All Tracks Algorithms Graphs Shortest Path Algorithms Problem

Furthest vertex
Tag(s):

Medium-Hard

Problem
Editorial
Analytics

There are n vertices.

Your task is to perform q queries:

1 a b - add an undirected edge of the length 1 between vertices a and b

2 a - find the distance to the furthest vertex reachable from the vertex a

Guaranteed that graph will not contain loops and cycles during all the time.

\(INPUT\)

First line of the input contains two integers n and q \((1 \leq n \leq 10^5, 1 \leq q \leq 3 \cdot 10^5)\)

Then follow q lines. The i-th of them contains integers: \(type_i\) \((1 \leq type_i \leq 2)\), \(a_i\) \((1 \leq a \leq n)\) and if \(type_i = 1\) \(b_i\) \((1 \leq b_i \leq n)\).

\(OUTPUT\)

Print the distance which is needed for each query of the second type.

SAMPLE INPUT
3 5
1 1 2
2 1
2 3
1 1 3
2 3
SAMPLE OUTPUT
1
0
2
Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

November Clash '16

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