Create 13. Missing Number In Arithmetic Progression.py

11_Binary-Search/13. Missing Number In Arithmetic Progression.py

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+# https://www.lintcode.com/problem/3633
+
+from typing import List
+
+########################### Solution 1 -> Binary Search ###########################
+class Solution:
+    def missing_number(self, arr: List[int]) -> int:
+        # An = A0 + (n-1) * d 
+        n = len(arr)+1
+        d = (arr[-1] - arr[0]) // (n-1)
+        l, r = 0, n-2
+        while l <= r:
+            m = l + (r-l)//2
+            nl = m+1
+            nr = n-m-1
+            if abs(arr[m] - arr[0]) // abs(d) + 1 > nl :
+                if m != 0 and arr[m-1] != arr[m] - d: return arr[m] - d 
+                r = m - 1
+            else:
+                if m != n-1 and arr[m+1] != arr[m] + d: return arr[m] + d 
+                l = m + 1
+
+        return -1
+
+# Time: O(log(n))
+# Space: O(1)
+
+
+########################### Solution 2 -> Math ###########################
+class Solution:
+    def missing_number(self, arr: List[int]) -> int:
+        # arr[-1] = arr[0] + (n-1)d 
+        # Sum of AP = (2*arr[0] + d(n-1)) * n//2
+        # Sum of AP = (arr[0] + arr[-1]) * n//2
+        # Removed number = sum of AP - sum of arr
+        n = len(arr)+1
+        return (arr[0] + arr[-1]) * n//2 - sum(arr)
+
+# Time: O(n) as time complexity of sum() function is O(n) in python
+# Space: O(1)
+