图形着色问题是图形标签的一种特殊情况。在此问题中,每个节点都被着色为某些颜色。但是着色有一些限制。我们不能将相同的颜色用于任何相邻的顶点。
为了解决这个问题,我们需要使用贪婪算法,但不能保证使用最小的颜色。
Input: Adjacency matrix of the graph. 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 Output: Node: 0, Assigned with Color: 0 Node: 1, Assigned with Color: 0 Node: 2, Assigned with Color: 1 Node: 3, Assigned with Color: 2 Node: 4, Assigned with Color: 1
graphColoring(graph)
输入-给定的图形。
输出-为 每个节点分配了某种颜色。
Begin declare a list of colors initially set the color 0 for first node define an array colorUsed to track which color is used, and which colors have never used. for all vertices i except first one, do mark i as unassigned to any color done mark colorUsed to false for all vertices for all vertices u in the graph except 1st vertex, do for all vertex v adjacent with u, do if color[v] is unassigned, then mark colorUsed[color[v]] := true done for all colors col in the color list, do if color is not used, then stop the loop done color[u] := col for each vertex v which is adjacent with u, do if color[v] is unassigned, then colorUsed[color[v]] := false done done for all vertices u in the graph, do display the node and its color done End
#include<iostream> #define NODE 6 using namespace std; int graph[NODE][NODE] = { {0, 1, 1, 1, 0, 0}, {1, 0, 0, 1, 1, 0}, {1, 0, 0, 1, 0, 1}, {1, 1, 1, 0, 1, 1}, {0, 1, 0, 1, 0, 1}, {0, 0, 1, 1, 1, 0} }; void graphColoring() { int color[NODE]; color[0] = 0; //Assign first color for the first node bool colorUsed[NODE]; //Used to check whether color is used or not for(int i = 1; i<NODE; i++) color[i] = -1; //initialize all other vertices are unassigned for(int i = 0; i<NODE; i++) colorUsed[i] = false; //initially any colors are not chosen for(int u = 1; u<NODE; u++) { //for all other NODE - 1 vertices for(int v = 0; v<NODE; v++) { if(graph[u][v]){ if(color[v] != -1) //when one color is assigned, make it unavailable colorUsed[color[v]] = true; } } int col; for(col = 0; col<NODE; col++) if(!colorUsed[col]) //find a color which is not assigned break; color[u] = col; //assign found color in the list for(int v = 0; v<NODE; v++) { //for next iteration make color availability to false if(graph[u][v]) { if(color[v] != -1) colorUsed[color[v]] = false; } } } for(int u = 0; u<NODE; u++) cout <<"Color: " << u << ", Assigned with Color: " <<color[u] <<endl; } main() { graphColoring(); }
输出结果
Node: 0, Assigned with Color: 0 Node: 1, Assigned with Color: 0 Node: 2, Assigned with Color: 1 Node: 3, Assigned with Color: 2 Node: 4, Assigned with Color: 1