Binary array after M range toggle operations

Consider a binary array consisting of N elements (initially all elements are 0). After that you are given M commands where each command is of form a b, which means you have to toggle all the elements of array in range a to b (both inclusive). After execution of all M commands you have to find the resultant array.

Examples:

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} 

Naive Approach : For given N we should create a bool array of n+1 element and for each of M commands we have to iterate from a to b and toggle all elements in range of a to b with help of XOR.
Complexity for this approach is O(n^2).



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

Efficient Approach : The idea is based on sample problem discussed in Prefix Sum Array article. For given n, we create a bool array of n+2 element and for each of M commands we have to just toggle element a and b+1 with help of XOR. After all commands we will process the array as arr[i] ^= arr[i-1];
Complexity for this approach is O(n).

C++

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// CPP program to find modified array after 
// m range toggle operations.
#include<bits/stdc++.h>
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;

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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PHP

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<?php
// PHP program to find modified array 
// after m range toggle operations. 
  
// function for toggle 
function command($arr, $a, $b
{
    $arr[$a] = $arr[$a] ^ 1;
    $arr[$b + 1] ^= 1;
}
  
// function for final processing 
// of array 
function process($arr, $n
{
    for ($k = 1; $k <= $n; $k++) 
    {
        $arr[$k] = $arr[$k] ^ $arr[$k - 1];
    }
}
  
// function for printing result 
function result($arr, $n
{
    for ($k = 1; $k <= $n; $k++) 
    echo $arr[$k] . " ";
}
  
// Driver Code
$n = 5; $m = 3;
$arr = new SplFixedArray(7);
$arr[6] = array(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);
  
// This code is contributed 
// by Mukul Singh
?>

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Output:

1 0 1 1 1

This article is contributed by Shivam Pradhan (anuj_charm). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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