pattern

Author: idf

390 Elimination Game.py

@@ -0,0 +1,50 @@
+"""
+There is a list of sorted integers from 1 to n. Starting from left to right, remove the first number and every other
+number afterward until you reach the end of the list.
+
+Repeat the previous step again, but this time from right to left, remove the right most number and every other number
+from the remaining numbers.
+
+We keep repeating the steps again, alternating left to right and right to left, until a single number remains.
+
+Find the last number that remains starting with a list of length n.
+
+Example:
+
+Input:
+n = 9,
+1 2 3 4 5 6 7 8 9
+2 4 6 8
+2 6
+6
+
+Output:
+6
+"""
+__author__ = 'Daniel'
+
+
+class Solution(object):
+    def lastRemaining(self, n):
+        """
+        Brute force O(n): A = A[::2][::-1]
+
+        Simulate the game and find pattern of head/first element: O(lg n)
+        :type n: int
+        :rtype: int
+        """
+        remain = n
+        head = 1
+        step = 1
+        from_left = True
+        while remain > 1:
+            if from_left:
+                head += step
+            elif remain % 2 == 1:
+                head += step
+
+            step *= 2
+            remain /= 2
+            from_left = not from_left
+
+        return head