diff --git a/Problem1.py b/Problem1.py
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+++ b/Problem1.py
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+# Time Complexity : O(log n)   # Binary search halves the search space each step
+# Space Complexity : O(1)      # Only a few variables used
+# Did this code successfully run on Leetcode : Yes
+# Approach:
+# 1. If first element is not 1 or last element is not n+1, handle those boundary cases directly.
+# 2. Otherwise, use binary search: if arr[mid] == mid+1 → left side is correct, move right.
+# 3. Else, move left. At the end, the missing number is (lo + 1).
+
+def missingNumber(arr):
+    n = len(arr)
+    
+    # Handle edge case: if the very first element is not 1, then 1 is missing
+    if arr[0] != 1:
+        return 1
+    
+    # Handle edge case: if the last element is not n+1, then the missing number is at the end
+    if arr[n - 1] != n + 1:
+        return n + 1
+        
+    # Binary search setup
+    lo, hi = 0, n - 1
+    
+    while lo <= hi:
+        mid = (lo + hi) // 2   # Find middle index
+        
+        if arr[mid] == mid + 1:
+            # If value matches expected (index+1), left side is correct
+            # Missing number must be on the right
+            lo = mid + 1
+        else:
+            # Otherwise mismatch happened here or earlier
+            # Move search to the left side
+            hi = mid - 1
+          
+    # At the end, 'lo' will stop at the index where mismatch begins
+    # Missing number is index + 1 because numbers are 1-based
+    return lo + 1
diff --git a/Problem2.py b/Problem2.py
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+# Time Complexity :
+# - Insert: O(log n) because we bubble up at most the height of the heap
+# - Extract Min: O(log n) because we bubble down at most the height of the heap
+# - Get Min: O(1) because root is always min
+# Space Complexity : O(n) for storing heap elements
+# Did this code successfully run on Leetcode : (Custom structure, but logic matches Leetcode heaps)
+# Approach:
+# 1. Represent the heap as an array where parent/child relations are derived from indices.
+# 2. Insert by appending to the end and bubbling up until parent is smaller.
+# 3. Extract min by swapping root with last element, removing it, then bubbling down.
+
+class MinHeap:
+    def __init__(self):
+        self.heap = []   # underlying array to store heap
+    
+    # Get parent index
+    def parent(self, i): 
+        return (i - 1) // 2
+    
+    # Get left child index
+    def left(self, i): 
+        return 2 * i + 1
+    
+    # Get right child index
+    def right(self, i): 
+        return 2 * i + 2
+    
+    # Insert a new key
+    def insert(self, key):
+        self.heap.append(key)       # Step 1: add at the end
+        i = len(self.heap) - 1
+        # Step 2: bubble up while parent is bigger
+        while i > 0 and self.heap[self.parent(i)] > self.heap[i]:
+            self.heap[i], self.heap[self.parent(i)] = self.heap[self.parent(i)], self.heap[i]
+            i = self.parent(i)
+    
+    # Heapify (bubble down) from index i
+    def heapify(self, i):
+        l = self.left(i)
+        r = self.right(i)
+        smallest = i
+        
+        # Compare with left child
+        if l < len(self.heap) and self.heap[l] < self.heap[smallest]:
+            smallest = l
+        # Compare with right child
+        if r < len(self.heap) and self.heap[r] < self.heap[smallest]:
+            smallest = r
+        
+        # If child is smaller, swap and continue
+        if smallest != i:
+            self.heap[i], self.heap[smallest] = self.heap[smallest], self.heap[i]
+            self.heapify(smallest)
+    
+    # Extract the minimum element (root)
+    def extractMin(self):
+        if not self.heap:
+            return None
+        if len(self.heap) == 1:
+            return self.heap.pop()
+        
+        # Step 1: Swap root with last element
+        root = self.heap[0]
+        self.heap[0] = self.heap.pop()
+        # Step 2: Heapify down from root
+        self.heapify(0)
+        return root
+    
+    # Get the minimum element without removing
+    def getMin(self):
+        return self.heap[0] if self.heap else None