bfs-1

Sample.py

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+# BFS-1
+# Problem 1
+# Binary Tree Level Order Traversal (https://leetcode.com/problems/binary-tree-level-order-traversal/)
+
+# Implemented BFS (level-order traversal) using a queue:
+# Initialize with root node in queue
+# For each level: Process all nodes currently in the queue (using for i in range(len(q)))
+# Collect values in temp list
+# Add children to queue for next level
+# Append each level's temp list to final result res
+# The for loop bound (len(q)) is fixed at start of each level, ensuring clean separation between levels. 
+# This pattern works for all BFS level-processing problems!
+
+# Time Complexity: O(N) — visit each node once
+# Space Complexity: O(W) — maximum width of tree (queue stores at most one level)
+
+# Definition for a binary tree node.
+# class TreeNode:
+#     def __init__(self, val=0, left=None, right=None):
+#         self.val = val
+#         self.left = left
+#         self.right = right
+class Solution:
+    def levelOrder(self, root: Optional[TreeNode]) -> List[List[int]]:
+        if root is None:
+            return []
+        q = [root]
+        res = []
+        while q:
+            temp = []
+            for i in range(len(q)):
+                curr = q.pop(0)
+                temp.append(curr.val)
+                if curr.left:
+                    q.append(curr.left)
+                if curr.right:
+                    q.append(curr.right)
+            res.append(temp)
+        return res
+
+
+
+
+# Problem 2
+# Course Schedule (https://leetcode.com/problems/course-schedule/)
+
+# Topological Sorting:
+# Build graph:  
+#    hashmap stores adjacency list (course → dependent courses)  
+#    indegrees tracks how many prerequisites each course has  
+# Initialize queue with all courses having 0 prerequisites (indegrees[i] == 0)  
+# Process courses:  
+#    For each course taken, reduce in-degree of its dependents  
+#    Add newly unlocked courses (in-degree = 0) to queue  
+#    Count total processed courses  
+# Check completion: If total == numCourses, all courses can be finished  
+# This detects cycles in a directed graph – if a cycle exists, some courses will never reach in-degree 0, making total < numCourses.
+
+# Time Complexity: O(V + E) (V = courses, E = dependencies)  
+# Space Complexity: O(V + E) (graph + in-degrees + queue)  
+
+
+
+class Solution:
+    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
+        indegrees = [0]*numCourses
+        hashmap = {}
+
+        for pr in prerequisites:
+            indegrees[pr[0]] += 1 # value at dependent index increases by 1
+            if pr[1] not in hashmap:
+                hashmap[pr[1]] = []
+            hashmap[pr[1]].append(pr[0])
+
+        q = deque()
+        total = 0
+
+        for i in range(numCourses):
+            if indegrees[i] == 0:
+                q.append(i)
+                total += 1
+
+        if not q:
+            return False
+        if total == numCourses:
+            return True
+
+        while q:
+            curr = q.popleft()
+            dependencies = hashmap.get(curr)
+            if dependencies:
+                for dep in dependencies:
+                    indegrees[dep] -= 1
+                    if indegrees[dep] == 0:
+                        q.append(dep)
+                        total += 1
+                        if total == numCourses:
+                            return True
+        return False