PROBLEM LINK:
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.