Java Solution Required Only You're given a simple undirected graph G with N vertices and M edges. You have to assign, to each vertex i, a number C; such that 1 ≤ C; < N and Vij, C; # Cj. For any such assignment, we define D; to be the number of neighbours j of i such that C; < C₁. You want to minimise maxi (1..N) Di - minic{1..N} Di. Output the minimum possible value of this expression for a valid assignment as described above, and also print the corresponding assignment.

Java Solution Required Only You're given a simple undirected graph G with N vertices and M edges. You have to assign, to each vertex i, a number C; such that 1 ≤ C; < N and Vij, C; # Cj. For any such assignment, we define D; to be the number of neighbours j of i such that C; < C₁. You want to minimise maxi (1..N) Di - minic{1..N} Di. Output the minimum possible value of this expression for a valid assignment as described above, and also print the corresponding assignment.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.

Question

Java Solution Required Only
You're given a simple undirected graph G with N vertices and M edges. You have to assign, to each
vertex i, a number C; such that 1 < 0; N and Vi‡j, C; ‡ Cj.
For any such assignment, we define D; to be the number of neighbours j of i such that C; < C₁.
You want to minimise maxi{1..N) Di - minic{1..N} Di.
Output the minimum possible value of this expression for a valid assignment as described above,
and also print the corresponding assignment.
Note:
• The given graph need not be connected.
. If there are multiple possible assignments, output anyone.
• Since the input is large, prefer using fast input-output methods.
Input
223
1
57
12
13
14
23
24
25
35
Output
2
32154

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