# Range Queries for number of Armstrong numbers in an array with updates

Last Updated : 25 Apr, 2023

Given an array arr[] of N integers, the task is to perform the following two queries:

• query(start, end): Print the number of Armstrong numbers in the subarray from start to end
• update(i, x): Add x to the array element referenced by array index i, that is: arr[i] = x

Examples:

Input: arr = { 18, 153, 8, 9, 14, 5}
Query 1: query(start = 0, end = 4)
Query 2: update(i = 3, x = 11)
Query 3: query(start = 0, end = 4)
Output:

Explanation
In Query 1
18 -> 1*1 + 8*8 != 18
153 -> 1*1*1 + 5*5*5 + 3*3*3 = 153
8 -> 8 = 8
9 -> 9 = 9
14 -> 1*1 + 4*4 != 14
the subarray [0…4] has 3 Armstrong numbers viz. {18, 153, 8, 9, 14}
In Query 2, the value at index 3 is updated to 11,
the array arr now is, { 18, 153, 8, 11, 14, 5}
In Query 3
18 -> 1*1 + 8*8 != 18
153 -> 1*1*1 + 5*5*5 + 3*3*3 = 153
8 -> 8 = 8
9 -> 1*1 + 1*1 != 11
14 -> 1*1 + 4*4 != 14
the subarray [0…4] has 2 Armstrong numbers viz. {18, 153, 8, 11, 14}

Approach: To handle both point updates and range queries, a segment tree is optimal for this purpose.
A positive integer of n digits is called an Armstrong number of order n (order is number of digits) if.

abcd… = pow(a, n) + pow(b, n) + pow(c, n) + pow(d, n) + ….

In order to check for Armstrong numbers, the idea is to first count number digits (or find order). Let the number of digits be n. For every digit r in input number x, compute r^n. If the sum of all such values is equal to n, then set it to 1 else to 0.

Building the segment tree:

• The problem is now reduced to the subarray sum using segment tree problem.
• Now, we can build the segment tree where a leaf node is represented as either 0 (if it is not an Armstrong number) or 1 (if it is Armstrong number).
• The internal nodes of the segment tree equal to the sum of its child nodes, thus a node represent the total Armstrong numbers in the range from L to R with range [L, R] falling under this node and the sub-tree underneath it.

• Whenever we receive a query from beginning to end, we can query the segment tree for the sum of nodes in the range from start to end, which in turn represents the number of Armstrong numbers in the range start to end.

• To perform a point update and to update the value at index i to x, we check for the following cases:
Let the old value of arri be y and the new value be x.
1. Case 1: If x and y both are Armstrong numbers
Count of Armstrong numbers in the subarray does not change so we just update array and do not modify the segment tree
2. Case 2: If x and y both are not Armstrong numbers
Count of Armstrong numbers in the subarray does not change so we just update array and do not modify the segment tree
3. Case 3: If y is a Armstrong number but x is not
Count of Armstrong numbers in the subarray decreases so we update array and add -1 to every range. The index i which is to be updated is a part of in the segment tree
4. Case 4: If y is not an Armstrong number but x is an Armstrong number
Count of Armstrong numbers in the subarray increases so we update array and add 1 to every range. The index i which is to be updated is a part of in the segment tree

Below is the implementation of the above approach:

## C++

 `// C++ program to find the number` `// of Armstrong numbers in a` `// subarray and performing updates`   `#include ` `using` `namespace` `std;`   `#define MAX 1000`   `// Function that return true` `// if num is armstrong` `// else return false` `bool` `isArmstrong(``int` `x)` `{` `    ``int` `n = to_string(x).size();` `    ``int` `sum1 = 0;` `    ``int` `temp = x;` `    ``while` `(temp > 0) {` `        ``int` `digit = temp % 10;` `        ``sum1 += ``pow``(digit, n);` `        ``temp /= 10;` `    ``}` `    ``if` `(sum1 == x)` `        ``return` `true``;` `    ``return` `false``;` `}`   `// A utility function to get the middle` `// index from corner indexes.` `int` `getMid(``int` `s, ``int` `e)` `{` `    ``return` `s + (e - s) / 2;` `}`   `// Recursive function to get the number` `// of Armstrong numbers in a given range` `/* where` `    ``st    --> Pointer to segment tree` `    ``index --> 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[index]` `    ``qs & qe  --> Starting and ending indexes` `              ``of query range   ` `    ``*/` `int` `queryArmstrongUtil(``int``* st, ``int` `ss,` `                       ``int` `se, ``int` `qs,` `                       ``int` `qe, ``int` `index)` `{` `    ``// If segment of this node is a part` `    ``// of given range, then return` `    ``// the number of Armstrong numbers` `    ``// in the segment` `    ``if` `(qs <= ss && qe >= se)` `        ``return` `st[index];`   `    ``// 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` `queryArmstrongUtil(` `               ``st, ss, mid, qs,` `               ``qe, 2 * index + 1)` `           ``+ queryArmstrongUtil(` `                 ``st, mid + 1, se,` `                 ``qs, qe, 2 * index + 2);` `}`   `// Recursive function to update` `// the nodes which have the given` `// index in their range.` `/* where` `    ``st, si, ss and se are same as getSumUtil()` `    ``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);` `    ``}` `}`   `// Function to update a value in the` `// 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``;` `    ``}`   `    ``int` `diff, oldValue;`   `    ``oldValue = arr[i];`   `    ``// Update the value in array` `    ``arr[i] = new_val;`   `    ``// Case 1: Old and new values` `    ``// both are Armstrong numbers` `    ``if` `(isArmstrong(oldValue)` `        ``&& isArmstrong(new_val))` `        ``return``;`   `    ``// Case 2: Old and new values` `    ``// both not Armstrong numbers` `    ``if` `(!isArmstrong(oldValue)` `        ``&& !isArmstrong(new_val))` `        ``return``;`   `    ``// Case 3: Old value was Armstrong,` `    ``// new value is non Armstrong` `    ``if` `(isArmstrong(oldValue) && !isArmstrong(new_val)) {` `        ``diff = -1;` `    ``}`   `    ``// Case 4: Old value was non Armstrong,` `    ``// new_val is Armstrong` `    ``if` `(!isArmstrong(oldValue)` `        ``&& !isArmstrong(new_val)) {` `        ``diff = 1;` `    ``}`   `    ``// Update the values of` `    ``// nodes in segment tree` `    ``updateValueUtil(` `        ``st, 0, n - 1,` `        ``i, diff, 0);` `}`   `// Return number of Armstrong numbers` `// in range from index qs (query start)` `// to qe (query end).` `// It mainly uses queryArmstrongUtil()` `void` `queryArmstrong(``int``* st, ``int` `n,` `                    ``int` `qs, ``int` `qe)` `{` `    ``int` `ArmstrongInRange` `        ``= queryArmstrongUtil(st, 0, n - 1,` `                             ``qs, qe, 0);`   `    ``cout << ``"Number of Armstrong numbers "` `         ``<< ``"in subarray from "` `         ``<< qs << ``" to "` `         ``<< qe << ``" = "` `         ``<< ArmstrongInRange << ``"\n"``;` `}`   `// 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,` `    ``// check if it is Armstrong number` `    ``// then store 1 in the segment tree` `    ``// else store 0 and return` `    ``if` `(ss == se) {`   `        ``// if arr[ss] is Armstrong number` `        ``if` `(isArmstrong(arr[ss]))` `            ``st[si] = 1;` `        ``else` `            ``st[si] = 0;`   `        ``return` `st[si];` `    ``}`   `    ``// If there are more than one elements,` `    ``// then recur for left and right subtrees` `    ``// and store the sum of the` `    ``// two 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 a 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;`   `    ``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` `int` `main()` `{`   `    ``int` `arr[] = { 18, 153, 8, 9, 14, 5 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);`   `    ``// Build segment tree from given array` `    ``int``* st = constructST(arr, n);`   `    ``// Query 1: Query(start = 0, end = 4)` `    ``int` `start = 0;` `    ``int` `end = 4;` `    ``queryArmstrong(st, n, start, end);`   `    ``// Query 2: Update(i = 3, x = 11),` `    ``// i.e Update a[i] to x` `    ``int` `i = 3;` `    ``int` `x = 11;` `    ``updateValue(arr, st, n, i, x);`   `    ``// Print array after update` `    ``cout << ``"Array after update: "``;` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``cout << arr[i] << ``", "``;` `    ``cout << endl;`   `    ``// Query 3: Query(start = 0, end = 4)` `    ``start = 0;` `    ``end = 4;` `    ``queryArmstrong(st, n, start, end);`   `    ``return` `0;` `}`

## Java

 `// Java program to find the number` `// of Armstrong numbers in a` `// subarray and performing updates` `import` `java.util.*;`   `class` `Main {`     `    ``// Function that return true` `    ``// if num is armstrong` `    ``// else return false` `    ``static` `boolean` `isArmstrong(``int` `x) {` `        ``int` `n = String.valueOf(x).length();` `        ``int` `sum1 = ``0``;` `        ``int` `temp = x;` `        ``while` `(temp > ``0``) {` `            ``int` `digit = temp % ``10``;` `            ``sum1 += Math.pow(digit, n);` `            ``temp /= ``10``;` `        ``}` `        ``if` `(sum1 == x)` `            ``return` `true``;` `        ``return` `false``;` `    ``}` `    `  `    ``// Recursive function to update` `    ``// the nodes which have the given` `    ``// index in their range.` `    ``/* where` `        ``st, si, ss and se are same as getSumUtil()` `        ``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 = (ss + se) / ``2``;` `            ``updateValueUtil(st, ss, mid, i, diff, ``2` `* si + ``1``);` `            ``updateValueUtil(st, mid + ``1``, se, i, diff, ``2` `* si + ``2``);` `        ``}` `    ``}` `    `  `    ``// Function to update a value in the` `    ``// 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` `diff, oldValue;` `        ``oldValue = arr[i];` `        ``// Update the value in array` `        ``arr[i] = new_val;` `        `  `        ``// Case 1: Old and new values` `        ``// both are Armstrong numbers` `        ``if` `(isArmstrong(oldValue) && isArmstrong(new_val))` `            ``return``;` `        `  `        ``// Case 2: Old and new values` `        ``// both not Armstrong numbers` `        ``if` `(!isArmstrong(oldValue) && !isArmstrong(new_val))` `            ``return``;` `        `  `        ``// Case 3: Old value was Armstrong,` `        ``// new value is non Armstrong` `        ``if` `(isArmstrong(oldValue) && !isArmstrong(new_val))` `            ``diff = -``1``;` `        ``else` `            ``diff = ``1``;` `        `  `        ``// Update the values of` `        ``// nodes in segment tree` `        ``updateValueUtil(st, ``0``, n - ``1``, i, diff, ``0``);` `    ``}`     `    ``// Recursive function to get the number` `    ``// of Armstrong numbers in a given range` `    ``/* where` `        ``st --> Pointer to segment tree` `        ``index --> 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[index]` `        ``qs & qe --> Starting and ending indexes` `                ``of query range` `        ``*/` `    ``static` `int` `queryArmstrongUtil(``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 number of Armstrong numbers` `        ``// in 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 = (ss + se) / ``2``;` `        ``return` `queryArmstrongUtil(st, ss, mid, qs, qe, ``2` `* si + ``1``) + queryArmstrongUtil(st, mid + ``1``, se, qs, qe, ``2` `* si + ``2``);` `    ``}` `    `  `    `  `    ``// Return number of Armstrong numbers` `    ``// in range from index qs (query start)` `    ``// to qe (query end).` `    ``// It mainly uses queryArmstrongUtil()` `    ``static` `void` `queryArmstrong(``int``[] st, ``int` `n, ``int` `qs, ``int` `qe) {` `        ``int` `ArmstrongInRange = queryArmstrongUtil(st, ``0``, n - ``1``, qs, qe, ``0``);`   `        ``System.out.println(``"Number of Armstrong numbers in subarray from "` `+ qs + ``" to "` `+ qe + ``" = "` `+ ArmstrongInRange);` `    ``}`   `    ``static` `int` `getMid(``int` `s, ``int` `e) {` `        ``return` `s + (e - s) / ``2``;` `    ``}` `    `  `    ``// 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,` `        ``// check if it is Armstrong number` `        ``// then store 1 in the segment tree` `        ``// else store 0 and return` `        ``if` `(ss == se) {` `            ``// if arr[ss] is Armstrong number` `            ``if` `(isArmstrong(arr[ss]))` `                ``st[si] = ``1``;` `            ``else` `                ``st[si] = ``0``;` `            ``return` `st[si];` `        ``}` `    `  `    ``// If there are more than one elements,` `    ``// then recur for left and right subtrees` `    ``// and store the sum of the` `    ``// two 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 a 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.ceil(Math.log(n) / Math.log(``2``)));` `        `  `        ``// Maximum size of segment tree` `        ``int` `max_size = ``2` `* (``int``)Math.pow(``2``, x) - ``1``;` `        ``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;` `    ``}` `    ``public` `static` `void` `main(String[] args) {` `        ``int``[] arr = {``18``, ``153``, ``8``, ``9``, ``14``, ``5``};` `        ``int` `n = arr.length;` `        `  `        ``// Build segment tree from given array` `        ``int``[] st = constructST(arr, n);` `        `  `        ``// Query 1: Query(start = 0, end = 4)` `        ``int` `start = ``0``;` `        ``int` `end = ``4``;` `        ``queryArmstrong(st, n, start, end);` `        `  `        ``// Query 2: Update(i = 3, x = 11),` `        ``// i.e Update a[i] to x` `        ``int` `i = ``3``;` `        ``int` `x = ``11``;` `        ``updateValue(arr, st, n, i, x);` `    `  `        ``System.out.print(``"Array after update: "``);` `        ``for` `(``int` `j = ``0``; j < n; j++) {` `            ``System.out.print(arr[j] + ``", "``);` `        ``}` `        ``System.out.println();` `        `  `        ``// Query 3: Query(start = 0, end = 4)` `        ``start = ``0``;` `        ``end = ``4``;` `        ``queryArmstrong(st, n, start, end);` `    ``}` `}` `// This code is contributed by shivhack999`

## Python3

 `# Python3 program to find the number ` `# of Armstrong numbers in a ` `# subarray and performing updates ` `import` `math`   `MAX` `=` `1000`   `# Function that return true ` `# if num is armstrong ` `# else return false ` `def` `isArmstrong(x):` `    `  `    ``n ``=` `len``(``str``(x))` `    ``sum1 ``=` `0` `    ``temp ``=` `x` `    `  `    ``while` `temp > ``0``:` `        ``digit ``=` `temp ``%` `10` `        ``sum1 ``+``=` `pow``(digit, n)` `        ``temp ``=` `temp ``/``/` `10` `    `  `    ``if` `sum1 ``=``=` `x:` `        ``return` `True` `    ``return` `False`   `# A utility function to get the middle ` `# index from corner indexes.` `def` `getMid(s, e):` `    `  `    ``return` `s ``+` `(e ``-` `s) ``/``/` `2`   `# Recursive function to get the number ` `# of Armstrong numbers in a given range ` `# where ` `# st --> Pointer to segment tree ` `# index --> 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[index] ` `# qs & qe --> Starting and ending indexes ` `#             of query range ` `def` `queryArmstrongUtil(st, ss, se, qs, qe, index):` `    `  `    ``# If segment of this node is a part ` `    ``# of given range, then return ` `    ``# the number of Armstrong numbers ` `    ``# in the segment ` `    ``if` `qs <``=` `ss ``and` `qe >``=` `se:` `        ``return` `st[index]` `    `  `    ``# 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` `(queryArmstrongUtil(st, ss, mid, qs,` `                               ``qe, ``2` `*` `index ``+` `1``) ``+` `            ``queryArmstrongUtil(st, mid ``+` `1``, se, qs,` `                               ``qe, ``2` `*` `index ``+` `2``))`   `# Recursive function to update ` `# the nodes which have the given ` `# index in their range. ` `# where ` `# st, si, ss and se are same as getSumUtil() ` `# 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` `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``)`   `# Function to update a value in the ` `# 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` `    `  `    ``oldValue ``=` `arr[i]` `    `  `    ``# Update the value in array` `    ``arr[i] ``=` `new_val` `    `  `    ``# Case 1: Old and new values ` `    ``# both are Armstrong numbers` `    ``if` `(isArmstrong(oldValue) ``and` `        ``isArmstrong(new_val)):` `        ``return` `    `  `    ``# Case 2: Old and new values ` `    ``# both not Armstrong numbers ` `    ``if` `(``not` `isArmstrong(oldValue) ``and` `        ``not` `isArmstrong(new_val)):` `        ``return` `    `  `    ``# Case 3: Old value was Armstrong, ` `    ``# new value is non Armstrong` `    ``if` `(isArmstrong(oldValue) ``and` `(``not` `        ``isArmstrong(new_val))):` `        ``diff ``=` `-``1` `    `  `    ``# Case 4: Old value was non Armstrong, ` `    ``# new_val is Armstrong ` `    ``if` `(``not` `isArmstrong(oldValue) ``and` `        ``not` `isArmstrong(new_val)): ` `        ``diff ``=` `1` `    `  `    ``# Update the values of ` `    ``# nodes in segment tree` `    ``updateValueUtil(st, ``0``, n ``-` `1``, i, diff, ``0``)`   `# Return number of Armstrong numbers ` `# in range from index qs (query start) ` `# to qe (query end). ` `# It mainly uses queryArmstrongUtil() ` `def` `queryArmstrong(st, n, qs, qe):` `    `  `    ``ArmstrongInRange ``=` `queryArmstrongUtil(st, ``0``, n ``-` `1``,` `                                          ``qs, qe, ``0``)` `    ``print``(``"Number of Armstrong numbers in "` `          ``"subarray from"``, qs, ``"to"``, qe, ``"="``, ` `           ``ArmstrongInRange)`   `# 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, ` `    ``# check if it is Armstrong number ` `    ``# then store 1 in the segment tree ` `    ``# else store 0 and return` `    ``if` `ss ``=``=` `se:` `        `  `        ``# If arr[ss] is Armstrong number` `        ``if` `isArmstrong(arr[ss]):` `            ``st[si] ``=` `1` `        ``else``:` `            ``st[si] ``=` `0` `            `  `        ``return` `st[si]` `    `  `    ``# If there are more than one elements, ` `    ``# then recur for left and right subtrees ` `    ``# and store the sum of the ` `    ``# two 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 a 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 ``=` `int``(math.ceil(math.log2(n)))` `    `  `    ``# Maximum size of segment tree ` `    ``max_size ``=` `2` `*` `int``(``pow``(``2``, x)) ``-` `1` `    `  `    ``st ``=` `[``-``1``] ``*` `max_size` `    `  `    ``# Fill the allocated memory st ` `    ``constructSTUtil(arr, ``0``, n ``-` `1``, st, ``0``)` `    `  `    ``# Return the constructed segment tree ` `    ``return` `st`   `# Driver code` `arr ``=` `[ ``18``, ``153``, ``8``, ``9``, ``14``, ``5` `]` `n ``=` `len``(arr)`   `# Build segment tree from given array ` `st ``=` `constructST(arr, n)`   `# Query 1: Query(start = 0, end = 4)` `start ``=` `0` `end ``=` `4` `queryArmstrong(st, n, start, end)`   `# Query 2: Update(i = 3, x = 11), ` `# i.e Update a[i] to x ` `i ``=` `3` `x ``=` `11` `updateValue(arr, st, n, i, x)`   `# Print array after update` `print``(``"Array after update:"``, end ``=` `" "``)` `for` `i ``in` `range``(n):` `    ``print``(arr[i], end ``=` `", "``)` `    `  `print``()`   `# Query 3: Query(start = 0, end = 4)` `start ``=` `0` `end ``=` `4` `queryArmstrong(st, n, start, end)`   `# This code is contributed by stutipathak31jan`

## C#

 `// C# program to find the number` `// of Armstrong numbers in a` `// subarray and performing updates` `using` `System;`   `class` `GFG{` `    `  `public` `int` `MAX = 1000;`   `// Function that return true` `// if num is armstrong` `// else return false` `static` `bool` `isArmstrong(``int` `x)` `{` `    ``int` `n = x.ToString().Length;` `    ``int` `sum1 = 0;` `    ``int` `temp = x;` `    `  `    ``while` `(temp > 0)` `    ``{` `        ``int` `digit = temp % 10;` `        ``sum1 += (``int``)Math.Pow(digit, n);` `        ``temp /= 10;` `    ``}` `    `  `    ``if` `(sum1 == x)` `        ``return` `true``;` `        `  `    ``return` `false``;` `}`   `// A utility function to get the middle` `// index from corner indexes.` `static` `int` `getMid(``int` `s, ``int` `e)` `{` `    ``return` `s + (e - s) / 2;` `}`   `// Recursive function to get the number` `// of Armstrong numbers in a given range` `/* where` `    ``st    --> Pointer to segment tree` `    ``index --> 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[index]` `    ``qs & qe  --> Starting and ending indexes` `              ``of query range` `    ``*/` `static` `int` `queryArmstrongUtil(``int``[] st, ``int` `ss, ``int` `se,` `                              ``int` `qs, ``int` `qe, ``int` `index)` `{` `    `  `    ``// If segment of this node is a part` `    ``// of given range, then return` `    ``// the number of Armstrong numbers` `    ``// in the segment` `    ``if` `(qs <= ss && qe >= se)` `        ``return` `st[index];`   `    ``// 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` `queryArmstrongUtil(st, ss, mid, qs, qe,` `                              ``2 * index + 1) + ` `           ``queryArmstrongUtil(st, mid + 1, se, qs, qe,` `                              ``2 * index + 2);` `}`   `// Recursive function to update` `// the nodes which have the given` `// index in their range.` `/* where` `    ``st, si, ss and se are same as getSumUtil()` `    ``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);` `    ``}` `}`   `// Function to update a value in the` `// 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.Write(``"Invalid Input"``);` `        ``return``;` `    ``}`   `    ``int` `diff = 0, oldValue = 0;`   `    ``oldValue = arr[i];`   `    ``// Update the value in array` `    ``arr[i] = new_val;`   `    ``// Case 1: Old and new values` `    ``// both are Armstrong numbers` `    ``if` `(isArmstrong(oldValue) && ` `        ``isArmstrong(new_val))` `        ``return``;`   `    ``// Case 2: Old and new values` `    ``// both not Armstrong numbers` `    ``if` `(!isArmstrong(oldValue) && ` `        ``!isArmstrong(new_val))` `        ``return``;`   `    ``// Case 3: Old value was Armstrong,` `    ``// new value is non Armstrong` `    ``if` `(isArmstrong(oldValue) && ` `        ``!isArmstrong(new_val))` `    ``{` `        ``diff = -1;` `    ``}`   `    ``// Case 4: Old value was non Armstrong,` `    ``// new_val is Armstrong` `    ``if` `(!isArmstrong(oldValue) && ` `        ``!isArmstrong(new_val)) ` `    ``{` `        ``diff = 1;` `    ``}`   `    ``// Update the values of` `    ``// nodes in segment tree` `    ``updateValueUtil(st, 0, n - 1, i, diff, 0);` `}`   `// Return number of Armstrong numbers` `// in range from index qs (query start)` `// to qe (query end).` `// It mainly uses queryArmstrongUtil()` `static` `void` `queryArmstrong(``int``[] st, ``int` `n, ``int` `qs,` `                           ``int` `qe)` `{` `    ``int` `ArmstrongInRange = queryArmstrongUtil(` `        ``st, 0, n - 1, qs, qe, 0);`   `    ``Console.WriteLine(``"Number of Armstrong numbers "` `+ ` `                      ``"in subarray from "` `+ qs + ``" to "` `+` `                      ``qe + ``" = "` `+ ArmstrongInRange);` `}`   `// 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,` `    ``// check if it is Armstrong number` `    ``// then store 1 in the segment tree` `    ``// else store 0 and return` `    ``if` `(ss == se)` `    ``{` `        `  `        ``// If arr[ss] is Armstrong number` `        ``if` `(isArmstrong(arr[ss]))` `            ``st[si] = 1;` `        ``else` `            ``st[si] = 0;`   `        ``return` `st[si];` `    ``}`   `    ``// If there are more than one elements,` `    ``// then recur for left and right subtrees` `    ``// and store the sum of the` `    ``// two 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 a 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.Ceiling(Math.Log(n, 2)));`   `    ``// Maximum size of segment tree` `    ``int` `max_size = 2 * (``int``)Math.Pow(2, x) - 1;`   `    ``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 = { 18, 153, 8, 9, 14, 5 };` `    ``int` `n = arr.Length;`   `    ``// Build segment tree from given array` `    ``int``[] st = constructST(arr, n);`   `    ``// Query 1: Query(start = 0, end = 4)` `    ``int` `start = 0;` `    ``int` `end = 4;` `    ``queryArmstrong(st, n, start, end);`   `    ``// Query 2: Update(i = 3, x = 11),` `    ``// i.e Update a[i] to x` `    ``int` `i = 3;` `    ``int` `x = 11;` `    ``updateValue(arr, st, n, i, x);`   `    ``// Print array after update` `    ``Console.Write(``"Array after update: "``);` `    ``for``(``int` `j = 0; j < n; j++)` `        ``Console.Write(arr[j] + ``", "``);` `        `  `    ``Console.WriteLine();`   `    ``// Query 3: Query(start = 0, end = 4)` `    ``start = 0;` `    ``end = 4;` `    ``queryArmstrong(st, n, start, end);` `}` `}`   `// This code is contributed by ukasp`

## Javascript

 `// Function that return true ` `// if num is armstrong ` `// else return false ` `function` `isArmstrong(x){` `    `  `    ``let n = x.toString().length;` `    ``let sum1 = 0;` `    ``let temp = x;` `    `  `    ``while` `(temp > 0) {` `        ``let digit = temp % 10;` `        ``sum1 += Math.pow(digit, n);` `        ``temp = Math.floor(temp / 10);` `    ``}` `    `  `    ``if` `(sum1 == x) {` `        ``return` `true``;` `    ``} ``else` `{` `        ``return` `false``;` `    ``}` `}`   `// A utility function to get the middle ` `// index from corner indexes.` `function` `getMid(s, e){` `    `  `    ``return` `s + Math.floor((e - s) / 2);` `}`   `// Recursive function to get the number ` `// of Armstrong numbers in a given range ` `// where ` `// st --> Pointer to segment tree ` `// index --> 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[index] ` `// qs & qe --> Starting and ending indexes ` `//             of query range ` `function` `queryArmstrongUtil(st, ss, se, qs, qe, index){` `    `  `    ``// If segment of this node is a part ` `    ``// of given range, then return ` `    ``// the number of Armstrong numbers ` `    ``// in the segment ` `    ``if` `(qs <= ss && qe >= se) {` `        ``return` `st[index];` `    ``}` `    `  `    ``// 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` `(queryArmstrongUtil(st, ss, mid, qs,` `                               ``qe, 2 * index + 1) + ` `            ``queryArmstrongUtil(st, mid + 1, se, qs,` `                               ``qe, 2 * index + 2));` `}`   `// Recursive function to update ` `// the nodes which have the given ` `// index in their range. ` `// where ` `// st, si, ss and se are same as getSumUtil() ` `// 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` `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);` `    ``}` `}`   `// Function to update a value in the ` `// 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) {` `        ``console.log(``"Invalid Input"``);` `        ``return``;` `    ``}` `    `  `    ``let oldValue = arr[i];` `    `  `    ``// Update the value in array` `    ``arr[i] = new_val;` `    `  `    ``// Case 1: Old and new values ` `    ``// both are Armstrong numbers` `    ``if` `(isArmstrong(oldValue) && ` `        ``isArmstrong(new_val)) {` `        ``return``;` `    ``}` `    `  `    ``// Case 2: Old and new values ` `    ``// both not Armstrong numbers ` `    ``if` `(!isArmstrong(oldValue) && ` `        ``!isArmstrong(new_val)) {` `        ``return``;` `    ``}` `    `  `    ``// Case 3: Old value was Armstrong, ` `    ``// new value is non Armstrong` `    ``let diff = 0;` `    ``if` `(isArmstrong(oldValue) && !` `        ``isArmstrong(new_val)) {` `        ``diff = -1;` `    ``}` `    `  `    ``// Case 4: Old value was non Armstrong, ` `    ``// new_val is Armstrong ` `    ``if` `(!isArmstrong(oldValue) &&` `        ``isArmstrong(new_val)) { ` `        ``diff = 1;` `    ``}` `    `  `    ``// Update the values of ` `    ``// nodes in segment tree` `    ``updateValueUtil(st, 0, n - 1, i, diff, 0);` `}`   `// Return number of Armstrong numbers ` `// in range from index qs (query start) ` `// to qe (query end). ` `// It mainly uses queryArmstrongUtil() ` `function` `queryArmstrong(st, n, qs, qe){` `    `  `    ``let ArmstrongInRange = queryArmstrongUtil(st, 0, n - 1,` `                              ``qs, qe, 0);` `    ``console.log(``"Number of Armstrong numbers in subarray from"``, qs, ``"to"``, qe, ``"="``,ArmstrongInRange);` `}`   `// 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, ` `    ``// check if it is Armstrong number ` `    ``// then store 1 in the segment tree ` `    ``// else store 0 and return` `    ``if` `(ss == se) {` `        `  `        ``// If arr[ss] is Armstrong number` `        ``if` `(isArmstrong(arr[ss])) {` `            ``st[si] = 1;` `        ``} ``else` `{` `            ``st[si] = 0;` `        ``}` `            `  `        ``return` `st[si];` `    ``}` `    `  `    ``// If there are more than one elements, ` `    ``// then recur for left and right subtrees ` `    ``// and store the sum of the ` `    ``// two 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 a 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.log2(n));` `    `  `    ``// Maximum size of segment tree ` `    ``let max_size = 2 * Math.pow(2, x) - 1;` `    `  `    ``let st = Array(max_size).fill(-1);` `    `  `    ``// Fill the allocated memory st ` `    ``constructSTUtil(arr, 0, n - 1, st, 0);` `    `  `    ``// Return the constructed segment tree ` `    ``return` `st;` `}`   `// Driver code` `let arr = [ 18, 153, 8, 9, 14, 5 ];` `let n = arr.length;`   `// Build segment tree from given array ` `let st = constructST(arr, n);`   `// Query 1: Query(start = 0, end = 4)` `let start = 0;` `let end = 4;` `queryArmstrong(st, n, start, end);`   `// Query 2: Update(i = 3, x = 11), ` `// i.e Update a[i] to x ` `let i = 3;` `let x = 11;` `updateValue(arr, st, n, i, x);`   `// Print array after update` `console.log(``"Array after update: "``, end = ``" "``);` `for` `(let i = 0; i < n; i++) {` `    ``console.log(arr[i]);` `}`   `console.log();`   `// Query 3: Query(start = 0, end = 4)` `start = 0;` `end = 4;` `queryArmstrong(st, n, start, end);`

Output:

```Number of Armstrong numbers in subarray from 0 to 4 = 3
Array after update: 18, 153, 8, 11, 14, 5,
Number of Armstrong numbers in subarray from 0 to 4 = 2```

Time Complexity: The time complexity of each query and update is O(log N) and that of building the segment tree is O(N)
Space Complexity: O(MAX + log x),  where MAX is defined as 1000 and O(log x) for the isArmstrong function.