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 the array in range a to b (both inclusive). After the 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 the given N we should create a bool array of n+1 elements and for each of M commands we have to iterate from a to b and toggle all elements in the range of a to b with help of XOR. 

The complexity of 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 the sample problem discussed in the Prefix Sum Array article. For the given n, we create a bool array of n+2 elements and for each of M commands, we have to just toggle elements a and b+1 with help of XOR. After all commands we will process the array as arr[i] ^= arr[i-1]; 

The complexity of this approach is O(n). 

Implementation:

// 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;
} 

// 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

# 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# 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

<?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
?>

<script>

// 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);


</script>  

1 0 1 1 1 

Time Complexity: O(n)
Auxiliary Space: O(1)