力扣labuladong——一刷day83

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前言

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Prim 算法和 Kruskal 算法都是经典的最小生成树算法，阅读本文之前，希望你读过前文 Kruskal 最小生成树算法，了解最小生成树的基本定义以及 Kruskal 算法的基本原理，这样就能很容易理解 Prim 算法逻辑了。

一、力扣1584. 连接所有点的最小费用

class Solution {
    public int minCostConnectPoints(int[][] points) {
        int n = points.length;
        List<int[]>[] graph = builderGraph(points,n);
        Prim prim = new Prim(graph);
        return prim.getWight();
    }
    public List<int[]>[] builderGraph(int[][] points, int n){
        List<int[]>[] graph = new LinkedList[n];
        for(int i = 0; i < n; i ++){
            graph[i] = new LinkedList<>();
        }
        for(int i = 0; i < n; i ++){
            for(int j = i+1; j < n; j ++){
                int x1 = points[i][0], y1 = points[i][1];
                int x2 = points[j][0], y2 = points[j][1];
                int z = Math.abs(x1 - x2) + Math.abs(y1 - y2);
                graph[i].add(new int[]{i,j,z});
                graph[j].add(new int[]{j,i,z});
            }
        }
        return graph;
    }
    class Prim{
        private PriorityQueue<int[]> pq;
        private boolean[] inMIT;
        private int weighSum;
        private List<int[]>[] graph;
        public Prim(List<int[]>[] graph){
            this.graph = graph;
            int n = graph.length;
            this.pq = new PriorityQueue<int[]>(
                (a,b)->{
                    return a[2] - b[2];
                }
            );
            this.inMIT = new boolean[n];
            cut(0);
            this.inMIT[0] = true;
            while(!pq.isEmpty()){
                int cur[] = pq.poll();
                int to = cur[1];
                int weigh = cur[2];
                if(inMIT[to]){
                    continue;
                }
                cut(to);
                weighSum += weigh;
                inMIT[to] = true;
            }
        }
        private void cut(int x){
            for(int[] edge : graph[x]){
                int to = edge[1];
                if(inMIT[to]){
                    continue;
                }
                pq.offer(edge);
            }
        }
        public int getWight(){
            return this.weighSum;
        }
        public boolean allConnected(){
            for(int i = 0; i < inMIT.length; i ++){
                if(inMIT[i] == false){
                    return false;
                }
            }
            return true;
        }
    }
}