Spring-1-H Number Sequence（HDU 5014）解题报告及测试数据

Number Sequence

Time Limit:2000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Problem Description

There is a special number sequence which has n+1 integers. For each number in sequence, we have two rules:

● a i ∈ [0,n]

● a i ≠ a j ( i ≠ j )

For sequence a and sequence b, the integrating degree t is defined as follows(“⊕” denotes exclusive or):

t = (a 0  ⊕ b 0 ) + (a 1  ⊕ b 1 ) +···+ (a n  ⊕ b n )

(sequence B should also satisfy the rules described above)

Now give you a number n and the sequence a. You should calculate the maximum integrating degree t and print the sequence b.

Input

There are multiple test cases. Please process till EOF.

For each case, the first line contains an integer n(1 ≤ n ≤ 10 5 ), The second line contains a 0 ,a 1 ,a 2 ,...,a n .

Output

For each case, output two lines.The first line contains the maximum integrating degree t. The second line contains n+1 integers b 0 ,b 1 ,b 2 ,...,b n . There is exactly one space between b i and b i+1 (0 ≤ i ≤ n - 1) . Don’t ouput any spaces after b n .

Sample Input

4 2 0 1 4 3

Sample Output

20 1 0 2 3 4

题解：

1. 要使xor值最大，那么应该是xor的结果每一位上全部为1，例如n=3,00与11,01与10,10与01,11与00， 贪心算法，从最大的那个数匹配开始，尽量满足大的数字。
2. i从n开始， 所以1不断左移，直到匹配的数比不比i小为止。判断某一位上是0还是1，需要用到&运算符，若i的第k位上是0，那么i&(1<<k)的值就是0。

以下是代码：