Daily problem done

Author: Kyrylo-Ktl

Python/Satisfiability of Equality Equations.py

@@ -0,0 +1,72 @@
+from random import randint
+from string import ascii_lowercase
+from typing import Iterable, List
+
+
+class DSU:
+    """
+    Disjoint set system with rank and path compression heuristics
+
+    Memory:
+        creation - O(n)
+        'find' - O(log(n))
+        'union' - O(log(n))
+
+    Time:
+        creation - O(n)
+        'find' - O(log(n))
+        'union' - O(log(n))
+
+    On average, operations 'find' and 'union' take O(1) time and space
+    """
+
+    def __init__(self, nodes: Iterable):
+        self.parent = {n: n for n in nodes}
+        self.rank = {n: 1 for n in nodes}
+
+    def find(self, a: int) -> int:
+        if a != self.parent[a]:
+            self.parent[a] = self.find(self.parent[a])
+        return self.parent[a]
+
+    def union(self, a: int, b: int):
+        a_root = self.find(a)
+        b_root = self.find(b)
+
+        if a_root == b_root:
+            return
+
+        if self.rank[a_root] > self.rank[b_root]:
+            self.parent[b_root] = a_root
+        elif self.rank[a_root] < self.rank[b_root]:
+            self.parent[a_root] = b_root
+        else:
+            if randint(0, 1) & 1:
+                a_root, b_root = b_root, a_root
+            self.parent[b_root] = a_root
+            self.rank[a_root] += 1
+
+
+class Solution:
+    """
+    Time:   O(n)
+    Memory: O(n)
+    """
+
+    EQUAL = '='
+    NOT_EQUAL = '!'
+
+    def equationsPossible(self, equations: List[str]) -> bool:
+        dsu = DSU(ascii_lowercase)
+
+        for eq in equations:
+            i, sign, _, j = list(eq)
+            if sign == self.EQUAL:
+                dsu.union(i, j)
+
+        for eq in equations:
+            i, sign, _, j = list(eq)
+            if sign == self.NOT_EQUAL and dsu.find(i) == dsu.find(j):
+                return False
+
+        return True