单源最短路径 Dijkstra算法 Java 代码实现（贪心算法）

单元最短路径

问题分析

• 可参考 图的应用——最短路径

Java 源代码

内含详细注释

package Dijkstra;

public class Dijkstra {

	public static void main(String[] args) {
		float max = Float.MAX_VALUE;
		float[][] a = new float[][] {{0, 0, 0, 0, 0, 0},
							{0, max, 10, max, 30, 100},
							{0, max, max, 60, max, max},
							{0, max, max, max, max, 20},
							{0, max, max, 10, max, 50},
							{0, max, max, max, max, max}};
		int v = 1;
		int n = 5;
		float[] dist = new float[n + 1];
		int[] prev = new int[n + 1];
		dijkstra(v, a, dist, prev);
		for (int i = 1; i <= n; i++) {
			if (i != v) {
				System.out.println(v + "->" + i + " : " + dist[i]);
			}
		}
	}
	
	/**
	 * 单元最短路径问题的 Dijkstra 算法 
	 * @param v: 源顶点
	 * @param a：邻接矩阵
	 * @param dist：存放最短路径
	 * @param prev：存放当前顶点的前一个顶点
	 */
	public static void dijkstra(int v, float[][] a, float[] dist, int[] prev) {
		
		int n = dist.length - 1;
		if (v < 1 || v > n) return;
		// 代表当前顶点是否被添加到集合S中
		boolean[] s = new boolean[n + 1];
		// 初始化
		for (int i = 1; i <= n; i++) {
			dist[i] = a[v][i];
			s[i] = false;
			if (dist[i] == Float.MAX_VALUE) prev[i] = 0;
			else prev[i] = v;
		}
		dist[v] = 0;
		s[v] = true;
		for (int i = 1; i < n; i++) {
			float temp = Float.MAX_VALUE;
			int u = v;
			for (int j = 1; j <= n; j++) {  // 寻找不在S中的最小值
				if (!s[j] && (dist[j] < temp)) {  // 从剩余顶点选择
					u = j;
					temp = dist[j];
				}
			}
			// 加入s中
			s[u] = true;
			for (int j = 1; j <= n; j++) {  // 更新dist
				if ((!s[j]) && (a[u][j] < Float.MAX_VALUE)){
					float newdist = dist[u] + a[u][j];
					if (newdist < dist[j]) {
						dist[j] = newdist;
						prev[j] = u;
					}
				}
			}
		}
	}
}

1->2 : 10.0
1->3 : 40.0
1->4 : 30.0
1->5 : 60.0