M coloring problem of graphs-the M coloring problem of the backtracking method of __ graphs

Problem Description:

Given a g= (V, E) and M different colors for a undirected connected graph, these colors are colored for each vertex of Fig g, and each vertex is a color. Is there a coloring method that makes the two vertices adjacent to G have different colors. This problem is the problem of the M-coloring determination of graphs. If a graph requires a minimum of M color in order to make each edge of the graph connect two vertices with different colors, the number m is called the color number of the graph. The problem of finding the chromatic number m of a graph is called the M-coloring optimization problem of graphs.

Algorithm Design:

Backtracking method: If the loading problem and the 0-1 backpack backtracking solution, this topic is easy to solve. The code is as follows:

Code:

#include <bits/stdc++.h> using namespace std;
int m;
int pointnum;
int edgenum;
int sum = 0;
int graph[100][100];
int x[100];
    void InPut () {int pos1, pos2;
    scanf ("%d%d", &pointnum, &m);
    scanf ("%d", &edgenum);
    memset (graph, 0, sizeof (graph));
        for (int i = 1; I <= edgenum ++i) {scanf ("%d%d", &AMP;POS1, &pos2);
    GRAPH[POS1][POS2] = graph[pos2][pos1] = 1;
            } bool IsOk (int i) {for (int j = 1; j < i; ++j) if (graph[i][j] = 1 && x[j] = = X[i])
    return false;
return true;
        } void BackTrack (int i) {if (i > Pointnum) {sum = 1;
        printf ("Method%d:", sum);
        for (int j = 1; j <= Pointnum; ++j) {printf ("%d", x[j]);
        printf ("\ n");
    Return
            else {for (int j = 1; j <= m; ++j) {x[i] = j;
            if (IsOk (i)) BackTrack (i + 1);
     X[i] = 0;   } void OutPut () {printf ("Total%d color scheme", sum);} int main () {InPut ();
    BackTrack (1);
OutPut (); }

Test Sample:

Input:

5 4
8
1 3
1 2
1 4
2 3
2 4
2 5
3 4

4 5

Output:

Method 1:1 2 3 4 1
Method 2:1 2 3 4 3
Method 3:1 2 4 3 1
Method 4:1 2 4 3 4
Method 5:1 3 2 4 1
Method 6:1 3 2 4 2
Method 7:1 3 4 2 1
Method 8:1 3 4 2 4
Method 9:1 4 2 3 1
Method 10:1 4 2 3 2
Method 11:1 4 3 2 1
Method 12:1 4 3 2 3
Method 13:2 1 3 4 2
Method 14:2 1 3 4 3
Method 15:2 1 4 3 2
Method 16:2 1 4 3 4
Method 17:2 3 1 4 1
Method 18:2 3 1 4 2
Method 19:2 3 4 1 2
Method 20:2 3 4 1 4
Method 21:2 4 1 3 1
Method 22:2 4 1 3 2
Method 23:2 4 3 1 2
Method 24:2 4 3 1 3
Method 25:3 1 2 4 2
Method 26:3 1 2 4 3
Method 27:3 1 4 2 3
Method 28:3 1 4 2 4
Method 29:3 2 1 4 1
Method 30:3 2 1 4 3
Method 31:3 2 4 1 3
Method 32:3 2 4 1 4
Method 33:3 4 1 2 1
Method 34:3 4 1 2 3
Method 35:3 4 2 1 2
Method 36:3 4 2 1 3
Method 37:4 1 2 3 2
Method 38:4 1 2 3 4
Method 39:4 1 3 2 3
Method 40:4 1 3 2 4
Method 41:4 2 1 3 1
Method 42:4 2 1 3 4
Method 43:4 2 3 1 3
Method 44:4 2 3 1 4
Method 45:4 3 1 2 1
Method 46:4 3 1 2 4
Method 47:4 3 2 1 2
Method 48:4 3 2 1 4

A total of 48 color painting scheme

Partial screenshot: