我们得到一个包含 n 个元素的数组 arr。我们需要计算非空子序列的数量，以便这些单独的子序列具有相同的按位 AND、OR 和 XOR 值。例如，如果 (x | y | z) 等于 (x & y & z) 和 (x ^ y ^ z)，我们需要对子序列 (x, y, z) 进行计数。对于单个元素子序列，我们将元素本身视为 XOR、AND 和 OR 的结果。因此，所有单个元素子序列始终被视为结果的一部分。
例子：
Input : a = [1, 3, 7]
Output : 3
Explanation:
There are 7 non empty subsequence .
subsequence OR AND XOR
{1} 1 1 1
{3} 3 3 3
{7} 7 7 7
{1, 3} 3 1 2
{1, 7} 7 1 6
{3, 7} 7 3 4
{1, 3, 7} 7 1 5
Out of 7, there are 3 subsequences {1}
{3} {7} which have same values of AND,
OR and XOR.
Input : a[] = [0, 0, 0]
Output : 7
Explanation: All 7 non empty subsequences
have same values of AND, OR and XOR.
Input : a[] = [2, 2, 2, 3, 4]
Output : 6
Explanation: subsequence {2}, {2}, {2},
{2, 2, 2}, {3}, {4} have same values of
AND, OR and XOR.
1) 如果给定数组中出现 n 个零，则这些零将贡献 2 n – 1 个子序列。
2) 如果非零元素 x 出现n次，则该元素的出现将贡献 2 n-1个子序列。请注意，在非零元素的情况下，对于按位运算运算符，只有奇数次出现才能导致相同的结果。
查找数组中每个元素的计数，然后应用上述公式。
C++
#include
using namespace std;
// function for finding count of possible subsequence
int countSubseq(int arr[], int n)
{
int count = 0;
// creating a map to count the frequency of each element
unordered_map mp;
// store frequency of each element
for (int i = 0; i < n; i++)
mp[arr[i]]++;
// iterate through the map
for (auto i : mp) {
// add all possible combination for key equal zero
if (i.first == 0)
count += pow(2, i.second) - 1;
// add all (odd number of elements) possible
// combination for key other than zero
else
count += pow(2, i.second - 1);
}
return count;
}
// driver function
int main()
{
int arr[] = { 2, 2, 2, 5, 6 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << countSubseq(arr, n);
return 0;
} Java
import java .io.*;
import java.util.*;
class GFG {
// function for finding count of possible subsequence
static int countSubseq(int arr[], int n)
{
int count = 0;
// creating a map to count the frequency of each element
HashMapmp=new HashMap();
// store frequency of each element
for (int i = 0; i < n; i++)
if (mp.containsKey(arr[i]))
mp.put(arr[i],mp.get(arr[i])+1);
else
mp.put(arr[i],1);
// iterate through the map
for (Map.Entryentry:mp.entrySet()) {
// add all possible combination for key equal zero
if (entry.getKey() == 0)
count += Math.pow(2, entry.getValue()) - 1;
// add all (odd number of elements) possible
// combination for key other than zero
else
count += Math.pow(2, entry.getValue()- 1);
}
return count;
}
// driver function
public static void main(String[] args)
{
int arr[] = { 2, 2, 2, 5, 6 };
int n=arr.length;
System.out.println(countSubseq(arr, n));
}
}
// This code is contributed by apurva raj C#
using System;
using System.Collections.Generic;
class GFG{
// function for finding count of possible subsequence
static int countSubseq(int []arr, int n)
{
int count = 0;
// creating a map to count the frequency of each element
Dictionary mp = new Dictionary();
// store frequency of each element
for (int i = 0; i < n; i++)
{
if (mp.ContainsKey(arr[i]))
{
var val = mp[arr[i]];
mp.Remove(arr[i]);
mp.Add(arr[i], val + 1);
}
else
{
mp.Add(arr[i], 1);
}
}
// iterate through the map
foreach(KeyValuePair entry in mp) {
// add all possible combination for key equal zero
if (entry.Key == 0)
count += (int)(Math.Pow(2, entry.Value - 1));
// add all (odd number of elements) possible
// combination for key other than zero
else
count += (int)(Math.Pow(2, entry.Value - 1));
}
return count;
}
// Driver function
public static void Main(String []args)
{
int []arr = { 2, 2, 2, 5, 6 };
int n = arr.Length;
Console.WriteLine(countSubseq(arr, n));
}
}
// This code is contributed by shivanisinghss2110 Python3
# function for finding count of possible subsequence
def countSubseq(arr, n):
count = 0
# creating a map to count the frequency of each element
mp = {}
# store frequency of each element
for x in arr:
if x in mp.keys():
mp[x]+=1
else:
mp[x]=1
# iterate through the map
for i in mp.keys():
# add all possible combination for key equal zero
if (i == 0):
count += pow(2, mp[i]) - 1
# add all (odd number of elements) possible
# combination for key other than zero
else:
count += pow(2, mp[i] - 1)
return count
# Driver function
arr= [2, 2, 2, 5, 6 ]
n = len(arr)
print(countSubseq(arr, n))
# This code is contributed by apurva raj输出：
6
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