M 范围切换操作后的二进制数组

考虑一个由 N 个元素组成的二进制数组（最初所有元素都是 0）。之后，您将获得 M 个命令，其中每个命令的格式为 ab，这意味着您必须在 a 到 b 范围内切换数组的所有元素（包括两者）。在执行完所有 M 个命令后，您必须找到结果数组。

例子：

Input : N = 5, M = 3
        C1 = 1 3, C2 = 4 5, C3 = 1 4
Output : Resultant array = {0, 0, 0, 0, 1} 
Explanation :
Initial array : {0, 0, 0, 0, 0}
After first toggle : {1, 1, 1, 0, 0}
After second toggle : {1, 1, 1, 1, 1}
After third toggle :  {0, 0, 0, 0, 1}

Input : N = 5, M = 5
        C1 = 1 5, C2 = 1 5, C3 = 1 5,
        C4 = 1 5, C5 = 1 5
Output : Resultant array = {1, 1, 1, 1, 1} 

天真的方法：对于给定的 N，我们应该创建一个包含 n+1 个元素的 bool 数组，并且对于每个 M 个命令，我们必须从 a 迭代到 b，并在 XOR 的帮助下切换 a 到 b 范围内的所有元素。

这种方法的复杂度是 O(n^2)。

for (int i = 1; i > a >> b;
    for (int j = a; j <= b; j++)
        arr[j] ^= 1;

高效方法：这个想法基于前缀和数组文章中讨论的示例问题。对于给定的 n，我们创建一个包含 n+2 个元素的 bool 数组，并且对于 M 个命令中的每一个，我们必须在 XOR 的帮助下切换元素 a 和 b+1。在所有命令之后，我们将数组处理为 arr[i] ^= arr[i-1];

这种方法的复杂度是 O(n)。

C++

// CPP program to find modified array after
// m range toggle operations.
#include
using namespace std;
 
// function for toggle
void command(bool arr[], int a, int b)
{
    arr[a] ^= 1;
    arr[b+1] ^= 1;
}
 
// function for final processing of array
void process(bool arr[], int n)
{
    for (int k=1; k<=n; k++)
        arr[k] ^= arr[k-1];
}
 
// function for printing result
void result(bool arr[], int n)
{
    for (int k=1; k<=n; k++)
        cout << arr[k] <<" ";
}
 
// driver program
int main()
{
    int n = 5, m = 3;
    bool arr[n+2] = {0};
 
    // function call for toggle
    command(arr, 1, 5);
    command(arr, 2, 5);
    command(arr, 3, 5);
     
    // process array
    process(arr, n);
     
    // print result
    result(arr, n);
    return 0;
}

Java

// Java program to find modified array
// after m range toggle operations.
class GFG
{
 
// function for toggle
static void command(boolean arr[],
                    int a, int b)
{
    arr[a] ^= true;
    arr[b + 1] ^= true;
}
 
// function for final processing of array
static void process(boolean arr[], int n)
{
    for (int k = 1; k <= n; k++)
    {
        arr[k] ^= arr[k - 1];
    }
}
 
// function for printing result
static void result(boolean arr[], int n)
{
    for (int k = 1; k <= n; k++)
    {
        if(arr[k] == true)
            System.out.print("1" + " ");
        else
            System.out.print("0" + " ");
    }
}
 
// Driver Code
public static void main(String args[])
{
    int n = 5, m = 3;
    boolean arr[] = new boolean[n + 2];
 
    // function call for toggle
    command(arr, 1, 5);
    command(arr, 2, 5);
    command(arr, 3, 5);
 
    // process array
    process(arr, n);
 
    // print result
    result(arr, n);
}
}
 
// This code is contributed
// by PrinciRaj1992

Python3

# Python 3 program to find modified array after
# m range toggle operations.
 
# function for toggle
def command(brr, a, b):
    arr[a] ^= 1
    arr[b+1] ^= 1
 
# function for final processing of array
def process(arr, n):
    for k in range(1, n + 1, 1):
        arr[k] ^= arr[k - 1]
 
# function for printing result
def result(arr, n):
    for k in range(1, n + 1, 1):
        print(arr[k], end = " ")
 
# Driver Code
if __name__ == '__main__':
    n = 5
    m = 3
    arr = [0 for i in range(n+2)]
 
    # function call for toggle
    command(arr, 1, 5)
    command(arr, 2, 5)
    command(arr, 3, 5)
     
    # process array
    process(arr, n)
     
    # print result
    result(arr, n)
 
# This code is contributed by
# Surendra_Gangwar

C#

// C# program to find modified array
// after m range toggle operations.
using System;
 
class GFG
{
 
// function for toggle
static void command(bool[] arr,
                    int a, int b)
{
    arr[a] ^= true;
    arr[b + 1] ^= true;
}
 
// function for final processing of array
static void process(bool[] arr, int n)
{
    for (int k = 1; k <= n; k++)
    {
        arr[k] ^= arr[k - 1];
    }
}
 
// function for printing result
static void result(bool[] arr, int n)
{
    for (int k = 1; k <= n; k++)
    {
        if(arr[k] == true)
            Console.Write("1" + " ");
        else
            Console.Write("0" + " ");
    }
}
 
// Driver Code
public static void Main()
{
    int n = 5, m = 3;
    bool[] arr = new bool[n + 2];
 
    // function call for toggle
    command(arr, 1, 5);
    command(arr, 2, 5);
    command(arr, 3, 5);
 
    // process array
    process(arr, n);
 
    // print result
    result(arr, n);
}
}
 
// This code is contributed
// by Akanksha Rai

Javascript

 
// Javascript program to find modified array after
// m range toggle operations.
 
// function for toggle
function command(arr, a, b)
{
    arr[a] ^= 1;
    arr[b+1] ^= 1;
}
 
// function for final processing of array
function process( arr, n)
{
    for (var k=1; k<=n; k++)
        arr[k] ^= arr[k-1];
}
 
// function for printing result
function result( arr, n)
{
    for (var k=1; k<=n; k++)
        document.write( arr[k] + " ");
}
 
// driver program
var n = 5, m = 3;
var arr = Array(n+2).fill(0);
// function call for toggle
command(arr, 1, 5);
command(arr, 2, 5);
command(arr, 3, 5);
 
// process array
process(arr, n);
 
// print result
result(arr, n);
 
 

输出：

1 0 1 1 1