In a deck of cards, every card has a unique integer.  You can order the deck in any order you want.

Initially, all the cards start face down (unrevealed) in one deck.

Now, you do the following steps repeatedly, until all cards are revealed:

1. Take the top card of the deck, reveal it, and take it out of the deck.
2. If there are still cards in the deck, put the next top card of the deck at the bottom of the deck.
3. If there are still unrevealed cards, go back to step 1.  Otherwise, stop.

Return an ordering of the deck that would reveal the cards in increasing order.

The first entry in the answer is considered to be the top of the deck.

Example 1:

Input: [17,13,11,2,3,5,7]
Output: [2,13,3,11,5,17,7]
Explanation: 
We get the deck in the order [17,13,11,2,3,5,7] (this order doesn't matter), and reorder it.
After reordering, the deck starts as [2,13,3,11,5,17,7], where 2 is the top of the deck.
We reveal 2, and move 13 to the bottom.  The deck is now [3,11,5,17,7,13].
We reveal 3, and move 11 to the bottom.  The deck is now [5,17,7,13,11].
We reveal 5, and move 17 to the bottom.  The deck is now [7,13,11,17].
We reveal 7, and move 13 to the bottom.  The deck is now [11,17,13].
We reveal 11, and move 17 to the bottom.  The deck is now [13,17].
We reveal 13, and move 17 to the bottom.  The deck is now [17].
We reveal 17.
Since all the cards revealed are in increasing order, the answer is correct.

Note:

1. 1 <= A.length <= 1000
2. 1 <= A[i] <= 10^6
3. A[i] != A[j] for all i != j

思路：找規律，陣列排序，分成前面小的一半，後面大的一半。

1. 一開始小的一半放在偶數index（從0開始）上面

2. 如果陣列長度為奇數，說明最後一位是剛好flip被丟掉的，下一個step是把頂端的牌放到底下，所以有一次錯位

3. 用一個flag標記這個錯位就好了

class Solution:
    def deckRevealedIncreasing(self, deck):
        """
        :type deck: List[int]
        :rtype: List[int]
        """
        deck.sort()
        def helper(a, flag):
            n=len(a)
            if n==1: return a
            res=[-1]*n
            if flag==1:
                mi = a[:n//2]
                ma = helper(a[n//2:], (n+1)%2)
                for i in range(0,n,2): res[i]=ma[i//2]
                for i in range(1,n,2): res[i]=mi[i//2]
            else:
                mi = a[:(n+1)//2]
                ma = helper(a[(n+1)//2:], n%2)
                for i in range(0,n,2): res[i]=mi[i//2]
                for i in range(1,n,2): res[i]=ma[i//2]
            return res
        
        ret = helper(deck, 0)
        return ret
    
s=Solution()
print(s.deckRevealedIncreasing([1,2]))
print(s.deckRevealedIncreasing([17,13,11,2,3,5,7]))