14864 - Map Color   

Description

(20 points)

Write a program to color the countries of a map.
A map contains n countries, and we want to determine whether it is possible to use c colors so that no two adjacent countries share the same color.

Each country has a unique ID from 1 to n, and each color has a unique ID from 1 to c.

Input

  • Line 1: Three integers

    n c p
    

    where

    • n = number of countries

    • c = number of available colors

    • p = number of adjacent country pairs

  • Next p lines: Each line contains two integers

     i j 

    meaning that country i and country j are adjacent and therefore cannot have the same color.

Output

  • If a valid coloring exists, output n integers, separated by spaces.
    The k-th integer represents the assigned color of country k.

  • Among all possible valid colorings, output the lexicographically smallest sequence.

  • If no valid coloring exists, output:

no solution

 

Sample Input  Download

Sample Output  Download

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