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Binary array after M range toggle operations
  • Difficulty Level : Hard
  • Last Updated : 29 Apr, 2021

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). 

C++




// 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




// 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

PHP




<?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
?>

Javascript




<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>

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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

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