[Helena] Week 13

find-median-from-data-stream/yolophg.py

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+# Time Complexity:
+#   - addNum(): O(log N) - use a heap operation (push/pop) which takes log N time.
+#   - findMedian(): O(1) - just accessing the top elements of heaps.
+# Space Complexity: O(N) - store all elements in two heaps.
+
+
+class MedianFinder:
+    def __init__(self):
+        # max heap (stores the smaller half of numbers, negated values for max heap behavior)
+        self.maxHeap = []
+        # min heap (stores the larger half of numbers)
+        self.minHeap = []
+
+    def addNum(self, num: int) -> None:
+        if not self.maxHeap or num <= -self.maxHeap[0]:
+            # store as negative to simulate max heap
+            heapq.heappush(self.maxHeap, -num)  
+        else:
+            heapq.heappush(self.minHeap, num)
+
+        # balance the heaps: maxHeap can have at most 1 more element than minHeap
+        if len(self.maxHeap) > len(self.minHeap) + 1:
+            heapq.heappush(self.minHeap, -heapq.heappop(self.maxHeap))
+        elif len(self.minHeap) > len(self.maxHeap):
+            heapq.heappush(self.maxHeap, -heapq.heappop(self.minHeap))
+
+    def findMedian(self) -> float:
+        if len(self.maxHeap) > len(self.minHeap):
+            return -self.maxHeap[0]  # odd number of elements, maxHeap has the median
+        else:
+            return (-self.maxHeap[0] + self.minHeap[0]) / 2.0  # even case, average of two middle numbers

insert-interval/yolophg.py

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+ # Time Complexity: O(N) - iterate through the intervals once.
+# Space Complexity: O(N) - store the merged intervals in a new list.
+
+class Solution:
+    def insert(self, intervals: List[List[int]], newInterval: List[int]) -> List[List[int]]:
+        output = []
+        start, end = newInterval
+
+        for interval in intervals:
+            if interval[1] < start:
+                # no overlap, and the current interval ends before newInterval starts
+                output.append(interval)
+            elif interval[0] > end:
+                # no overlap, and the current interval starts after newInterval ends
+                output.append([start, end])  # insert merged interval before appending the remaining ones
+                output.extend(intervals[intervals.index(interval):])  # append remaining intervals
+                return output
+            else:
+                # overlapping case: merge intervals
+                start = min(start, interval[0])
+                end = max(end, interval[1])
+
+        # add the merged interval at the end if it wasn't added earlier
+        output.append([start, end])
+
+        return output

kth-smallest-element-in-a-bst/yolophg.py

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+# Time Complexity: O(N) - visit each node once in an inorder traversal.
+# Space Complexity: O(N) - store all node values in a list.
+
+class Solution:
+    def kthSmallest(self, root: Optional[TreeNode], k: int) -> int:
+        def inorder(node):
+            if not node:
+                return
+
+            # go left (smaller values first)
+            inorder(node.left) 
+            # add the current node's value
+            values.append(node.val)  
+            # go right (larger values next)
+            inorder(node.right) 
+
+        values = []
+        inorder(root)
+
+        # get the k-th smallest element (1-based index)
+        return values[k - 1]  

lowest-common-ancestor-of-a-binary-search-tree/yolophg.py

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+# Time Complexity: O(log N) on average (for balanced BST), worst case O(N) (skewed tree).
+# Space Complexity: O(1) - don't use extra space, just a few variables.
+
+class Solution:
+    def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
+         # start from the root
+        node = root 
+
+        while node:  
+            if p.val > node.val and q.val > node.val:
+                # both p and q are in the right subtree, so move right
+                node = node.right  
+            elif p.val < node.val and q.val < node.val:
+                # both p and q are in the left subtree, so move left
+                node = node.left  
+            else:
+                # found the split point where one is on the left and the other is on the right
+                # or when we reach p or q directly (since a node can be its own ancestor)
+                return node  
+
+        return None

meeting-rooms/yolophg.py

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+# Time Complexity: O(N log N) - sorting the intervals takes O(N log N), and the iteration takes O(N).
+# Space Complexity: O(1) - sorting is done in place, and we use only a few extra variables.
+
+class Solution:
+    def can_attend_meetings(intervals):
+        if not intervals:
+            return True  
+
+        # sort intervals based on start times
+        intervals.sort()  # O(N log N) sorting
+
+        # check for overlapping meetings
+        for i in range(len(intervals) - 1):
+            if intervals[i][1] > intervals[i + 1][0]:  
+                # if the current meeting's end time is later than the next meeting's start time, have a conflict
+                return False
+
+        # no conflicts found, all meetings can be attended
+        return True