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Dijkstra貪心演算法求單源最短路徑

 給定一個帶權有向圖G=(V,E),其中每條邊的權是一個非負實數。另外,還給定V中的一個頂點,稱為源。現在要計算從源到其他所有各頂點的最短路徑長度。這裡的長度就是指路上各邊權之和。

Dijkstra演算法是解單源最短路徑的貪心演算法。

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;
		
		// this variable store next candidate point which has shortest distance;
		
		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;
			
			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
	}