给定大小为N的数组arr [] ,任务是从给定数组中按位XOR为偶数的子数组计数。
例子:
Input: arr[] = {1, 2, 3, 4}
Output: 4
Explanation: The subarrays having even Bitwise XOR are {{2}, {4}, {1, 2, 3}, {1, 2, 3, 4}}.
Input: arr[] = {2, 4, 6}
Output: 6
Explanation: The subarrays having even Bitwise XOR are {{2}, {4}, {6}, {2, 4}, {4, 6}, {2, 4, 6}}.
天真的方法:解决此问题的最简单方法是生成所有可能的子数组,并检查每个子数组,无论其所有元素的按位XOR是否为偶数。如果发现是偶数,则增加计数。最后,将计数打印为结果。
下面是上述方法的实现:
C++
// C++ program for the above approach
#include
using namespace std;
// Function to count the number of
// subarrays having even Bitwise XOR
void evenXorSubarray(int arr[], int n)
{
// Store the required result
int ans = 0;
// Generate subarrays with
// arr[i] as the first element
for (int i = 0; i < n; i++) {
// Store XOR of current subarray
int XOR = 0;
// Generate subarrays with
// arr[j] as the last element
for (int j = i; j < n; j++) {
// Calculate Bitwise XOR
// of the current subarray
XOR = XOR ^ arr[j];
// If XOR is even,
// increase ans by 1
if ((XOR & 1) == 0)
ans++;
}
}
// Print the result
cout << ans;
}
// Driver Code
int main()
{
// Given array
int arr[] = { 1, 2, 3, 4 };
// Stores the size of the array
int N = sizeof(arr) / sizeof(arr[0]);
// Function Call
evenXorSubarray(arr, N);
return 0;
}
Java
// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;
class GFG {
// Function to count the number of
// subarrays having even Bitwise XOR
static void evenXorSubarray(int arr[], int n)
{
// Store the required result
int ans = 0;
// Generate subarrays with
// arr[i] as the first element
for (int i = 0; i < n; i++) {
// Store XOR of current subarray
int XOR = 0;
// Generate subarrays with
// arr[j] as the last element
for (int j = i; j < n; j++) {
// Calculate Bitwise XOR
// of the current subarray
XOR = XOR ^ arr[j];
// If XOR is even,
// increase ans by 1
if ((XOR & 1) == 0)
ans++;
}
}
// Print the result
System.out.println(ans);
}
// Driver Code
public static void main(String[] args)
{
// Given array
int arr[] = { 1, 2, 3, 4 };
// Stores the size of the array
int N = arr.length;
evenXorSubarray(arr, N);
}
}
// This code is contributed by Kingash.
Python3
# Python3 program for the above approach
# Function to count the number of
# subarrays having even Bitwise XOR
def evenXorSubarray(arr, n):
# Store the required result
ans = 0
# Generate subarrays with
# arr[i] as the first element
for i in range(n):
# Store XOR of current subarray
XOR = 0
# Generate subarrays with
# arr[j] as the last element
for j in range(i, n):
# Calculate Bitwise XOR
# of the current subarray
XOR = XOR ^ arr[j]
# If XOR is even,
# increase ans by 1
if ((XOR & 1) == 0):
ans += 1
# Prthe result
print (ans)
# Driver Code
if __name__ == '__main__':
# Given array
arr = [1, 2, 3, 4]
# Stores the size of the array
N = len(arr)
# Function Call
evenXorSubarray(arr, N)
# This code is contributed by mohit kumar 29.
C#
// C# program for the above approach
using System;
class GFG
{
// Function to count the number of
// subarrays having even Bitwise XOR
static void evenXorSubarray(int[] arr, int n)
{
// Store the required result
int ans = 0;
// Generate subarrays with
// arr[i] as the first element
for (int i = 0; i < n; i++) {
// Store XOR of current subarray
int XOR = 0;
// Generate subarrays with
// arr[j] as the last element
for (int j = i; j < n; j++) {
// Calculate Bitwise XOR
// of the current subarray
XOR = XOR ^ arr[j];
// If XOR is even,
// increase ans by 1
if ((XOR & 1) == 0)
ans++;
}
}
// Print the result
Console.WriteLine(ans);
}
// Driver Code
public static void Main()
{
// Given array
int[] arr = { 1, 2, 3, 4 };
// Stores the size of the array
int N = arr.Length;
evenXorSubarray(arr, N);
}
}
// This code is contributed by souravghosh0416.
Javascript
C++
// C++ program for the above approach
#include
using namespace std;
// Function to count subarrays
// having even Bitwise XOR
void evenXorSubarray(int arr[], int n)
{
// Store the required result
int ans = 0;
// Stores count of subarrays
// with even and odd XOR values
int freq[] = { 0, 0 };
// Stores Bitwise XOR of
// current subarray
int XOR = 0;
// Traverse the array
for (int i = 0; i < n; i++) {
// Update current Xor
XOR = XOR ^ arr[i];
// If XOR is even
if (XOR % 2 == 0) {
// Update ans
ans += freq[0] + 1;
// Increment count of
// subarrays with even XOR
freq[0]++;
}
else {
// Otherwise, increment count
// of subarrays with odd XOR
ans += freq[1];
freq[1]++;
}
}
// Print the result
cout << ans;
}
// Driver Code
int main()
{
// Given array
int arr[] = { 1, 2, 3, 4 };
// Stores the size of the array
int N = sizeof(arr) / sizeof(arr[0]);
evenXorSubarray(arr, N);
return 0;
}
Java
// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;
class GFG {
// Function to count subarrays
// having even Bitwise XOR
static void evenXorSubarray(int arr[], int n)
{
// Store the required result
int ans = 0;
// Stores count of subarrays
// with even and odd XOR values
int freq[] = { 0, 0 };
// Stores Bitwise XOR of
// current subarray
int XOR = 0;
// Traverse the array
for (int i = 0; i < n; i++) {
// Update current Xor
XOR = XOR ^ arr[i];
// If XOR is even
if (XOR % 2 == 0) {
// Update ans
ans += freq[0] + 1;
// Increment count of
// subarrays with even XOR
freq[0]++;
}
else {
// Otherwise, increment count
// of subarrays with odd XOR
ans += freq[1];
freq[1]++;
}
}
// Print the result
System.out.println(ans);
}
// Driver Code
public static void main(String[] args)
{
// Given array
int arr[] = { 1, 2, 3, 4 };
// Stores the size of the array
int N = arr.length;
evenXorSubarray(arr, N);
}
}
Python3
# Python3 program for the above approach
# Function to count subarrays
# having even Bitwise XOR
def evenXorSubarray(arr, n):
# Store the required result
ans = 0
# Stores count of subarrays
# with even and odd XOR values
freq = [0] * n
# Stores Bitwise XOR of
# current subarray
XOR = 0
# Traverse the array
for i in range(n):
# Update current Xor
XOR = XOR ^ arr[i]
# If XOR is even
if (XOR % 2 == 0):
# Update ans
ans += freq[0] + 1
# Increment count of
# subarrays with even XOR
freq[0] += 1
else:
# Otherwise, increment count
# of subarrays with odd XOR
ans += freq[1]
freq[1] += 1
# Print the result
print(ans)
# Driver Code
# Given array
arr = [ 1, 2, 3, 4 ]
# Stores the size of the array
N = len(arr)
evenXorSubarray(arr, N)
# This code is contributed by sanjoy_62
C#
// C# program for the above approach
using System;
class GFG
{
// Function to count subarrays
// having even Bitwise XOR
static void evenXorSubarray(int[] arr, int n)
{
// Store the required result
int ans = 0;
// Stores count of subarrays
// with even and odd XOR values
int[] freq = { 0, 0 };
// Stores Bitwise XOR of
// current subarray
int XOR = 0;
// Traverse the array
for (int i = 0; i < n; i++) {
// Update current Xor
XOR = XOR ^ arr[i];
// If XOR is even
if (XOR % 2 == 0) {
// Update ans
ans += freq[0] + 1;
// Increment count of
// subarrays with even XOR
freq[0]++;
}
else {
// Otherwise, increment count
// of subarrays with odd XOR
ans += freq[1];
freq[1]++;
}
}
// Print the result
Console.WriteLine(ans);
}
// Driver Code
public static void Main(String[] args)
{
// Given array
int[] arr = { 1, 2, 3, 4 };
// Stores the size of the array
int N = arr.Length;
evenXorSubarray(arr, N);
}
}
// This code is contributed by susmitakundugoaldanga.
Javascript
4
时间复杂度: O(N 2 )
辅助空间: O(1)
高效的方法:可以基于以下观察来优化上述方法:
Bitwise XOR of all elements in the range of indices [i + 1, j] be A.
Bitwise XOR of all elements in the range of indices [0, i] be B.
Bitwise XOR of all elements in the range of indices [0, j] be C.
By performing B ^ C, the the common elements from the two ranges cancel out, resulting in XOR of all elements from the range [i + 1, j].
因此,该想法是从索引0开始更新具有偶数和奇数XOR值的子数组的数量,同时遍历该数组并相应地更新计数。请按照以下步骤解决问题:
- 初始化两个变量,例如ans和XOR,以存储所需的子数组计数和分别存储子数组的XOR值。
- 初始化一个数组,说大小为2的freq [] ,其中freq [0]表示具有偶数XOR值的子数组的数量, freq [1]表示具有奇数XOR值的子数组的数量,从索引0开始。
- 对于每个数组元素,使用变量i遍历数组arr [] :
- 将XOR的值更新为XOR ^ arr [i] 。
- 如果XOR为偶数,则将ans的值增加1 + freq [0] 。
- 将freq [0]递增1,因为当子数组{arr [0],i]与其他具有偶数xor值的子数组进行XOR运算时,它将导致偶数XOR值。同样,添加1以考虑整个子数组[0,i]。
- 同样,如果XOR为奇数,则将ans增加freq [1] ,将freq [1]增加1。
- 完成上述步骤后,输出ans的值作为结果。
下面是上述方法的实现:
C++
// C++ program for the above approach
#include
using namespace std;
// Function to count subarrays
// having even Bitwise XOR
void evenXorSubarray(int arr[], int n)
{
// Store the required result
int ans = 0;
// Stores count of subarrays
// with even and odd XOR values
int freq[] = { 0, 0 };
// Stores Bitwise XOR of
// current subarray
int XOR = 0;
// Traverse the array
for (int i = 0; i < n; i++) {
// Update current Xor
XOR = XOR ^ arr[i];
// If XOR is even
if (XOR % 2 == 0) {
// Update ans
ans += freq[0] + 1;
// Increment count of
// subarrays with even XOR
freq[0]++;
}
else {
// Otherwise, increment count
// of subarrays with odd XOR
ans += freq[1];
freq[1]++;
}
}
// Print the result
cout << ans;
}
// Driver Code
int main()
{
// Given array
int arr[] = { 1, 2, 3, 4 };
// Stores the size of the array
int N = sizeof(arr) / sizeof(arr[0]);
evenXorSubarray(arr, N);
return 0;
}
Java
// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;
class GFG {
// Function to count subarrays
// having even Bitwise XOR
static void evenXorSubarray(int arr[], int n)
{
// Store the required result
int ans = 0;
// Stores count of subarrays
// with even and odd XOR values
int freq[] = { 0, 0 };
// Stores Bitwise XOR of
// current subarray
int XOR = 0;
// Traverse the array
for (int i = 0; i < n; i++) {
// Update current Xor
XOR = XOR ^ arr[i];
// If XOR is even
if (XOR % 2 == 0) {
// Update ans
ans += freq[0] + 1;
// Increment count of
// subarrays with even XOR
freq[0]++;
}
else {
// Otherwise, increment count
// of subarrays with odd XOR
ans += freq[1];
freq[1]++;
}
}
// Print the result
System.out.println(ans);
}
// Driver Code
public static void main(String[] args)
{
// Given array
int arr[] = { 1, 2, 3, 4 };
// Stores the size of the array
int N = arr.length;
evenXorSubarray(arr, N);
}
}
Python3
# Python3 program for the above approach
# Function to count subarrays
# having even Bitwise XOR
def evenXorSubarray(arr, n):
# Store the required result
ans = 0
# Stores count of subarrays
# with even and odd XOR values
freq = [0] * n
# Stores Bitwise XOR of
# current subarray
XOR = 0
# Traverse the array
for i in range(n):
# Update current Xor
XOR = XOR ^ arr[i]
# If XOR is even
if (XOR % 2 == 0):
# Update ans
ans += freq[0] + 1
# Increment count of
# subarrays with even XOR
freq[0] += 1
else:
# Otherwise, increment count
# of subarrays with odd XOR
ans += freq[1]
freq[1] += 1
# Print the result
print(ans)
# Driver Code
# Given array
arr = [ 1, 2, 3, 4 ]
# Stores the size of the array
N = len(arr)
evenXorSubarray(arr, N)
# This code is contributed by sanjoy_62
C#
// C# program for the above approach
using System;
class GFG
{
// Function to count subarrays
// having even Bitwise XOR
static void evenXorSubarray(int[] arr, int n)
{
// Store the required result
int ans = 0;
// Stores count of subarrays
// with even and odd XOR values
int[] freq = { 0, 0 };
// Stores Bitwise XOR of
// current subarray
int XOR = 0;
// Traverse the array
for (int i = 0; i < n; i++) {
// Update current Xor
XOR = XOR ^ arr[i];
// If XOR is even
if (XOR % 2 == 0) {
// Update ans
ans += freq[0] + 1;
// Increment count of
// subarrays with even XOR
freq[0]++;
}
else {
// Otherwise, increment count
// of subarrays with odd XOR
ans += freq[1];
freq[1]++;
}
}
// Print the result
Console.WriteLine(ans);
}
// Driver Code
public static void Main(String[] args)
{
// Given array
int[] arr = { 1, 2, 3, 4 };
// Stores the size of the array
int N = arr.Length;
evenXorSubarray(arr, N);
}
}
// This code is contributed by susmitakundugoaldanga.
Java脚本
4
时间复杂度: O(N)
辅助空间: O(1)