leetcode-1734 解码异或后的排列

解题思路

1. 异或运算特性

\[a \bigoplus b=c\ \ \ \ \ \ c\bigoplus a=b \]

2. encode数组长度为n-1，则perm数组长度为n
   perm=[1,2,3,......,n]的排列
3. 假设perm=[A,B,C,D,E],encode=[F,G,H,I],n为奇数
   \(A\bigoplus B=F \ \ \ B\bigoplus C=G\ \ \ C\bigoplus D=H \ \ \ D\bigoplus E=I\)
   \(A\bigoplus B\bigoplus C\bigoplus D\bigoplus E=A\bigoplus (B\bigoplus C)\bigoplus (D\bigoplus E)\)
   \(encode=[F,G,H,I]=[A\bigoplus B,B\bigoplus C,C\bigoplus D,D\bigoplus E]\)
   \(A=A\bigoplus (B\bigoplus C)\bigoplus (D\bigoplus E)\ \ \bigoplus \ \ \ (B\bigoplus C)\bigoplus (D\bigoplus E)\)
   因为n为奇数，所以可以从1开始，后每面两个元素的异或值，可以求出perm数组的第一个元素，剩余步骤同leetcode1720一致

代码

class Solution:
    def decode(self, encoded):
        ABCDE=0
        n=len(encoded)+1
        for i in range(1,n+1):
            ABCDE^=i
        i=1
        BCDE=0
        while i<n:
            BCDE^=encoded[i]
            i+=2
        perm=[0]*n
        perm[0]=ABCDE^BCDE
        for i in range(1,n):
            perm[i]=perm[i-1]^encoded[i-1]
        return perm