solve:alienDictionary

Author: yolophg

alien-dictionary/yolophg.py

@@ -0,0 +1,52 @@
+# Time Complexity: O(N + K) - where N is total number of characters in all words, and K is total number of unique character relations (edges) we derive
+# Space Complexity: O(N + K) - for graph, in-degree map, and heap
+
+class Solution:
+    def alien_order(self, words):
+        # adjacency list, u -> set of v
+        graph = defaultdict(set)  
+        # how many chars come before this one
+        in_degree = {}  
+
+        # initialize in_degree with all unique chars
+        for word in words:
+            for char in word:
+                in_degree[char] = 0
+
+        # compare each adjacent pair of words
+        for i in range(len(words) - 1):
+            w1, w2 = words[i], words[i + 1]
+            min_len = min(len(w1), len(w2))
+            # handle invalid case like ["abc", "ab"]
+            if len(w1) > len(w2) and w1[:min_len] == w2[:min_len]:
+                return ""
+
+            for j in range(min_len):
+                if w1[j] != w2[j]:
+                    # first different char tells us the order
+                    if w2[j] not in graph[w1[j]]:
+                        graph[w1[j]].add(w2[j])
+                        in_degree[w2[j]] += 1
+                    # only first different char matters
+                    break  
+
+        # topological sort (use min heap for smallest lex order)
+        heap = []
+        for char in in_degree:
+            if in_degree[char] == 0:
+                heapq.heappush(heap, char)
+
+        result = []
+        while heap:
+            char = heapq.heappop(heap)
+            result.append(char)
+            for neighbor in sorted(graph[char]):
+                in_degree[neighbor] -= 1
+                if in_degree[neighbor] == 0:
+                    heapq.heappush(heap, neighbor)
+
+        # if we added all characters into result, it's valid
+        if len(result) == len(in_degree):
+            return ''.join(result)
+        else:
+            return ""