3-coloring problem

最新推荐文章于 2022-01-01 18:16:47 发布

KusanoNEU

最新推荐文章于 2022-01-01 18:16:47 发布

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分类专栏：算法文章标签： 3 Color

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本文介绍了一种解决图染色问题的方法，通过递归回溯算法为图中每个节点分配颜色，确保相邻节点颜色不同。该算法适用于解决实际场景中的资源分配问题。

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#include <iostream>
#include <vector>
#include <Windows.h>

using namespace std;

bool isSafe(const vector<vector<int>> &graph, const vector<int> &color, int v, int c)
{
	for (int i = 0; i != graph.size(); ++i)
		if (graph[v][i] == 1 && color[i] == c)
			return false;
	return true;
}

void printSolution(const vector<int> &color)
{
	cout << "Solution exist: " << endl;
	for (auto a : color)
		cout << a << " ";
}

bool graphColoringUti(const vector<vector<int>> &graph, vector<int> &color,  int v, int m)
{
	if (v == graph.size())
		return true;

	for (int c = 1; c <= m; ++c)
	{
		if (isSafe(graph, color, v, c))
		{
			color[v] = c;

			if (graphColoringUti(graph, color, v + 1, m))
				return true;
			// if assign color c does not lead to a solution, reset it
			color[v] = 0;
		}
	}

	return false;
}

bool graphColoring(const vector<vector<int>> &graph, int m)
{
	vector<int> color(graph.size(), 0);

	if (!graphColoringUti(graph, color, 0, 3))
	{
		cout << "Solution Not Exist";
		return false;
	}

	printSolution(color);
	return true;
}


int main()
{
	vector<vector<int>> graph = { { 0, 1, 1, 1 },
	{ 1, 0, 1, 0 },
	{ 1, 1, 0, 1 },
	{ 1, 0, 1, 0 },
	};
	int m = 3;

	graphColoring(graph, 3);
	cout << endl;
	system("PAUSE");
	return 0;
}