GRAPHCOL - Editorial

blup2019
combinatorics
editorial
graph

#1

PROBLEM LINK:

Practice

Author: Aman Kumar Gupta
Tester: D Teja Vardhan Reddy
Editorialist: Aman Kumar Gupta

DIFFICULTY:

EASY-MEDIUM

PREREQUISITES:

Graph theory, Combinatorics

PROBLEM:

A short and concise description of the problem statement.

QUICK EXPLANATION:

Given a graph with N nodes and M - 1 edges. You have also been given K colours and you are required to find the number of ways to colour the nodes which can be reached from-and-to each other using the same colour, and the ones not reachable in both ways, with different colours.

EXPLANATION:

Basically, it’s clear from the problem itself that the nodes which are reachable from-and-to each other form strongly connected components.
So, we just need to find the number of strongly connected components. Let this count be ‘s’. Then if K is less than ‘s’, answer is -1. Else the answer is k! / (k - s)!.

AUTHOR’S AND TESTER’S SOLUTIONS:

Author’s solution can be found here.

Tester’s solution can be found here.