Create elimination-game.py

Author: kamyu104

Python/elimination-game.py

@@ -0,0 +1,39 @@
+# Time:  O(logn)
+# Space: O(1)
+
+# 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
+
+class Solution(object):
+    def lastRemaining(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        start, step, direction = 1, 2, 1
+        while n > 1:
+            start += direction * (step * (n / 2) - step / 2)
+            n /= 2
+            step *= 2
+            direction *= -1
+        return start