Segment Tree | Set 3 (XOR of given range)
We have an array arr[0 . . . n-1]. There are two type of queries
- Find the XOR of elements from index l to r where 0 <= l <= r <= n-1
- 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> |
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)