A13513 | Maximum Subsequence Value
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内存限制256MB
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题目描述
Ridhiman challenged Ashish to find the maximum valued subsequence of an array $a$ of size $n$ consisting of positive integers.
The value of a non-empty subsequence of $k$ elements of $a$ is defined as $\sum 2^i$ over all integers $i \ge 0$ such that at least $\max(1, k - 2)$ elements of the subsequence have the $i$ -th bit set in their binary representation (value $x$ has the $i$ -th bit set in its binary representation if $\lfloor \frac{x}{2^i} \rfloor \mod 2$ is equal to $1$ ).
Recall that $b$ is a subsequence of $a$ , if $b$ can be obtained by deleting some(possibly zero) elements from $a$ .
Help Ashish find the maximum value he can get by choosing some subsequence of $a$ .
The value of a non-empty subsequence of $k$ elements of $a$ is defined as $\sum 2^i$ over all integers $i \ge 0$ such that at least $\max(1, k - 2)$ elements of the subsequence have the $i$ -th bit set in their binary representation (value $x$ has the $i$ -th bit set in its binary representation if $\lfloor \frac{x}{2^i} \rfloor \mod 2$ is equal to $1$ ).
Recall that $b$ is a subsequence of $a$ , if $b$ can be obtained by deleting some(possibly zero) elements from $a$ .
Help Ashish find the maximum value he can get by choosing some subsequence of $a$ .
输入格式
The first line of the input consists of a single integer $n$ $(1 \le n \le 500)$ — the size of $a$ .
The next line consists of $n$ space-separated integers — the elements of the array $(1 \le a_i \le 10^{18})$ .
The next line consists of $n$ space-separated integers — the elements of the array $(1 \le a_i \le 10^{18})$ .
输出格式
Print a single integer — the maximum value Ashish can get by choosing some subsequence of $a$ .
输入输出样例
输入 #1
3 2 1 3
输出 #1
3
输入 #2
3 3 1 4
输出 #2
7
输入 #3
1 1
输出 #3
1
输入 #4
4 7 7 1 1
输出 #4
7
For the first test case, Ashish can pick the subsequence $\{{2, 3}\}$ of size $2$ . The binary representation of $2$ is 10 and that of $3$ is 11. Since $\max(k - 2, 1)$ is equal to $1$ , the value of the subsequence is $2^0 + 2^1$ (both $2$ and $3$ have $1$ -st bit set in their binary representation and $3$ has $0$ -th bit set in its binary representation). Note that he could also pick the subsequence $\{{3\}}$ or $\{{2, 1, 3\}}$ .
For the second test case, Ashish can pick the subsequence $\{{3, 4\}}$ with value $7$ .
For the third test case, Ashish can pick the subsequence $\{{1\}}$ with value $1$ .
For the fourth test case, Ashish can pick the subsequence $\{{7, 7\}}$ with value $7$ .
For the second test case, Ashish can pick the subsequence $\{{3, 4\}}$ with value $7$ .
For the third test case, Ashish can pick the subsequence $\{{1\}}$ with value $1$ .
For the fourth test case, Ashish can pick the subsequence $\{{7, 7\}}$ with value $7$ .
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评测结果：Accepted