From b95350d70a5eb213ff0ff78c2e646ff29d4d711c Mon Sep 17 00:00:00 2001
From: Mahim Mahbub <mahim.mahbub.97@gmail.com>
Date: Thu, 28 Jul 2022 00:36:12 +0600
Subject: [PATCH] 1584. Min Cost to connect all points in Java

---
 java/1584-Min-Cost-to-Connect-All-Points.java | 129 ++++++++++++++++++
 1 file changed, 129 insertions(+)
 create mode 100644 java/1584-Min-Cost-to-Connect-All-Points.java

diff --git a/java/1584-Min-Cost-to-Connect-All-Points.java b/java/1584-Min-Cost-to-Connect-All-Points.java
new file mode 100644
index 000000000..e18e93bf5
--- /dev/null
+++ b/java/1584-Min-Cost-to-Connect-All-Points.java
@@ -0,0 +1,129 @@
+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;
+            }
+            
+            if(numEdgesTaken == (numVertices - 1)) // tree is formed, early exit
+                break;
+        }
+        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);
+    }
+}
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