
            graph[y].pb(x);
            cost[x].pb(w);
            cost[y].pb(w);
        }
        BFS(0);
        b=a;
        loop(i,n+1)
            dis[i]=-1;
        max_dis=-1;
        BFS(b);
        b=a;
        BFS1(b);
        PRINT_CASE;
        loop(i,n)
        {
            pf("%d\n",max(dis[i],dis1[i]));
        }
    }
    return 0;
}

Algorithm:

1. Run a BFS from any node and determine the farthest node from it and Name this node as b.
2. Run another BFS from b and save all node’s distance from b (dis array). and determine the farthest node from b and name this node as a;
3. Run another BFS from a and save all nodes distance from a (dis1 array).
4. Now print for all node max(dis[node], dis1[node]).