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:Â
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.Â
The complexity of this approach is O(n^2). Â
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];Â
The complexity of this approach is O(n).Â
Implementation:
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
Time Complexity: O(n)
Auxiliary Space: O(1)
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