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You are given an undirected graph with N vertices and M edges, where the weights are unique. 

There is a function Cost(u, v), which is defined as follows:

While there is a path between vertex u and v, delete the edge with the smallest weight. Cost(u,v) is the sum of the weights of the edges that were deleted in this process.


For example, from the graph above (same as the sample input), Cost(2,6) is 2+3+4+5+6 = 20.

Given an undirected graph, your task is to calculate the sum of Cost(u,v) for all vertices u and v, where u < v. Since the answer can get large, output the answer modulo 10^9.


The first line of the input consists of two integers, N and M. (1 <= N <= 100,000, 0 <= M <= 100,000)

The next M lines consists of three integers, u, v, and w. This means that there is an edge between vertex u and v with weight w. (1 <= u, v <= N, 1 <= w <= 100,000)


Output the sum specified in the problem statement.


6 7
1 2 10
2 3 2
4 3 5
6 3 15
3 5 4
4 5 3
2 6 6 Output: 256

hide comments
ankhang277: 2021-08-03 15:27:24

Wr in someway that i strongly believe my code was right

jeaf_dean: 2021-06-05 15:57:30

"While there is a path between vertex u and v, delete the edge with the smallest weight" doesn't imply weight in a given path.
wasted much time in getting this.

greenindia: 2021-03-06 18:19:25

i think its the best question on dsu

lamda_cdm_10: 2021-02-26 17:07:10

Beautiful problem on DSU . Enjoy solving it !!

iamfarraz: 2020-11-02 22:18:06

why sigabrt : (((

anish1712: 2020-06-28 22:59:07

I removed SIGSEGV by adding
if(!m) return cout << 0, 0;

It passed too!

Last edit: 2020-06-28 22:59:42
luvkumbi: 2020-03-13 09:28:52

getting SIGSEGV ....any help?.....perfectly runs on my ide

nadstratosfer: 2020-03-01 22:12:29

From TLE in C to AC in pure Python =) Great problem, came upon more ideas just improving my code here than I usually get solving several tasks.

kushagra_2: 2020-02-26 13:54:37

undoubtedly the best mst problem on spoj
Some hints to those who are struggling to solve it :
1) Try to think it in reverse fashion like instead of deleting try to join nodes and create a maximum spanning tree.
2) Now to get to the answer think that what will be the contribution of a particular edge into the answer like how many times will this edge get into the answer. One crucial observation is that that a particular edge of wieght w will contribute to only those pairs (u,v) when w is the smallest edge in that path...

coolio_1: 2020-02-25 17:14:08

Take MOD 10^9 :)

Added by:Lawl
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:2011 KOI Regional