Merge pull request neetcode-gh#821 from nguyencongkhai1407/main

Ahmad-A0 · web-flow · commit 36cff8eb5024 · 2022-08-15T17:24:02.000+01:00
Update 1584-Min-Cost-to-Connect-All-Points.java (Shorter, more readable and followed neetcode's approach)
diff --git a/java/1584-Min-Cost-to-Connect-All-Points.java b/java/1584-Min-Cost-to-Connect-All-Points.java
@@ -1,129 +1,35 @@
-class Edge {
-    public int source;
-    public int destination;
-    public int weight; // manhattan distance
-    
-    public Edge(int s, int d, int w){
-        this.source = s;
-        this.destination = d;
-        this.weight = w;
-    }
-    
-    @Override
-    public String toString() {
-        return "Edge(u=" + source + ", v=" + destination + ", w=" + weight + ")";
-    }
-}
-
-class DisjointSet {
-    private int[] roots;
-    private int[] ranks;
-    
-    public DisjointSet(int n) {
-        this.roots = new int[n];
-        this.ranks = new int[n];
-        
-        // intializing
-        for(int i=0; i<n; i++){
-            this.roots[i] = i;
-            this.ranks[i] = 0; // initially ranking 0
-        }
-    }
-    
-    // get the root, use path compression
-    public int find(int u) {
-        if(this.roots[u] == u)
-            return u;
-        
-        int root = find(this.roots[u]);
-        this.roots[u] = root;
-        return root;
-    }
-    
-    // use ranking
-    public void union(int x, int y) {
-        int rootX = find(x), rootY = find(y);
-        int rankX = this.ranks[rootX], rankY = this.ranks[rootY];
-        
-        if(rootX == rootY) // already same roots
-            return;
-        
-        if(rankX < rankY){
-            // put into rootY
-            this.roots[rootX] = this.roots[rootY];
-            this.ranks[rootY]++;
-        }
-        else{
-            // default, put into rootX
-            this.roots[rootY] = this.roots[rootX];
-            this.ranks[rootX]++;
-        }
-    }
-    
-    public boolean areDisjoint(int u, int v) {
-        return (find(u) != find(v));
-    }
-}
-
 class Solution {
-    private int getManhattanDistance(int[] p1, int[] p2){
-        return (
-            Math.abs(p1[0] - p2[0]) +
-            Math.abs(p1[1] - p2[1])
-        );
-    }
-    
-    private List<Edge> getEdges(int[][] points) {
-        int n = points.length;
-        List<Edge> edges = new ArrayList<>();
-        
-        // edge case
-        if(n <= 1)
-            return edges;
-        
-        for(int i=0; i<(n - 1); i++){
-            for(int j=i+1; j<n; j++){
-                int w = getManhattanDistance(points[i], points[j]);
-                edges.add(new Edge(i, j, w));
-            }
-        }
-        
-        return edges;
-    }
-    
-    private boolean isEdgeCase(int[][] points) {
-        return (points.length <= 1);
-    }
-    
-    private int getCostMST(List<Edge> edges, int numVertices) {
-        DisjointSet ds = new DisjointSet(numVertices);
-        int minCost = 0, numEdgesTaken = 0;
-        
-        for(Edge edge: edges){
-            if(ds.areDisjoint(edge.source, edge.destination)){
-                ds.union(edge.source, edge.destination);
-                numEdgesTaken++;
-                minCost += edge.weight;
-            }
+    // Time Complexity: O(N^2 log(N)) where N is the length of points. N^2 comes from the fact we need to find the distance between a currNode and every other node to pick the shortest distance. log(N) comes from Priority Queue
+    // Space Complexity: O(N^2)
+    public int minCostConnectPoints(int[][] points) {
+        PriorityQueue<int[]> pq = new PriorityQueue<>((a,b) -> a[0] - b[0]); // edge weight, the index of next node
+        pq.offer(new int[]{0,0});
+        int len = points.length;
+        Set<Integer> visited = new HashSet<>();
+        int cost = 0;
+        
+        // When visited.size() == points.len meaning that all the nodes has been connected. 
+        while(visited.size() < len){
+            int[] arr = pq.poll();
             
-            if(numEdgesTaken == (numVertices - 1)) // tree is formed, early exit
-                break;
+            int weight = arr[0];
+            int currNode = arr[1];
+            
+            if(visited.contains(currNode))
+                continue;
+            
+            visited.add(currNode);
+            cost += weight;
+            
+            for(int nextNode = 0; nextNode < len; nextNode++){
+                if(!visited.contains(nextNode)){
+                   int nextWeight = Math.abs(points[nextNode][0] - points[currNode][0]) + Math.abs(points[nextNode][1] - points[currNode][1]); 
+                    pq.offer(new int[]{nextWeight, nextNode});
+                }
+            }
         }
-        return minCost;
-    }
-    
-    public int minCostConnectPoints(int[][] points) {
-        // edge cases
-        if(isEdgeCase(points))
-            return 0;
         
-        // edges        
-        List<Edge> edges = getEdges(points);
         
-        // sort the edges in ascending order
-        edges.sort((x1, x2) -> (x1.weight - x2.weight));
-        
-        // Kruskals algorithm for MST [Union Find]
-        return getCostMST(edges, points.length);
+        return cost;
     }
-}
+}
