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# Queries to update a given index and find gcd in range

• Difficulty Level : Medium
• Last Updated : 26 Jul, 2022

Given an array arr[] of N integers and queries Q. Queries are of two types:

1. Update a given index ind by X.
2. Find the gcd of the elements in the index range [L, R].

Examples:

Input: arr[] = {1, 3, 6, 9, 9, 11}
Type 2 query: L = 1, R = 3
Type 1 query: ind = 1, X = 10
Type 2 query: L = 1, R = 3
Output:

Input: arr[] = {1, 2, 4, 9, 3}
Type 2 query: L = 1, R = 2
Type 1 query: ind = 2, X = 7
Type 2 query: L = 1, R = 2
Type 2 query: L = 3, R = 4
Output:

3

Approach: The following problem can be solved using the Segment Tree

A segment tree can be used to do preprocessing and query in moderate time. With the segment tree, preprocessing time is O(n) and the time for the GCD query is O(Logn). The extra space required is O(n) to store the segment tree.

Representation of Segment trees

• Leaf Nodes are the elements of the input array.
• Each internal node represents the GCD of all leaves under it.

Array representation of the tree is used to represent Segment Trees i.e., for each node at index i

• The left child is at index 2*i+1
• Right child at 2*i+2 and the parent is at floor((i-1)/2).

Construction of Segment Tree from the given array

• Begin with a segment arr[0 . . . n-1] and keep dividing into two halves. Every time we divide the current segment into two halves (if it has not yet become a segment of length 1), then call the same procedure on both halves, and for each such segment, we store the GCD value in a segment tree node.
• All levels of the constructed segment tree will be completely filled except the last level. Also, the tree will be a Full Binary Tree (every node has 0 or two children) because we always divide segments into two halves at every level.
• Since the constructed tree is always a full binary tree with n leaves, there will be n-1 internal nodes. So the total number of nodes will be 2*n â€“ 1.
• Like tree construction and query operations, the update can also be done recursively.
• We are given an index that needs to be updated. Let diff be the value to be added. We start from the root of the segment tree and add diff to all nodes which have given index in their range. If a node doesnâ€™t have a given index in its range, we donâ€™t make any changes to that node.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `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 gcd 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` `getGcdUtil(``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 gcd 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` `__gcd(getGcdUtil(st, ss, mid, qs, qe, 2 * si + 1),` `                 ``getGcdUtil(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 getSumUtil()` `// i --> index of the element to be updated. This index is` `// in the 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` `new_val, ``int` `si)` `{` `    ``// Base Case: If the input index lies outside the range of` `    ``// this segment` `    ``if` `(i < ss || i > se)` `        ``return``;`   `    ``// If only single element is left in the range` `    ``if``(ss == se)` `    ``{` `        ``st[si] = new_val;` `        ``return``;` `    ``}` `    `  `    ``int` `mid = getMid(ss, se);` `    ``updateValueUtil(st, ss, mid, i, new_val, 2 * si + 1);` `    ``updateValueUtil(st, mid + 1, se, i, new_val, 2 * si + 2);` `    `  `    ``st[si] = __gcd(st[2*si + 1], st[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``;` `    ``}`   `    ``// Update the values of nodes in segment tree` `    ``updateValueUtil(st, 0, n - 1, i, new_val, 0);` `}`   `// Function to return the sum of elements in range` `// from index qs (query start) to qe (query end)` `// It mainly uses getSumUtil()` `int` `getGcd(``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` `getGcdUtil(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` `constructGcdUtil(``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 element then recur for left and` `    ``// right subtrees and store the sum of values in this node` `    ``int` `mid = getMid(ss, se);` `    ``st[si] = __gcd(constructGcdUtil(arr, ss, mid, st, si * 2 + 1),` `                   ``constructGcdUtil(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``* constructGcd(``int` `arr[], ``int` `n)` `{` `    ``// Allocate memory for the 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 = ``new` `int``[max_size];`   `    ``// Fill the allocated memory st` `    ``constructGcdUtil(arr, 0, n - 1, st, 0);`   `    ``// Return the constructed segment tree` `    ``return` `st;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 1, 3, 6, 9, 9, 11 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);`   `    ``// Build segment tree from given array` `    ``int``* st = constructGcd(arr, n);`   `    ``// Print GCD of values in array from index 1 to 3` `    ``cout << getGcd(st, n, 1, 3) << endl;`   `    ``// Update: set arr[1] = 10 and update corresponding` `    ``// segment tree nodes` `    ``updateValue(arr, st, n, 1, 10);`   `    ``// Find GCD after the value is updated` `    ``cout << getGcd(st, n, 1, 3) << endl;`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach ` `class` `GFG` `{` `    `  `// segment tree` `static` `int` `st[];`   `// Recursive function to return gcd of a and b ` `static` `int` `__gcd(``int` `a, ``int` `b) ` `{ ` `    ``if` `(b == ``0``) ` `        ``return` `a; ` `    ``return` `__gcd(b, a % b); ` `    `  `} `   `// 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 gcd 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` `getGcdUtil( ``int` `ss, ``int` `se, ``int` `qs, ``int` `qe, ``int` `si) ` `{ ` `    ``// If segment of this node is a part of given range ` `    ``// then return the gcd 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` `__gcd(getGcdUtil( ss, mid, qs, qe, ``2` `* si + ``1``), ` `                ``getGcdUtil( 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 ` `// si, ss and se are same as getSumUtil() ` `// i --> index of the element to be updated. This index is ` `// in the input array. ` `// diff --> Value to be added to all nodes which have i in range ` `static` `void` `updateValueUtil( ``int` `ss, ``int` `se, ``int` `i, ``int` `new_val, ``int` `si) ` `{ ` `    ``// Base Case: If the input index lies outside the range of` `    ``// this segment` `    ``if` `(i < ss || i > se)` `        ``return``;`   `    ``// If only single element is left in the range` `    ``if``(ss == se)` `    ``{` `        ``st[si] = new_val;` `        ``return``;` `    ``}` `    `  `    ``int` `mid = getMid(ss, se);` `    ``updateValueUtil(ss, mid, i, new_val, ``2` `* si + ``1``);` `    ``updateValueUtil(mid + ``1``, se, i, new_val, ``2` `* si + ``2``);` `    `  `    ``st[si] = __gcd(st[``2``*si + ``1``], st[``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` `n, ``int` `i, ``int` `new_val) ` `{ ` `    ``// Check for erroneous input index ` `    ``if` `(i < ``0` `|| i > n - ``1``) ` `    ``{ ` `        ``System.out.println(``"Invalid Input"``); ` `        ``return``; ` `    ``} ` `  `  `    ``// Update the values of nodes in segment tree ` `    ``updateValueUtil( ``0``, n - ``1``, i, new_val, ``0``); ` `} `   `// Function to return the sum of elements in range ` `// from index qs (query start) to qe (query end) ` `// It mainly uses getSumUtil() ` `static` `int` `getGcd( ``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` `getGcdUtil( ``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` `constructGcdUtil(``int` `arr[], ``int` `ss, ``int` `se, ``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 element then recur for left and ` `    ``// right subtrees and store the sum of values in this node ` `    ``int` `mid = getMid(ss, se); ` `    ``st[si] = __gcd(constructGcdUtil(arr, ss, mid, si * ``2` `+ ``1``), ` `                ``constructGcdUtil(arr, mid + ``1``, se, 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` `void` `constructGcd(``int` `arr[], ``int` `n) ` `{ ` `    ``// Allocate memory for the 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 ` `    ``st = ``new` `int``[max_size];`   `    ``// Fill the allocated memory st ` `    ``constructGcdUtil(arr, ``0``, n - ``1``, ``0``); `   `} `   `// Driver code ` `public` `static` `void` `main(String args[])` `{ ` `    ``int` `arr[] = { ``1``, ``3``, ``6``, ``9``, ``9``, ``11` `}; ` `    ``int` `n = arr.length; `   `    ``// Build segment tree from given array ` `    ``constructGcd(arr, n); `   `    ``// Print GCD of values in array from index 1 to 3 ` `    ``System.out.println( getGcd( n, ``1``, ``3``) ); `   `    ``// Update: set arr[1] = 10 and update corresponding ` `    ``// segment tree nodes ` `    ``updateValue(arr, n, ``1``, ``10``); `   `    ``// Find GCD after the value is updated ` `    ``System.out.println( getGcd( n, ``1``, ``3``) ); ` `}` `} `   `// This code is constructed by Arnab Kundu`

## Python3

 `# Python 3 implementation of the approach`   `from` `math ``import` `gcd,ceil,log2,``pow`   `# A utility function to get the` `# middle index from corner indexes` `def` `getMid(s, e):` `    ``return` `(s ``+` `int``((e ``-` `s) ``/` `2``))`   `# A recursive function to get the gcd 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` `def` `getGcdUtil(st,ss,se,qs,qe,si):` `    `  `    ``# If segment of this node is a part of given range` `    ``# then return the gcd 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` `gcd(getGcdUtil(st, ss, mid, qs, qe, ``2` `*` `si ``+` `1``),` `            ``getGcdUtil(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 getSumUtil()` `# i --> index of the element to be updated. This index is` `# in the input array.` `# diff --> Value to be added to all nodes which have i in range` `def` `updateValueUtil(st,ss,se,i,new_val,si):` `    `  `    ``# Base Case: If the input index lies outside the range of` `    ``# this segment` `    ``if` `(i < ss ``or` `i > se):` `        ``return` `    `  `    ``if``(ss ``=``=` `se):` `        ``st[si] ``=` `new_val` `        ``return`   `    ``# If the input index is in range of this node, then update` `    ``# the value of the node and its children` `    `  `    ``mid ``=` `getMid(ss, se)` `    ``updateValueUtil(st, ss, mid, i, new_val, ``2` `*` `si ``+` `1``)` `    ``updateValueUtil(st, mid ``+` `1``, se, i, new_val, ``2` `*` `si ``+` `2``)` `    `  `    ``st[si] ``=` `gcd(st[``2``*``si ``+` `1``], st[``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`   `    ``# Update the values of nodes in segment tree` `    ``updateValueUtil(st, ``0``, n ``-` `1``, i, new_val, ``0``)`   `# Function to return the sum of elements in range` `# from index qs (query start) to qe (query end)` `# It mainly uses getSumUtil()` `def` `getGcd(st,n,qs,qe):` `    `  `    ``# Check for erroneous input values` `    ``if` `(qs < ``0` `or` `qe > n ``-` `1` `or` `qs > qe):` `        ``cout << ``"Invalid Input"` `        ``return` `-``1`   `    ``return` `getGcdUtil(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` `constructGcdUtil(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 element then recur for left and` `    ``# right subtrees and store the sum of values in this node` `    ``mid ``=` `getMid(ss, se)` `    ``st[si] ``=` `gcd(constructGcdUtil(arr, ss, mid, st, si ``*` `2` `+` `1``),` `                ``constructGcdUtil(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` `constructGcd(arr, n):` `    `  `    ``# Allocate memory for the segment tree`   `    ``# Height of segment tree` `    ``x ``=` `int``(ceil(log2(n)))`   `    ``# Maximum size of segment tree` `    ``max_size ``=` `2` `*` `int``(``pow``(``2``, x) ``-` `1``)`   `    ``# Allocate memory` `    ``st ``=` `[``0` `for` `i ``in` `range``(max_size)]`   `    ``# Fill the allocated memory st` `    ``constructGcdUtil(arr, ``0``, n ``-` `1``, st, ``0``)`   `    ``# Return the constructed segment tree` `    ``return` `st`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``1``, ``3``, ``6``, ``9``, ``9``, ``11``]` `    ``n ``=` `len``(arr)`   `    ``# Build segment tree from given array` `    ``st ``=` `constructGcd(arr, n)`   `    ``# Print GCD of values in array from index 1 to 3` `    ``print``(getGcd(st, n, ``1``, ``3``))`   `    ``# Update: set arr[1] = 10 and update corresponding` `    ``# segment tree nodes` `    ``updateValue(arr, st, n, ``1``, ``10``)`   `    ``# Find GCD after the value is updated` `    ``print``(getGcd(st, n, ``1``, ``3``))`   `# This code is contributed by` `# SURENDRA_GANGWAR`

## C#

 `// C# implementation of the approach.` `using` `System;` `    `  `class` `GFG` `{` `    `  `// segment tree` `static` `int` `[]st;`   `// Recursive function to return gcd of a and b ` `static` `int` `__gcd(``int` `a, ``int` `b) ` `{ ` `    ``if` `(b == 0) ` `        ``return` `a; ` `    ``return` `__gcd(b, a % b); ` `    `  `} `   `// 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 gcd 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` `getGcdUtil( ``int` `ss, ``int` `se, ``int` `qs, ``int` `qe, ``int` `si) ` `{ ` `    ``// If segment of this node is a part of given range ` `    ``// then return the gcd 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` `__gcd(getGcdUtil( ss, mid, qs, qe, 2 * si + 1), ` `                ``getGcdUtil( 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 ` `// si, ss and se are same as getSumUtil() ` `// i --> index of the element to be updated. This index is ` `// in the input array. ` `// diff --> Value to be added to all nodes which have i in range ` `static` `void` `updateValueUtil( ``int` `ss, ``int` `se, ``int` `i, ``int` `new_val, ``int` `si) ` `{ ` `    ``// Base Case: If the input index lies outside the range of` `    ``// this segment` `    ``if` `(i < ss || i > se)` `        ``return``;`   `    ``// If only single element is left in the range` `    ``if``(ss == se)` `    ``{` `        ``st[si] = new_val;` `        ``return``;` `    ``}` `    `  `    ``int` `mid = getMid(ss, se);` `    ``updateValueUtil(ss, mid, i, new_val, 2 * si + 1);` `    ``updateValueUtil(mid + 1, se, i, new_val, 2 * si + 2);` `    `  `    ``st[si] = __gcd(st[2*si + 1], st[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` `n, ``int` `i, ``int` `new_val) ` `{ ` `    ``// Check for erroneous input index ` `    ``if` `(i < 0 || i > n - 1) ` `    ``{ ` `        ``Console.WriteLine(``"Invalid Input"``); ` `        ``return``; ` `    ``} `   `    ``// Update the values of nodes in segment tree ` `    ``updateValueUtil( 0, n - 1, i, new_val, 0); ` `} `   `// Function to return the sum of elements in range ` `// from index qs (query start) to qe (query end) ` `// It mainly uses getSumUtil() ` `static` `int` `getGcd( ``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` `getGcdUtil( 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` `constructGcdUtil(``int` `[]arr, ``int` `ss, ``int` `se, ``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 element then recur for left and ` `    ``// right subtrees and store the sum of values in this node ` `    ``int` `mid = getMid(ss, se); ` `    ``st[si] = __gcd(constructGcdUtil(arr, ss, mid, si * 2 + 1), ` `                ``constructGcdUtil(arr, mid + 1, se, 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` `void` `constructGcd(``int` `[]arr, ``int` `n) ` `{ ` `    ``// Allocate memory for the segment tree `   `    ``// Height of segment tree ` `    ``int` `x = (``int``)(Math.Ceiling(Math.Log(n)/Math.Log(2))); `   `    ``// Maximum size of segment tree ` `    ``int` `max_size = 2 * (``int``)Math.Pow(2, x) - 1; `   `    ``// Allocate memory ` `    ``st = ``new` `int``[max_size];`   `    ``// Fill the allocated memory st ` `    ``constructGcdUtil(arr, 0, n - 1, 0); `   `} `   `// Driver code ` `public` `static` `void` `Main(String []args)` `{ ` `    ``int` `[]arr = { 1, 3, 6, 9, 9, 11 }; ` `    ``int` `n = arr.Length; `   `    ``// Build segment tree from given array ` `    ``constructGcd(arr, n); `   `    ``// Print GCD of values in array from index 1 to 3 ` `    ``Console.WriteLine( getGcd( n, 1, 3) ); `   `    ``// Update: set arr[1] = 10 and update corresponding ` `    ``// segment tree nodes ` `    ``updateValue(arr, n, 1, 10); `   `    ``// Find GCD after the value is updated ` `    ``Console.WriteLine( getGcd( n, 1, 3) ); ` `}` `}`   `// This code contributed by Rajput-Ji`

## Javascript

 ``

Output

```3
1
```

Time Complexity: O(n log n), as segment tree construction will take O(n log n) time. Where n is the number of elements in the array.
Auxiliary Space: O(n log n), as we are using extra space for the segment tree. Where n is the number of elements in the array.

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