# Light OJ 1257 – Farthest Nodes in a Tree (II)

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]).

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