Problem Difficulty Level: Medium

Author: Naganathan05

Graphs/Union Find Algorithm - [DSU]/3493. Properties Graph.cpp

@@ -0,0 +1,91 @@
+/*---------------------------------------------
+  Time Complexity: O(n * m * logn) + O(mlogm)
+  Space Complexity: O(m)
+-----------------------------------------------*/
+
+class DisJointSet {
+public:
+    vector<int> size, parent;
+
+    DisJointSet(int n) {
+        size.resize(n, 1);
+        parent.resize(n);
+        for(int i = 0; i < n; i++) parent[i] = i;
+    }
+
+    int findUParent(int node) {
+        if(parent[node] == node) return node;
+        return parent[node] = findUParent(parent[node]);
+    }
+
+    void UnionBySize(int u, int v) {
+        int ult_u = findUParent(u);
+        int ult_v = findUParent(v);
+        if(ult_u == ult_v) return;
+        if(size[ult_u] < size[ult_v]) {
+            parent[ult_u] = ult_v;
+            size[ult_v] += size[ult_u];
+        } else {
+            parent[ult_v] = ult_u;
+            size[ult_u] += size[ult_v];
+        }
+    }
+};
+
+class Solution {
+public:
+    bool intersect(vector<int> &a, vector<int> &b, int k) {
+        int i = 0, j = 0;
+        int numCommon = 0;
+        while(i < a.size() && j < b.size()) {
+            if (a[i] == b[j]) {
+                i += 1;
+                j += 1;
+                numCommon += 1;
+            }
+            else if(a[i] > b[j]) j += 1;
+            else i += 1;
+        }
+        return numCommon >= k;
+    }
+
+    int numberOfComponents(vector<vector<int>>& properties, int k) {
+        int n = properties.size();
+        int m = properties[0].size();
+
+        for(int i = 0; i < n; i++) {
+            sort(properties[i].begin(), properties[i].end());
+            
+            unordered_set<int> visited;
+            vector<int> newArray;
+
+            for(int j = 0; j < m; j++) {
+                if(visited.find(properties[i][j]) == visited.end()) {
+                    newArray.push_back(properties[i][j]);
+                    visited.insert(properties[i][j]);
+                }
+            }
+            properties[i] = newArray;
+        }
+
+        DisJointSet ds(n);
+
+        for(int i = 0; i < n; i++) {
+            for(int j = i + 1; j < n; j++) {
+                if(!intersect(properties[i], properties[j], k)) continue;
+                ds.UnionBySize(i, j);
+            }
+        }
+
+        int numComponents = 0;
+        for(int i = 0; i < n; i++) {
+            if(ds.findUParent(i) == i) numComponents += 1;
+        }
+        return numComponents;
+    }
+};
+
+/*
+Question Link: https://leetcode.com/problems/properties-graph/
+Author: M.R.Naganathan
+*/