2014.1.4

来源：互联网发布：地图数据采集软件安卓编辑：程序博客网时间：2024/06/18 05:18

* 最小生成树, Minimal Spanning Tree（带权无向图）

Prime算法，Kruskal算法，两者皆为贪心算法；O（ElogE）；

1. Prim在稠密图中比Kruskal优，在稀疏图中比Kruskal劣；

2. Prim+Heap在任何时候都有令人满意的时间复杂度，但是代价是空间消耗大，算法复杂；

最小生成树小结及prim与kruskal效率比较 - noname01.pas - 未命名-oi

上图转载自，http://noname01.pas.blog.163.com/blog/static/1243636342010101683743714/

贪心算法：局部最优解能决定全局最优解。简单地说，问题能够分解成子问题来解决，子问题的最优解能递推到最终问题的最优解。

基于数组实现的优先级队列的Prim，MST算法@java/DataStructure/unit13

class Vertex{public char label;public boolean wasVisited;public Vertex(char lab){label=lab;wasVisited=false;}}class Edge{public int start;public int end;public int weight;public Edge(int start, int end, int weight){this.start=start;this.end=end;this.weight=weight;}public void display(){System.out.println(start+"->"+end+", "+weight);}}class Queue{public Edge [] eArr;public int max;public int current;public Queue(int max){this.max=max;eArr=new Edge [max];current=0;}public void insert(Edge eTemp){int i=current-1;for(; i>=0 && eTemp.weight>eArr[i].weight; i--) eArr[i+1]=eArr[i];eArr[i+1]=eTemp;current++;}public Edge remove(){return eArr[--current];}public Edge peek(){return eArr[current-1];}public void hasSameEnd(){for(int i=current-1; i>=1; i--){for(int j=i-1; j>=0; j--){if(eArr[i].end==eArr[j].end){for(int k=j; k<current-1; k++){eArr[k]=eArr[k+1];}i--;current--;}}}}public boolean isEmpty(){return current==0;}public boolean isFull(){return current==max;}public void display(){for(int i=current-1; i>=0; i--){eArr[i].display();}}}class Graph{private final int MAX_VERTS=20;private Vertex vArr[];private int adjMat [] [];private int number;public Graph(){vArr=new Vertex[MAX_VERTS];adjMat=new int [MAX_VERTS][MAX_VERTS];number=0;for(int j=0; j<MAX_VERTS; j++)for(int k=0; k<MAX_VERTS; k++)adjMat[j][k]=0;}public void add(char lab){vArr[number++]=new Vertex(lab);for(int i=0; i<number; i++){adjMat[number][i]=0;adjMat[i][number]=0;}}public void addEdge(int i, int j, int weight){adjMat[i][j]=weight;adjMat[j][i]=weight;}public void displayMat(){System.out.println("The Adjacent Matrix is: ");System.out.print("   ");for(int i=0; i<number; i++){System.out.print(vArr[i].label+"  ");}System.out.println();for(int i=0; i<number; i++){System.out.print(vArr[i].label+" ");for(int j=0; j<number; j++){if(adjMat[i][j]<10){System.out.print(" "+adjMat[i][j]+" ");}else System.out.print(adjMat[i][j]+" ");}System.out.println();}}public boolean notExistInIArr(int i, int [] iArr){for(int j=0; j<iArr.length; j++){if(iArr[j]==i)return false;}return true;}public void mst(){System.out.println("Minimal Spanning Tree of this Graph is: ");int [] iArr=new int [number];int current=1;Queue queue=new Queue(50);iArr[0]=0;boolean flag=false;for(int i=0; i<number; i++){if(adjMat[0][i]>0){queue.insert(new Edge(0, i, adjMat[0][i]));flag=true;}}if(flag==false){System.out.println("No Road!");return;}while(current!=number){Edge eTemp=queue.remove();for(int i=0; i<number; i++){if(adjMat[eTemp.end][i]>0 && notExistInIArr(i, iArr)){queue.insert(new Edge(eTemp.end, i, adjMat[eTemp.end][i]));}queue.hasSameEnd();}iArr[current++]=eTemp.end;System.out.println(vArr[eTemp.start].label+"->"+vArr[eTemp.end].label+", "+eTemp.weight);}}}

* 最短路径（带权有向图）

0 0