A tree is a connected graph containing no cycles. A vertex is called a median vertex if the total cost to reach all vertices is minimal. There could be more than one median vertex in a tree, that’s why we define median as the set of all median vertices. To find median in a tree with small number of vertices is fairly easy task as you can solve this by a simple brute force program.
In the left figure, we can see a weighted tree with 5 vertices. The tree median is {B} because the total cost from vertex B to all other vertices is minimal.
B-A = 2 B-D = 7
B-C = 1 B-E = 7 + 5 = 12
TOTAL = 2 + 1 + 7 + 12 = 22
What if the number of vertices is quite large? This might be a problem since brute force program cost too much time. Given a weighted tree with
N vertices, output the total cost to reach all vertices from its median.
Input
Input consists of several cases. Each case begins with an integer
n (1<=
n <= 10,000) denoting the number of vertices in a tree. Each vertex is numbered from 0...
n-1. Each of the next
n-1 lines contains three integers:
a,
b, and
w (1<=
w <= 100), which means
a and
b is connected by an edge with weight
w.
Input is terminated when
n is equal to 0. This input should not be processed.
Output
For each case, output a line containing the sum of cost of path to all other vertices from the tree median.
Sample Input
5
0 1 2
1 2 1
1 3 7
3 4 5
6
0 1 1
1 2 4
2 3 1
3 4 4
4 5 1
0
Sample Output
22
21
Problem Setter: Suhendry Effendy