# Segment Trees | (Product of given Range Modulo m)

• Difficulty Level : Medium
• Last Updated : 08 Feb, 2022

Let us consider the following problem to understand Segment Trees.
We have an array arr[0 . . . n-1]. We should be able to
1 Find the product of elements from index l to r where 0 <= l <= r <= n-1 take its modulus by an integer m.
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.

A simple solution is to run a loop from l to r and calculate product of elements in a given range and modulo it by m. To update a value, simply do arr[i] = x. The first operation takes O(n) time and second operation takes O(1) time.

Another solution is to create two arrays and store the product modulo m from start to l-1 in first array and the product from r+1 to end of the array modulo m in another array. Product of a given range can now be calculated in O(1) time, but update operation takes O(n) time now.
Lets say the product of all the elements be P, then product P from a given range l to r can be calculated as :
P: Product of all the elements of the array modulo m.
A: Product of all the elements till l-1 modulo m.
B: Product of all the elements till r+1 modulo m.
PDT = P*(modInverse(A))*(modInverse(B))
This works well if the number of query operations are large and very few updates.

Segment Tree Solution :
If the number of query and updates are equal, we can perform both the operations in O(log n) time. We can use a Segment Tree to do both operations in O(Logn) time.

Representation of Segment trees
1. Leaf Nodes are the elements of the input array.
2. Each internal node represents some merging of the leaf nodes. The merging may be different for different problems. For this problem, merging is product of leaves under a node.
An array representation of tree is used to represent Segment Trees. 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 (i-1)/2.

Query for Product of given range
Once the tree is constructed, how to get the product using the constructed segment tree. Following is algorithm to get the product of elements.

```int getPdt(node, l, r)
{
if range of node is within l and r
return value in node
else if range of node is completely outside l and r
return 1
else
return (getPdt(node's left child, l, r)%mod *
getPdt(node's right child, l, r)%mod)%mod
}```

Update a value
Like tree construction and query operations, update can also be done recursively. We are given an index which needs to update. We start from root of the segment tree, and multiply the range product with new value and divide the range product with previous value. If a node doesn’t have given index in its range, we don’t make any changes to that node.

Implementation:
Following is the implementation of segment tree. The program implements construction of segment tree for any given array. It also implements query and updates operations.

## C++

 `// C++ program to show segment tree operations like``// construction, query and update``#include ``#include ``using` `namespace` `std;``int` `mod = 1000000000;`` ` `// 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 Pdt 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` `getPdtUtil(``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 Pdt 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` `1;`` ` `    ``// If a part of this segment overlaps with the``    ``// given range``    ``int` `mid = getMid(ss, se);``    ``return` `(getPdtUtil(st, ss, mid, qs, qe, 2*si+1)%mod *``           ``getPdtUtil(st, mid+1, se, qs, qe, 2*si+2)%mod)%mod;``}`` ` `/* 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 getPdtUtil()``    ``i    --> index of the element to be updated. ``             ``This index is in input array.*/`   `void` `updateValueUtil(``int` `*st, ``int` `ss, ``int` `se, ``int` `i,``                        ``int` `prev_val, ``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 the input index is in range of this node, then ``    ``// update the value of the node and its children``    ``st[si] = (st[si]*new_val)/prev_val;``    ``if` `(se != ss)``    ``{``        ``int` `mid = getMid(ss, se);``        ``updateValueUtil(st, ss, mid, i, prev_val,``                                ``new_val, 2*si + 1);``        ``updateValueUtil(st, mid+1, se, i, prev_val,``                                ``new_val, 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``;``    ``}``    ``int` `temp = 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, temp, new_val, 0);``}`` ` `// Return Pdt of elements in range from index qs``// (query start)to qe (query end).  It mainly``// uses getPdtUtil()``int` `getPdt(``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` `getPdtUtil(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 Pdt of values in this node``    ``int` `mid = getMid(ss, se);``    ``st[si] =  (constructSTUtil(arr, ss, mid, st, si*2+1)%mod *``              ``constructSTUtil(arr, mid+1, se, st, si*2+2)%mod)%mod;``    ``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 = ``new` `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, 2, 3, 4, 5, 6};``    ``int` `n = ``sizeof``(arr)/``sizeof``(arr);` `    ``// Build segment tree from given array``    ``int` `*st = constructST(arr, n);`` ` `    ``// Print Product of values in array from index 1 to 3``    ``cout << ``"Product of values in given range = "``         ``<< getPdt(st, n, 1, 3) << endl;``           ` `    ``// Update: set arr = 10 and update corresponding``    ``// segment tree nodes``    ``updateValue(arr, st, n, 1, 10);`` ` `    ``// Find Product after the value is updated``    ``cout << ``"Updated Product of values in given range = "``         ``<< getPdt(st, n, 1, 3) << endl;``    ``return` `0;``}`

## Java

 `// Java program to show segment tree operations``// like construction, query and update``class` `GFG{` `static` `final` `int` `mod = ``1000000000``;` `// 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 Pdt 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` `getPdtUtil(``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 Pdt 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` `1``;` `    ``// If a part of this segment overlaps``    ``// with the given range``    ``int` `mid = getMid(ss, se);``    ``return` `(getPdtUtil(st, ss, mid, qs,``                       ``qe, ``2` `* si + ``1``) % mod *``           ``getPdtUtil(st, mid + ``1``, se, qs,``                      ``qe, ``2` `* si + ``2``) % mod) % mod;``}` `/*`` ``* 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 getPdtUtil()`` ``* i --> index of the element to be updated.`` ``*        This index is in input array.`` ``*/``static` `void` `updateValueUtil(``int``[] st, ``int` `ss, ``int` `se,``                            ``int` `i, ``int` `prev_val,``                            ``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 the input index is in range of this node, then``    ``// update the value of the node and its children``    ``st[si] = (st[si] * new_val) / prev_val;``    ``if` `(se != ss)``    ``{``        ``int` `mid = getMid(ss, se);``        ``updateValueUtil(st, ss, mid, i, prev_val,``                        ``new_val, ``2` `* si + ``1``);``        ``updateValueUtil(st, mid + ``1``, se, i, prev_val,``                        ``new_val, ``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``;``    ``}``    ``int` `temp = 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,``                    ``temp, new_val, ``0``);``}` `// Return Pdt of elements in range from index qs``// (query start)to qe (query end). It mainly``// uses getPdtUtil()``static` `int` `getPdt(``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` `getPdtUtil(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 Pdt of values in this node``    ``int` `mid = getMid(ss, se);``    ``st[si] = (constructSTUtil(arr, ss, mid, st,``                              ``si * ``2` `+ ``1``) % mod *``              ``constructSTUtil(arr, mid + ``1``, se, st,``                              ``si * ``2` `+ ``2``) % mod) % mod;``    ``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``, ``2``, ``3``, ``4``, ``5``, ``6` `};``    ``int` `n = arr.length;` `    ``// Build segment tree from given array``    ``int``[] st = constructST(arr, n);` `    ``// Print Product of values in array from``    ``// index 1 to 3``    ``System.out.printf(``"Product of values in "` `+``                      ``"given range = %d\n"``,``                      ``getPdt(st, n, ``1``, ``3``));` `    ``// Update: set arr = 10 and update``    ``// corresponding segment tree nodes``    ``updateValue(arr, st, n, ``1``, ``10``);` `    ``// Find Product after the value is updated``    ``System.out.printf(``"Updated Product of values "` `+``                      ``"in given range = %d\n"``,``                      ``getPdt(st, n, ``1``, ``3``));``}``}` `// This code is contributed by sanjeev2552`

## Python3

 `# Python3 program to show segment tree operations like``# construction, query and update``from` `math ``import` `ceil,log``mod ``=` `1000000000` `# A utility function to get the middle index from``# corner indexes.``def` `getMid(s, e):``    ``return` `s ``+` `(e ``-``s)``/``/``2` `"""A recursive function to get the Pdt 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` `getPdtUtil(st, ss, se, qs, qe,si):``    ` `    ``# If segment of this node is a part of given``    ``# range, then return the Pdt 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` `1` `    ``# If a part of this segment overlaps with the``    ``# given range``    ``mid ``=` `getMid(ss, se)``    ``return` `(getPdtUtil(st, ss, mid, qs, qe, ``2``*``si``+``1``)``%``mod``*``        ``getPdtUtil(st, mid``+``1``, se, qs, qe, ``2``*``si``+``2``)``%``mod)``%``mod``"""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 getPdtUtil()``    ``i --> index of the element to be updated.``            ``This index is in input array."""``def` `updateValueUtil(st, ss, se, i, prev_val, new_val, 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]``*``new_val)``/``/``prev_val``    ``if` `(se !``=` `ss):``        ``mid ``=` `getMid(ss, se)``        ``updateValueUtil(st, ss, mid, i, prev_val,``                                ``new_val, ``2``*``si ``+` `1``)``        ``updateValueUtil(st, mid``+``1``, se, i, prev_val,``                                ``new_val, ``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``):``        ``cout<<``"Invalid Input"``        ``return``    ``temp ``=` `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, temp, new_val, ``0``)` `# Return Pdt of elements in range from index qs``# (query start)to qe (query end). It mainly``# uses getPdtUtil()``def` `getPdt(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` `getPdtUtil(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 Pdt of values in this node``    ``mid ``=` `getMid(ss, se)``    ``st[si] ``=` `(constructSTUtil(arr, ss, mid, st, si``*``2``+``1``)``%``mod``*``            ``constructSTUtil(arr, mid``+``1``, se, st, si``*``2``+``2``)``%``mod)``%``mod``    ``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 ``=` `(ceil(log(n,``2``)))` `    ``# Maximum size of segment tree``    ``max_size ``=` `2``*``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` `# Driver program to test above functions``if` `__name__ ``=``=` `'__main__'``:``    ``arr``=``[``1``, ``2``, ``3``, ``4``, ``5``, ``6``]``    ``n ``=` `len``(arr)` `    ``# Build segment tree from given array``    ``st ``=` `constructST(arr, n)` `    ``# Print Product of values in array from index 1 to 3``    ``print``(``"Product of values in given range = "``,getPdt(st, n, ``1``, ``3``))` `    ``# Update: set arr = 10 and update corresponding``    ``# segment tree nodes``    ``updateValue(arr, st, n, ``1``, ``10``)` `    ``# Find Product after the value is updated``    ``print``(``"Updated Product of values in given range = "``,getPdt(st, n, ``1``, ``3``))` `# This code is contributed by mohit kumar 29`` `

## C#

 `// C# program to show segment tree operations``// like construction, query and update``using` `System;``class` `GFG``{``    ``static` `int` `mod = 1000000000;``  ` `    ``// A utility function to get the middle``    ``// index from corner indexes.``    ``public` `static` `int` `getMid(``int` `s, ``int` `e)``    ``{``        ``return` `s + (e - s) / 2;``    ``}``     ` `/*`` ``* A recursive function to get the Pdt 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`` ``*/``    ``public` `static` `int` `getPdtUtil(``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 Pdt 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` `1;``        ``}``      ` `        ``// If a part of this segment overlaps``        ``// with the given range``        ``int` `mid=getMid(ss, se);``        ``return` `(getPdtUtil(st, ss, mid, qs,qe, 2 * si + 1) % mod *``                ``getPdtUtil(st, mid + 1, se, qs,qe, 2 * si + 2) % mod) % mod;``    ``}``  ` `    ``/*``    ``* 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 getPdtUtil()``    ``* i --> index of the element to be updated.``    ``*        This index is in input array.``    ``*/``    ``public` `static` `void` `updateValueUtil(``int``[] st, ``int` `ss,``                                       ``int` `se, ``int` `i,``                                       ``int` `prev_val,``                                       ``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 the input index is in range of this node, then``        ``// update the value of the node and its children``        ``st[si] = (st[si] * new_val) / prev_val;``        ``if` `(se != ss)``        ``{``            ``int` `mid = getMid(ss, se);``            ``updateValueUtil(st, ss, mid, i, prev_val,new_val, 2 * si + 1);``            ``updateValueUtil(st, mid + 1, se, i, prev_val,new_val, 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``    ``public` `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``;``        ``}``        ``int` `temp = 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, temp, new_val, 0);``        ` `    ``}``  ` `    ``// Return Pdt of elements in range from index qs``    ``// (query start)to qe (query end). It mainly``    ``// uses getPdtUtil()``    ``public` `static` `int` `getPdt(``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` `getPdtUtil(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``    ``public` `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 Pdt of values in this node``        ``int` `mid = getMid(ss, se);``        ``st[si] = (constructSTUtil(arr, ss, mid, st, si * 2 + 1) % mod *``                  ``constructSTUtil(arr, mid + 1, se, st,si * 2 + 2) % mod) % mod;``        ``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``    ``*/``    ``public` `static` `int``[] constructST(``int``[] arr, ``int` `n)``    ``{``      ` `        ``// Allocate memory for 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``        ``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``    ``static` `public` `void` `Main ()``    ``{``       ``int``[] arr = { 1, 2, 3, 4, 5, 6 };``       ``int` `n = arr.Length;``      ` `       ``// Build segment tree from given array``       ``int``[] st = constructST(arr, n);``      ` `       ``// Print Product of values in array from``        ``// index 1 to 3``       ``Console.WriteLine(``"Product of values in "` `+``                         ``"given range = "` `+ getPdt(st, n, 1, 3));``      ` `       ``// Update: set arr = 10 and update``        ``// corresponding segment tree nodes``       ``updateValue(arr, st, n, 1, 10);``      ` `       ``// Find Product after the value is updated``       ``Console.WriteLine(``"Updated Product of values "` `+``                         ``"in given range = "` `+ getPdt(st, n, 1, 3));``    ``}``}` `// This code is contributed by avanitrachhadiya2155`

## Javascript

 ``

Output:

```Product of values in given range = 24
Updated Product of values in given range = 120```

My Personal Notes arrow_drop_up