SOLVE
LATER
You are given a directed weighted graph with n nodes and \(2n-2\) edges. The nodes are labeled from 1 to n, while the edges are labeled from 1 to \(2n-2\). The graph's edges can be split into two parts.
You are given q queries. There are two types of queries
Given these queries, print the shortest path lengths.
The first line of input will contain two integers \(n,q\), the number of nodes, and the number of queries, respectively.
The next \(2n-2\) integers will contain 3 integers \(a_i, b_i, c_i\), denoting a directed edge from node \(a_i\) to node \(b_i\) with weight \(c_i\).
The first \(n-1\) of these lines will describe a rooted spanning tree pointing away from node 1, while the last \(n-1\) of these lines will have \(b_i = 1\).
The next q lines will contain 3 integers, describing a query in the format described in the statement.
For each type 2 query, print the length of the shortest path in its own line.
\(2 \leq n \leq 200\,000\)
\(1 \leq q \leq 200\,000\)
\(1 \leq a_i, b_i \leq n\)
All edge weights will be between 1 and \(10^6\).
The edges \((a_1,b_1), (a_2,b_2), \ldots (a_{n-1},b_{n-1})\) will describe a rooted spanning tree pointing away from node 1.
\(b_j = 1\) for \(n \leq j \leq 2n-2\).
\(a_n, a_{n+1}, \ldots, a_{2n-2}\) will be distinct and between 2 and n.
5 9 1 3 1 3 2 2 1 4 3 3 5 4 5 1 5 3 1 6 2 1 7 4 1 8 2 1 1 2 1 3 2 3 5 2 5 2 1 1 100 2 1 3 1 8 30 2 4 2 2 2 4
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Challenge Name
IndiaHacks 2017: Programming [Wave 2.0- Eliminator]
IndiaHacks 2017: Programming [Wave 2.0- Eliminator]