From 530fd0d89cde288e6c485a36a38db4b32a64f3d2 Mon Sep 17 00:00:00 2001
From: web-advisor <sinnaamar68@gmail.com>
Date: Tue, 25 Oct 2022 12:48:26 +0530
Subject: [PATCH] Added LeetCode Question Satisfiablity of Equality Equations

---
 .../SatisfiabilityOfEqualityEquations.cpp     | 101 ++++++++++++++++++
 1 file changed, 101 insertions(+)
 create mode 100644 leetcode/SatisfiabilityOfEqualityEquations.cpp

diff --git a/leetcode/SatisfiabilityOfEqualityEquations.cpp b/leetcode/SatisfiabilityOfEqualityEquations.cpp
new file mode 100644
index 0000000..c756b07
--- /dev/null
+++ b/leetcode/SatisfiabilityOfEqualityEquations.cpp
@@ -0,0 +1,101 @@
+// https://leetcode.com/problems/satisfiability-of-equality-equations/
+
+/*
+
+Solution Approach :
+Using DSU. Initialize all the variables in all the equations, their parents as themselves, 
+their rank as 1. Perform union operation for all the equality eqautions. Once unified, 
+check for all inequality equations if in any equation the variables involved have the 
+same parent then all equations cannot be simultaneously true.
+
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+class DSU
+{
+private:
+    unordered_map<char, char> parent;
+    unordered_map<char, int> rank;
+
+public:
+    DSU(vector<string> &equations)
+    {
+        for (auto eq : equations)
+        {
+            if (parent.find(eq[0]) == parent.end())
+            {
+                parent[eq[0]] = eq[0];
+                rank[eq[0]] = 1;
+            }
+            if (parent.find(eq[3]) == parent.end())
+            {
+                parent[eq[3]] = eq[3];
+                rank[eq[3]] = 1;
+            }
+        }
+
+        for (auto eq : equations)
+        {
+            if (eq[1] == '=')
+            {
+                unionByRank(eq[0], eq[3]);
+            }
+        }
+    }
+
+    char find(char var)
+    {
+        if (parent[var] == var)
+            return var;
+        return parent[var] = find(parent[var]);
+    }
+
+    void unionByRank(char u, char v)
+    {
+        char pu = find(u);
+        char pv = find(v);
+
+        if (pu != pv)
+        {
+            if (rank[pu] < rank[pv])
+            {
+                parent[pu] = pv;
+            }
+            else if (rank[pv] < rank[pu])
+            {
+                parent[pv] = pu;
+            }
+            else
+            {
+                parent[pv] = pu;
+                rank[pu]++;
+            }
+        }
+    }
+};
+
+class Solution
+{
+public:
+    bool equationsPossible(vector<string> &equations)
+    {
+        DSU solver(equations);
+
+        for (auto eq : equations)
+        {
+            if (eq[1] == '!')
+            {
+                char p1 = solver.find(eq[0]);
+                char p2 = solver.find(eq[3]);
+                if (p1 == p2)
+                {
+                    return false;
+                }
+            }
+        }
+
+        return true;
+    }
+};
\ No newline at end of file