Queries on XOR of greatest odd divisor of the range

Given an array of N positive integers. There are Q queries, each include a range [L, R]. For each query output the xor of greatest odd divisor of each number in that range.

Examples:

Input : arr[] = { 3, 4, 5 }
query 1: [0, 2]
query 2: [1, 2]
Output : 7 4
Greatest odd divisor are: { 3, 1, 5 }
XOR of 3, 1, 5 is 7
XOR of 1, 5 is 4

Input : arr[] = { 2, 1, 2 }
query 1: [0, 2]
Output : 1

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea is to precompute the greatest odd divisor of the array and store it in an array, say preXOR[]. Now, precompute and store prefix XOR of the array preXOR[]. To answer each query, return (preXOR[r] xor preXOR[l-1]).

Below is the implementatin of this approach:

C++

#include <bits/stdc++.h> 
using namespace std; 
  
// Precompute the prefix XOR of greatest  
// odd divisor 
void prefixXOR(int arr[], int preXOR[], int n) 
{ 
    // Finding the Greatest Odd divisor 
    for (int i = 0; i < n; i++) { 
        while (arr[i] % 2 != 1) 
            arr[i] /= 2; 
  
        preXOR[i] = arr[i]; 
    } 
  
    // Finding prefix XOR 
    for (int i = 1; i < n; i++) 
        preXOR[i] = preXOR[i - 1] ^ preXOR[i]; 
} 
  
// Return XOR of the range 
int query(int preXOR[], int l, int r) 
{ 
    if (l == 0) 
        return preXOR[r]; 
    else
        return preXOR[r] ^ preXOR[l - 1]; 
} 
  
// Driven Program 
int main() 
{ 
    int arr[] = { 3, 4, 5 }; 
    int n = sizeof(arr) / sizeof(arr[0]); 
  
    int preXOR[n]; 
    prefixXOR(arr, preXOR, n); 
  
    cout << query(preXOR, 0, 2) << endl; 
    cout << query(preXOR, 1, 2) << endl; 
  
    return 0; 
} 

Java

// Java code Queries on XOR of  
// greatest odd divisor of the range 
import java.io.*; 
  
class GFG  
{ 
    // Precompute the prefix XOR of greatest  
    // odd divisor 
    static void prefixXOR(int arr[], int preXOR[], int n) 
    { 
        // Finding the Greatest Odd divisor 
        for (int i = 0; i < n; i++)  
        { 
            while (arr[i] % 2 != 1) 
                arr[i] /= 2; 
      
            preXOR[i] = arr[i]; 
        } 
      
        // Finding prefix XOR 
        for (int i = 1; i < n; i++) 
            preXOR[i] = preXOR[i - 1] ^ preXOR[i]; 
    } 
      
    // Return XOR of the range 
    static int query(int preXOR[], int l, int r) 
    { 
        if (l == 0) 
            return preXOR[r]; 
        else
            return preXOR[r] ^ preXOR[l - 1]; 
    } 
      
    // Driven Program 
    public static void main (String[] args)  
    { 
        int arr[] = { 3, 4, 5 }; 
        int n = arr.length; 
      
        int preXOR[] = new int[n]; 
        prefixXOR(arr, preXOR, n); 
      
        System.out.println(query(preXOR, 0, 2)) ; 
        System.out.println (query(preXOR, 1, 2)); 
      
              
    } 
} 
  
// This article is contributed by vt_m 

Python3

# Precompute the prefix XOR of greatest  
# odd divisor 
def prefixXOR(arr, preXOR, n): 
      
    # Finding the Greatest Odd divisor 
    for i in range(0, n, 1): 
        while (arr[i] % 2 != 1): 
            arr[i] = int(arr[i] / 2)  
  
        preXOR[i] = arr[i] 
  
    # Finding prefix XOR 
    for i in range(1, n, 1): 
        preXOR[i] = preXOR[i - 1] ^ preXOR[i] 
  
# Return XOR of the range 
def query(preXOR, l, r): 
    if (l == 0): 
        return preXOR[r] 
    else: 
        return preXOR[r] ^ preXOR[l - 1] 
  
# Driver Code 
if __name__ == '__main__': 
    arr = [3, 4, 5] 
    n = len(arr) 
  
    preXOR = [0 for i in range(n)] 
    prefixXOR(arr, preXOR, n) 
  
    print(query(preXOR, 0, 2)) 
    print(query(preXOR, 1, 2)) 
      
# This code is contributed by 
# Sahil_shelangia 

C#

// C# code Queries on XOR of  
// greatest odd divisor of the range 
using System; 
  
class GFG  
{ 
    // Precompute the prefix XOR of greatest  
    // odd divisor 
    static void prefixXOR(int []arr,  
                    int []preXOR, int n) 
    { 
        // Finding the Greatest Odd divisor 
        for (int i = 0; i < n; i++)  
        { 
            while (arr[i] % 2 != 1) 
                arr[i] /= 2; 
      
            preXOR[i] = arr[i]; 
        } 
      
        // Finding prefix XOR 
        for (int i = 1; i < n; i++) 
            preXOR[i] = preXOR[i - 1] ^ preXOR[i]; 
    } 
      
    // Return XOR of the range 
    static int query(int [] preXOR, int l, int r) 
    { 
        if (l == 0) 
            return preXOR[r]; 
        else
            return preXOR[r] ^ preXOR[l - 1]; 
    } 
      
    // Driven Program 
    public static void Main ()  
    { 
        int []arr = { 3, 4, 5 }; 
        int n = arr.Length; 
      
        int []preXOR = new int[n]; 
        prefixXOR(arr, preXOR, n); 
      
        Console.WriteLine(query(preXOR, 0, 2)) ; 
        Console.WriteLine (query(preXOR, 1, 2)); 
    } 
} 
  
// This code is contributed by vt_m 

Output:

7
4

This article is contributed by Anuj Chauhan. 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.

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

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