Done Graph 3

findCeleb.py

@@ -0,0 +1,20 @@
+# The knows API is already defined for you.
+# return a bool, whether a knows b
+# def knows(a: int, b: int) -> bool:
+
+
+class Solution:
+    def findCelebrity(self, n: int) -> int:
+        # T: O(n), S: O(1)
+        # First pass: find the candidate
+        candidate = 0
+        for i in range(1, n):
+            if knows(candidate, i):
+                candidate = i
+
+        # Second pass: verify the candidate
+        for i in range(n):
+            if i != candidate:
+                if knows(candidate, i) or not knows(i, candidate):
+                    return -1
+        return candidate

optimizeWater.py

@@ -0,0 +1,34 @@
+class Solution:
+    def minCostToSupplyWater(
+        self, n: int, wells: List[int], pipes: List[List[int]]
+    ) -> int:
+        # T: O(E log E), S: O(1)
+        # Initialize parent pointers for Union-Find
+        parent = [i for i in range(n + 1)]
+
+        def find(x):
+            while parent[x] != x:
+                parent[x] = parent[parent[x]]  # Path compression
+                x = parent[x]
+            return x
+
+        def union(x, y):
+            root_x, root_y = find(x), find(y)
+            if root_x == root_y:
+                return False
+            parent[root_x] = root_y
+            return True
+
+        # Add virtual edges from node 0 to each house with well cost
+        edges = [[0, i + 1, cost] for i, cost in enumerate(wells)]
+        # Add existing pipes
+        edges += pipes
+        # Sort all edges by cost
+        edges.sort(key=lambda x: x[2])
+
+        total_cost = 0
+        for u, v, cost in edges:
+            if union(u, v):
+                total_cost += cost
+
+        return total_cost