Segment Tree | Set 3 (XOR of given range)

We have an array arr[0 . . . n-1]. There are two type of queries

1. Find the XOR of elements from index l to r where 0 <= l <= r <= n-1
2. Change value of a specified element of the array to a new value x. We need to do arr[i] = x where 0 <= i <= n-1.

There will be total of q queries.

Input Constraint

 n <= 10^5, q <= 10^5

Solution 1: A simple solution is to run a loop from l to r and calculate xor of elements in given range. To update a value, simply do arr[i] = x. The first operation takes O(n) time and second operation takes O(1) time. Worst case time complexity is O(n*q) for q queries 
which will take huge time for n ~ 10^5 and q ~ 10^5. Hence this solution will exceed time limit.

Solution 2: Another solution is to store xor in all possible ranges but there are O(n^2) possible ranges hence with n ~ 10^5 it will exceed space complexity, hence without considering time complexity, we can state this solution will not work.

Solution 3 (Segment Tree):

Prerequisite : Segment Tree
We build a segment tree of given array such that array elements are at leaves and internal nodes store XOR of leaves covered under them.

Implementation:

C++

// C++ program to show segment tree operations like construction,
// query and update
#include <iostream>
#include <math.h>
using namespace std;

// A utility function to get the middle index from corner indexes.
int getMid(int s, int e) {  return s + (e -s)/2;  }

/*  A recursive function to get the xor of values in given range
    of the array. The following are parameters for this function.

    st    --> Pointer to segment tree
    si    --> Index of current node in the segment tree. Initially
              0 is passed as root is always at index 0
    ss & se  --> Starting and ending indexes of the segment
                 represented by current node, i.e., st[si]
    qs & qe  --> Starting and ending indexes of query range */
int getXorUtil(int *st, int ss, int se, int qs, int qe, int si)
{
    // If segment of this node is a part of given range, then return
    // the xor of the segment
    if (qs <= ss && qe >= se)
        return st[si];

    // If segment of this node is outside the given range
    if (se < qs || ss > qe)
        return 0;

    // If a part of this segment overlaps with the given range
    int mid = getMid(ss, se);
    return getXorUtil(st, ss, mid, qs, qe, 2*si+1) ^
           getXorUtil(st, mid+1, se, qs, qe, 2*si+2);
}

/* A recursive function to update the nodes which have the given
   index in their range. The following are parameters
    st, si, ss and se are same as getXorUtil()
    i    --> index of the element to be updated. This index is
             in input array.
   diff --> Value to be added to all nodes which have i in range */
void updateValueUtil(int *st, int ss, int se, int i, int diff, int si)
{
    // Base Case: If the input index lies outside the range of
    // this segment
    if (i < ss || i > se)
        return;

    // If the input index is in range of this node, then update
    // the value of the node and its children
    st[si] = st[si] + diff;
    if (se != ss)
    {
        int mid = getMid(ss, se);
        updateValueUtil(st, ss, mid, i, diff, 2*si + 1);
        updateValueUtil(st, mid+1, se, i, diff, 2*si + 2);
    }
}

// The function to update a value in input array and segment tree.
// It uses updateValueUtil() to update the value in segment tree
void updateValue(int arr[], int *st, int n, int i, int new_val)
{
    // Check for erroneous input index
    if (i < 0 || i > n-1)
    {
        cout <<"Invalid Input";
        return;
    }

    // Get the difference between new value and old value
    int diff = new_val - arr[i];

    // Update the value in array
    arr[i] = new_val;

    // Update the values of nodes in segment tree
    updateValueUtil(st, 0, n-1, i, diff, 0);
}

// Return xor of elements in range from index qs (query start)
// to qe (query end).  It mainly uses getXorUtil()
int getXor(int *st, int n, int qs, int qe)
{
    // Check for erroneous input values
    if (qs < 0 || qe > n-1 || qs > qe)
    {
        cout <<"Invalid Input";
        return -1;
    }

    return getXorUtil(st, 0, n-1, qs, qe, 0);
}

// A recursive function that constructs Segment Tree for array[ss..se].
// si is index of current node in segment tree st
int constructSTUtil(int arr[], int ss, int se, int *st, int si)
{
    // If there is one element in array, store it in current node of
    // segment tree and return
    if (ss == se)
    {
        st[si] = arr[ss];
        return arr[ss];
    }

    // If there are more than one elements, then recur for left and
    // right subtrees and store the xor of values in this node
    int mid = getMid(ss, se);
    st[si] =  constructSTUtil(arr, ss, mid, st, si*2+1) ^
              constructSTUtil(arr, mid+1, se, st, si*2+2);
    return st[si];
}

/* Function to construct segment tree from given array. This function
   allocates memory for segment tree and calls constructSTUtil() to
   fill the allocated memory */
int *constructST(int arr[], int n)
{
    // Allocate memory for segment tree

    //Height of segment tree
    int x = (int)(ceil(log2(n)));

    //Maximum size of segment tree
    int max_size = 2*(int)pow(2, x) - 1;

    // Allocate memory
    int *st =  (int *)malloc(sizeof(int)*max_size);

    // Fill the allocated memory st
    constructSTUtil(arr, 0, n-1, st, 0);

    // Return the constructed segment tree
    return st;
}

// Driver program to test above functions
int main()
{
    int arr[] = {1, 3, 5, 7, 9, 11};
    int n = sizeof(arr)/sizeof(arr[0]);

    // Build segment tree from given array
    int *st = constructST(arr, n);

    // Print xor of values in array from index 1 to 3
    cout <<"Xor of values in given range = "<< getXor(st, n, 1, 3) << endl;

    // Update: set arr[1] = 10 and update corresponding
    // segment tree nodes
    updateValue(arr, st, n, 1, 10);

    // Find xor after the value is updated
    cout <<"Updated xor of values in given range = " << getXor(st, n, 1, 3) << endl;
    return 0;
}

// This code is contributed by shivanisinghss2110

C

// C program to show segment tree operations like construction,
// query and update
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

// A utility function to get the middle index from corner indexes.
int getMid(int s, int e) {  return s + (e -s)/2;  }

/*  A recursive function to get the xor of values in given range
    of the array. The following are parameters for this function.

    st    --> Pointer to segment tree
    si    --> Index of current node in the segment tree. Initially
              0 is passed as root is always at index 0
    ss & se  --> Starting and ending indexes of the segment
                 represented by current node, i.e., st[si]
    qs & qe  --> Starting and ending indexes of query range */
int getXorUtil(int *st, int ss, int se, int qs, int qe, int si)
{
    // If segment of this node is a part of given range, then return
    // the xor of the segment
    if (qs <= ss && qe >= se)
        return st[si];

    // If segment of this node is outside the given range
    if (se < qs || ss > qe)
        return 0;

    // If a part of this segment overlaps with the given range
    int mid = getMid(ss, se);
    return getXorUtil(st, ss, mid, qs, qe, 2*si+1) ^
           getXorUtil(st, mid+1, se, qs, qe, 2*si+2);
}

/* A recursive function to update the nodes which have the given
   index in their range. The following are parameters
    st, si, ss and se are same as getXorUtil()
    i    --> index of the element to be updated. This index is
             in input array.
   diff --> Value to be added to all nodes which have i in range */
void updateValueUtil(int *st, int ss, int se, int i, int diff, int si)
{
    // Base Case: If the input index lies outside the range of
    // this segment
    if (i < ss || i > se)
        return;

    // If the input index is in range of this node, then update
    // the value of the node and its children
    st[si] = st[si] + diff;
    if (se != ss)
    {
        int mid = getMid(ss, se);
        updateValueUtil(st, ss, mid, i, diff, 2*si + 1);
        updateValueUtil(st, mid+1, se, i, diff, 2*si + 2);
    }
}

// The function to update a value in input array and segment tree.
// It uses updateValueUtil() to update the value in segment tree
void updateValue(int arr[], int *st, int n, int i, int new_val)
{
    // Check for erroneous input index
    if (i < 0 || i > n-1)
    {
        printf("Invalid Input");
        return;
    }

    // Get the difference between new value and old value
    int diff = new_val - arr[i];

    // Update the value in array
    arr[i] = new_val;

    // Update the values of nodes in segment tree
    updateValueUtil(st, 0, n-1, i, diff, 0);
}

// Return xor of elements in range from index qs (query start)
// to qe (query end).  It mainly uses getXorUtil()
int getXor(int *st, int n, int qs, int qe)
{
    // Check for erroneous input values
    if (qs < 0 || qe > n-1 || qs > qe)
    {
        printf("Invalid Input");
        return -1;
    }

    return getXorUtil(st, 0, n-1, qs, qe, 0);
}

// A recursive function that constructs Segment Tree for array[ss..se].
// si is index of current node in segment tree st
int constructSTUtil(int arr[], int ss, int se, int *st, int si)
{
    // If there is one element in array, store it in current node of
    // segment tree and return
    if (ss == se)
    {
        st[si] = arr[ss];
        return arr[ss];
    }

    // If there are more than one elements, then recur for left and
    // right subtrees and store the xor of values in this node
    int mid = getMid(ss, se);
    st[si] =  constructSTUtil(arr, ss, mid, st, si*2+1) ^
              constructSTUtil(arr, mid+1, se, st, si*2+2);
    return st[si];
}

/* Function to construct segment tree from given array. This function
   allocates memory for segment tree and calls constructSTUtil() to
   fill the allocated memory */
int *constructST(int arr[], int n)
{
    // Allocate memory for segment tree

    //Height of segment tree
    int x = (int)(ceil(log2(n)));

    //Maximum size of segment tree
    int max_size = 2*(int)pow(2, x) - 1;

    // Allocate memory
    int *st =  (int *)malloc(sizeof(int)*max_size);

    // Fill the allocated memory st
    constructSTUtil(arr, 0, n-1, st, 0);

    // Return the constructed segment tree
    return st;
}

// Driver program to test above functions
int main()
{
    int arr[] = {1, 3, 5, 7, 9, 11};
    int n = sizeof(arr)/sizeof(arr[0]);

    // Build segment tree from given array
    int *st = constructST(arr, n);

    // Print xor of values in array from index 1 to 3
    printf("Xor of values in given range = %d\n",
            getXor(st, n, 1, 3));

    // Update: set arr[1] = 10 and update corresponding
    // segment tree nodes
    updateValue(arr, st, n, 1, 10);

    // Find xor after the value is updated
    printf("Updated xor of values in given range = %d\n",
             getXor(st, n, 1, 3));
    return 0;
}

Java

// Java program to show segment tree operations
// like construction, query and update
class GFG{

// A utility function to get the middle
// index from corner indexes.
static int getMid(int s, int e)
{
    return s + (e - s) / 2;
}

/*
 * A recursive function to get the xor of values
 * in given range of the array.
 * The following are parameters for this function.
 *
 * st --> Pointer to segment tree
 * si --> Index of current node in the segment tree. Initially
 *        0 is passed as root is always at index 0
 * ss & se --> Starting and ending indexes of the segment
 *             represented by current node, i.e., st[si]
 * qs & qe --> Starting and ending indexes of query range
 */
static int getXorUtil(int[] st, int ss, int se,
                      int qs, int qe, int si)
{

    // If segment of this node is a part of
    // given range, then return the xor of
    // the segment
    if (qs <= ss && qe >= se)
        return st[si];

    // If segment of this node is
    // outside the given range
    if (se < qs || ss > qe)
        return 0;

    // If a part of this segment overlaps
    // with the given range
    int mid = getMid(ss, se);
    return getXorUtil(st, ss, mid, qs,
                      qe, 2 * si + 1) ^
           getXorUtil(st, mid + 1, se, qs,
                      qe, 2 * si + 2);
}

/*
 * A recursive function to update the nodes which have the given
 * index in their range. The following are parameters
 * st, si, ss and se are same as getXorUtil()
 * i --> index of the element to be updated. This index is in
 *       input array.
 * diff --> Value to be added to all nodes which have i in range
 */
static void updateValueUtil(int[] st, int ss, int se,
                            int i, int diff, int si)
{

    // Base Case: If the input index lies outside the
    // range of this segment
    if (i < ss || i > se)
        return;

    // If the input index is in range of this node,
    // then update the value of the node and its children
    st[si] = st[si] + diff;
    if (se != ss)
    {
        int mid = getMid(ss, se);
        updateValueUtil(st, ss, mid, i, diff,
                         2 * si + 1);
        updateValueUtil(st, mid + 1, se, i, diff,
                         2 * si + 2);
    }
}

// The function to update a value in input array
// and segment tree. It uses updateValueUtil()
// to update the value in segment tree
static void updateValue(int[] arr, int[] st, int n,
                        int i, int new_val)
{

    // Check for erroneous input index
    if (i < 0 || i > n - 1)
    {
        System.out.println("Invalid Input");
        return;
    }

    // Get the difference between new
    // value and old value
    int diff = new_val - arr[i];

    // Update the value in array
    arr[i] = new_val;

    // Update the values of nodes in segment tree
    updateValueUtil(st, 0, n - 1, i, diff, 0);
}

// Return xor of elements in range from
// index qs (query start) to qe (query end).
// It mainly uses getXorUtil()
static int getXor(int[] st, int n, int qs, int qe)
{

    // Check for erroneous input values
    if (qs < 0 || qe > n - 1 || qs > qe)
    {
        System.out.println("Invalid Input");
        return -1;
    }

    return getXorUtil(st, 0, n - 1, qs, qe, 0);
}

// A recursive function that constructs Segment
// Tree for array[ss..se]. si is index of current
// node in segment tree st
static int constructSTUtil(int arr[], int ss,
                           int se, int[] st, int si)
{

    // If there is one element in array, store
    // it in current node of segment tree and return
    if (ss == se)
    {
        st[si] = arr[ss];
        return arr[ss];
    }

    // If there are more than one elements,
    // then recur for left and right subtrees
    // and store the xor of values in this node
    int mid = getMid(ss, se);
    st[si] = constructSTUtil(arr, ss, mid, st,
                             si * 2 + 1) ^
             constructSTUtil(arr, mid + 1, se, st,
                             si * 2 + 2);
    return st[si];
}

/*
 * Function to construct segment tree from
 * given array. This function allocates memory
 * for segment tree and calls constructSTUtil()
 * to fill the allocated memory
 */
static int[] constructST(int arr[], int n)
{

    // Allocate memory for segment tree

    // Height of segment tree
    int x = (int)(Math.ceil(Math.log(n) /
                            Math.log(2)));

    // Maximum size of segment tree
    int max_size = 2 * (int) Math.pow(2, x) - 1;

    // Allocate memory
    int[] st = new int[max_size];

    // Fill the allocated memory st
    constructSTUtil(arr, 0, n - 1, st, 0);

    // Return the constructed segment tree
    return st;
}

// Driver code
public static void main(String[] args)
{
    int[] arr = { 1, 3, 5, 7, 9, 11 };
    int n = arr.length;

    // Build segment tree from given array
    int[] st = constructST(arr, n);

    // Print xor of values in array from index 1 to 3
    System.out.printf("Xor of values in given " +
                      "range = %d\n",
                      getXor(st, n, 1, 3));

    // Update: set arr[1] = 10 and update
    // corresponding segment tree nodes
    updateValue(arr, st, n, 1, 10);

    // Find xor after the value is updated
    System.out.printf("Updated xor of values in " +
                      "given range = %d\n",
                      getXor(st, n, 1, 3));
}
}

// This code is contributed by sanjeev2552

Python3

# Python program to show segment tree operations
# like construction, query and update

import math as Math

# A utility function to get the middle
# index from corner indexes.


def getMid(s, e):
    return s + ((e - s) // 2)


def getXorUtil(st, ss, se, qs, qe, si):

    # If segment of this node is a part of
    # given range, then return the xor of
    # the segment
    if (qs <= ss and qe >= se):
        return st[si]

    # If segment of this node is
    # outside the given range
    if (se < qs or ss > qe):
        return 0

    # If a part of this segment overlaps
    # with the given range
    mid = getMid(ss, se)
    return getXorUtil(st, ss, mid, qs, qe, 2 * si + 1) ^ getXorUtil(st, mid + 1, se, qs, qe, 2 * si + 2)


def updateValueUtil(st, ss, se, i, diff, si):

    # Base Case: If the input index lies outside the
    # range of this segment
    if (i < ss or i > se):
        return

    # If the input index is in range of this node,
    # then update the value of the node and its children
    st[si] = st[si] + diff
    if (se != ss):
        mid = getMid(ss, se)
        updateValueUtil(st, ss, mid, i, diff,
                        2 * si + 1)
        updateValueUtil(st, mid + 1, se, i, diff,
                        2 * si + 2)


# The function to update a value in input array
# and segment tree. It uses updateValueUtil()
# to update the value in segment tree
def updateValue(arr, st, n, i, new_val):

    # Check for erroneous input index
    if (i < 0 or i > n - 1):
        print("Invalid Input")
        return

    # Get the difference between new
    # value and old value
    diff = new_val - arr[i]

    # Update the value in array
    arr[i] = new_val

    # Update the values of nodes in segment tree
    updateValueUtil(st, 0, n - 1, i, diff, 0)


# Return xor of elements in range from
# index qs (query start) to qe (query end).
# It mainly uses getXorUtil()
def getXor(st, n, qs, qe):

    # Check for erroneous input values
    if (qs < 0 or qe > n - 1 or qs > qe):
        print("Invalid Input")
        return -1
    return getXorUtil(st, 0, n - 1, qs, qe, 0)


# A recursive function that constructs Segment
# Tree for array[ss..se]. si is index of current
# node in segment tree st
def constructSTUtil(arr, ss, se, st, si):

    # If there is one element in array, store
    # it in current node of segment tree and return
    if (ss == se):
        st[si] = arr[ss]
        return arr[ss]

    # If there are more than one elements,
    # then recur for left and right subtrees
    # and store the xor of values in this node
    mid = getMid(ss, se)
    st[si] = constructSTUtil(arr, ss, mid, st, si * 2 +
                             1) ^ constructSTUtil(arr, mid + 1, se, st, si * 2 + 2)
    return st[si]


"""
    * Function to construct segment tree from
    * given array. This function allocates memory
    * for segment tree and calls constructSTUtil()
    * to fill the allocated memory
"""


def constructST(arr, n):

    # Allocate memory for segment tree

    # Height of segment tree
    x = (Math.ceil(Math.log(n) / Math.log(2)))

    # Maximum size of segment tree
    max_size = Math.floor(2 * (Math.pow(2, x)) - 1)

    # Allocate memory
    st = [0] * max_size

    # Fill the allocated memory st
    constructSTUtil(arr, 0, n - 1, st, 0)

    # Return the constructed segment tree
    return st


arr = [1, 3, 5, 7, 9, 11]
n = len(arr)

# Build segment tree from given array
st = constructST(arr, n)

# Print xor of values in array from index 1 to 3
print(f"Xor of values in given range = {getXor(st, n, 1, 3)}")

# Update: set arr[1] = 10 and update
# corresponding segment tree nodes
updateValue(arr, st, n, 1, 10)

# Find xor after the value is updated
print(f"Updated xor of values in given range = {getXor(st, n, 1, 3)}")

# This code is contributed by Saurabh Jaiswal

C#

// C# code for the above approach
using System;

class GFG {
  // A utility function to get the middle
  // index from corner indexes.
  static int getMid(int s, int e)
  {
    return s + (e - s) / 2;
  }

  /*
     * A recursive function to get the xor of values
     * in given range of the array.
     * The following are parameters for this function.
     *
     * st --> Pointer to segment tree
     * si --> Index of current node in the segment tree.
     * Initially 0 is passed as root is always at index 0 ss
     * & se --> Starting and ending indexes of the segment
     *             represented by current node, i.e., st[si]
     * qs & qe --> Starting and ending indexes of query
     * range
     */
  static int getXorUtil(int[] st, int ss, int se, int qs,
                        int qe, int si)
  {

    // If segment of this node is a part of
    // given range, then return the xor of
    // the segment
    if (qs <= ss && qe >= se)
      return st[si];

    // If segment of this node is
    // outside the given range
    if (se < qs || ss > qe)
      return 0;

    // If a part of this segment overlaps
    // with the given range
    int mid = getMid(ss, se);
    return getXorUtil(st, ss, mid, qs, qe, 2 * si + 1)
      ^ getXorUtil(st, mid + 1, se, qs, qe,
                   2 * si + 2);
  }

  /*
     * A recursive function to update the nodes which have
     * the given index in their range. The following are
     * parameters st, si, ss and se are same as getXorUtil()
     * i --> index of the element to be updated. This index
     * is in input array. diff --> Value to be added to all
     * nodes which have i in range
     */
  static void updateValueUtil(int[] st, int ss, int se,
                              int i, int diff, int si)
  {

    // Base Case: If the input index lies outside the
    // rangeof this segment
    if (i < ss || i > se)
      return;
    // If the input index is in range of this node,
    // then update the value of the node and its
    // children
    st[si] = st[si] + diff;
    if (se != ss) {
      int mid = getMid(ss, se);
      updateValueUtil(st, ss, mid, i, diff,
                      2 * si + 1);
      updateValueUtil(st, mid + 1, se, i, diff,
                      2 * si + 2);
    }
  }

  // The function to update a value in input array
  // and segment tree. It uses updateValueUtil()
  // to update the value in segment tree
  static void updateValue(int[] arr, int[] st, int n,
                          int i, int new_val)
  {

    // Check for erroneous input index
    if (i < 0 || i > n - 1) {
      Console.WriteLine("Invalid Input");
      return;
    }

    // Get the difference between new
    // value and old value
    int diff = new_val - arr[i];

    // Update the value in array
    arr[i] = new_val;
    // Update the values of nodes in segment tree
    updateValueUtil(st, 0, n - 1, i, diff, 0);
  }
  // Return xor of elements in range from
  // index qs (query start) to qe (query end).
  // It mainly uses getXorUtil()
  static int getXor(int[] st, int n, int qs, int qe)
  {

    // Check for erroneous input values
    if (qs < 0 || qe > n - 1 || qs > qe) {
      Console.WriteLine("Invalid Input");
      return -1;
    }

    return getXorUtil(st, 0, n - 1, qs, qe, 0);
  }

  // A recursive function that constructs Segment
  // Tree for array[ss..se]. si is index of current
  // node in segment tree st
  static int[] constructSTUtil(int[] arr, int ss, int se,
                               int[] st, int si)
  {

    // If there is one element in array, store it
    // in current node of segment tree and return
    if (ss == se) {
      st[si] = arr[ss];
      return st;
    }

    // If there are more than one elements, then recur
    // for left and right subtrees and store the sum
    // of values in this node
    int mid = getMid(ss, se);
    st = constructSTUtil(arr, ss, mid, st, si * 2 + 1);
    st = constructSTUtil(arr, mid + 1, se, st,
                         si * 2 + 2);

    st[si] = st[si * 2 + 1] ^ st[si * 2 + 2];
    return st;
  }

  /*
     * Function to construct segment tree from given array.
     * This function allocates memory for segment tree and
     * calls constructSTUtil() to fill the allocated memory
     */
  static int[] constructST(int[] arr, int n)
  {
    // Allocate memory for segment tree
    int[] st = new int[4 * n];

    // Fill the allocated memory st
    return constructSTUtil(arr, 0, n - 1, st, 0);
  }

  // Driver program to test above functions
  public static void Main()
  {
    int[] arr = { 1, 3, 5, 7, 9, 11 };
    int n = arr.Length;

    // Build segment tree from given array
    int[] st = constructST(arr, n);

    int qs = 1; // Starting index of query range
    int qe = 3; // Ending index of query range

    // Print sum of values in array from index 1 to 3
    Console.WriteLine("XOR of values in given range = "
                      + getXor(st, n, qs, qe));

    // Update: set arr[1] = 10 and update
    // corresponding segment tree nodes
    updateValue(arr, st, n, 1, 10);

    // Find sum after the value is updated
    qs = 1;
    qe = 3;
    Console.WriteLine(
      "Updated XOR of values in given range = "
      + getXor(st, n, qs, qe));
  }
}

// This code is contributed by Potta Lokesh

Javascript

<script>
    // Javascript program to show segment tree operations
    // like construction, query and update

    // A utility function to get the middle
    // index from corner indexes.
    function getMid(s, e)
    {
        return s + parseInt((e - s) / 2, 10);
    }

    function getXorUtil(st, ss, se, qs, qe, si)
    {

        // If segment of this node is a part of
        // given range, then return the xor of
        // the segment
        if (qs <= ss && qe >= se)
            return st[si];

        // If segment of this node is
        // outside the given range
        if (se < qs || ss > qe)
            return 0;

        // If a part of this segment overlaps
        // with the given range
        let mid = getMid(ss, se);
        return getXorUtil(st, ss, mid, qs,
                          qe, 2 * si + 1) ^
               getXorUtil(st, mid + 1, se, qs,
                          qe, 2 * si + 2);
    }

    function updateValueUtil(st, ss, se, i, diff, si)
    {

        // Base Case: If the input index lies outside the
        // range of this segment
        if (i < ss || i > se)
            return;

        // If the input index is in range of this node,
        // then update the value of the node and its children
        st[si] = st[si] + diff;
        if (se != ss)
        {
            let mid = getMid(ss, se);
            updateValueUtil(st, ss, mid, i, diff,
                             2 * si + 1);
            updateValueUtil(st, mid + 1, se, i, diff,
                             2 * si + 2);
        }
    }

    // The function to update a value in input array
    // and segment tree. It uses updateValueUtil()
    // to update the value in segment tree
    function updateValue(arr, st, n, i, new_val)
    {

        // Check for erroneous input index
        if (i < 0 || i > n - 1)
        {
            document.write("Invalid Input");
            return;
        }

        // Get the difference between new
        // value and old value
        let diff = new_val - arr[i];

        // Update the value in array
        arr[i] = new_val;

        // Update the values of nodes in segment tree
        updateValueUtil(st, 0, n - 1, i, diff, 0);
    }

    // Return xor of elements in range from
    // index qs (query start) to qe (query end).
    // It mainly uses getXorUtil()
    function getXor(st, n, qs, qe)
    {

        // Check for erroneous input values
        if (qs < 0 || qe > n - 1 || qs > qe)
        {
            document.write("Invalid Input");
            return -1;
        }

        return getXorUtil(st, 0, n - 1, qs, qe, 0);
    }

    // A recursive function that constructs Segment
    // Tree for array[ss..se]. si is index of current
    // node in segment tree st
    function constructSTUtil(arr, ss, se, st, si)
    {

        // If there is one element in array, store
        // it in current node of segment tree and return
        if (ss == se)
        {
            st[si] = arr[ss];
            return arr[ss];
        }

        // If there are more than one elements,
        // then recur for left and right subtrees
        // and store the xor of values in this node
        let mid = getMid(ss, se);
        st[si] = constructSTUtil(arr, ss, mid, st,
                                 si * 2 + 1) ^
                 constructSTUtil(arr, mid + 1, se, st,
                                 si * 2 + 2);
        return st[si];
    }

    /*
     * Function to construct segment tree from
     * given array. This function allocates memory
     * for segment tree and calls constructSTUtil()
     * to fill the allocated memory
     */
    function constructST(arr, n)
    {

        // Allocate memory for segment tree

        // Height of segment tree
        let x = (Math.ceil(Math.log(n) / Math.log(2)));

        // Maximum size of segment tree
        let max_size = 2 * parseInt(Math.pow(2, x), 10) - 1;

        // Allocate memory
        let st = new Array(max_size);
        st.fill(0);

        // Fill the allocated memory st
        constructSTUtil(arr, 0, n - 1, st, 0);

        // Return the constructed segment tree
        return st;
    }

    let arr = [ 1, 3, 5, 7, 9, 11 ];
    let n = arr.length;

    // Build segment tree from given array
    let st = constructST(arr, n);

    // Print xor of values in array from index 1 to 3
    document.write("Xor of values in given " +
                      "range = " +
                      getXor(st, n, 1, 3) + "</br>");

    // Update: set arr[1] = 10 and update
    // corresponding segment tree nodes
    updateValue(arr, st, n, 1, 10);

    // Find xor after the value is updated
    document.write("Updated xor of values in " +
                      "given range = " +
                      getXor(st, n, 1, 3) + "</br>");

// This code is contributed by divyeshrabadiya07.
</script>

Output

Xor of values in given range = 1
Updated xor of values in given range = 8

Time and Space Complexity:

Time Complexity for tree construction is O(n). 
There are total 2n-1 nodes, and value of every node is calculated only once in tree construction.
Time complexity to query is O(log n). 
The time complexity of update is also O(log n).
Total time Complexity is : O(n) for construction + O(log n) for each query = O(n) + O(n * log n) = O(n * log n)

Time Complexity: O(n * log n)
Auxiliary Space: O(n)