Dijkstra贪心算法求单源最短路径

 给定一个带权有向图G=（V,E），其中每条边的权是一个非负实数。另外，还给定V中的一个顶点，称为源。现在要计算从源到其他所有各顶点的最短路径长度。这里的长度就是指路上各边权之和。

Dijkstra算法是解单源最短路径的贪心算法。《算法设计与分析》一书中给出的代码存在问题，其中一个明显的错误就是用==对浮点数进行相等判断。对书中的代码进行修订后实现如下：

public static void dijkstra(int sourcePoint, float[][] weightMatrix, float[] distance, int[] previousPoints) {
		// the numbers of points;
		int pointNumber = distance.length;
		if (sourcePoint <0 || sourcePoint >= pointNumber) {
			// the sourcePoint exceed the valid point index;
			return ;
		}
		
		boolean[] selectedPoints = new boolean[pointNumber];
		
		// initialize three array:
		// 1. initialize the array of distance  from source point to each  point;
		// 2. initialize the array of selected points  with false;
		// 3. initialize the array of previous points with 0;
		for(int i=0; i< pointNumber; i++) {
			distance[i] = weightMatrix[sourcePoint][i];
			selectedPoints[i] = false;
			if (Math.abs(distance[i]- Float.MAX_VALUE) < 0.0001f ) {
				previousPoints[i] = -1;
			}else {
				// there is a line link between sourcePoint and currentPoint;
				previousPoints[i] = sourcePoint;
			}
		}
		
		// step 1: put source point into selected set;
		selectedPoints[sourcePoint] = true;
		
		
		for(int i=0; i< pointNumber; i++) {
			// a temp variable that store the shortest distance; initialize value with float max.
			float tempShortestDist = Float.MAX_VALUE;
			
		    // this variable store next candidate point which has shortest distance;
			int candidatePoint = sourcePoint;
			// step 2: find a point which has shortest distance;
			// traverse the set of All Points minus Selected Points and calculate the shorted distance from source to each point
			for (int j=0; j<pointNumber; j++) {
				if(!selectedPoints[j] && distance[j] < tempShortestDist) {
					candidatePoint = j;
					tempShortestDist = distance[j];
				}
			}
			
			//  step3 : add the candidate point to selected set;
			selectedPoints[candidatePoint] = true;
			
			// step 4: calculate the distance of  SPECIAL Path that start from candidatePoint to each point;
			for (int j=0; j<pointNumber; j++) {
				if (!selectedPoints[j] && weightMatrix[candidatePoint][j] < Float.MAX_VALUE) {
					// point j is not in selected points set and there is a line between point candidatePoint and j;
					float newDistance = distance[candidatePoint]  + weightMatrix[candidatePoint][j];
					if (newDistance < distance[j]) {
						// the distance from cadidatePoint is less than before(start from previous point);
						distance[j] = newDistance;
						previousPoints[j] = candidatePoint;
					}
				}
			}// end of for
		}// end of for
	}

 

本文地址：https://blog.csdn.net/redredxcar/article/details/85929100