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# Queries to calculate sum by alternating signs of array elements in a given range

• Difficulty Level : Expert
• Last Updated : 12 May, 2021

Given an array arr[] of size N and a 2D array Q[][], consisting of queries of the following two types:

Examples:

Input: arr[] = { 1, 2, 3, 4 }, Q[][] = { { 2, 0, 3 }, { 1, 1, 5 }, { 2, 1, 2 } }
Output:-2 2
Explanation:
Query1: Print (arr[0] – arr[1] + arr[2] – arr[3]) = 1 – 2 + 3 – 4 = -2
Query2: Updating arr[1] to 5 modifies arr[] to { 1, 5, 3, 4 }
Query3: Print (arr[1] – arr[2]) = 5 – 3 = 2

Input: arr[] = { 4, 2, 6, 1, 8, 9, 2}, Q = { { 2, 1, 4 }, { 1, 3, 4 }, { 2, 0, 3 } }
Output: -11 5

Approach: The problem can be solved using Segment Tree. The idea is to traverse the array and check if the index of the array element is negative then multiply the array elements by -1. Follow the steps below to solve the problem:

• Traverse the array arr[] using variable i and check if the index i is odd or not. If found to be true, then update arr[i] = -Val.
• For query of type 1, X, Val, check if X is even or not. If found to be true, then update arr[X] = Val using segment tree.
• Otherwise, update arr[X] = -Val using segment tree.
• For query of type 2 L R:, check if L is even or not. If found to be true, then print the sum of array elements in the range [L, R] using the segment tree.
• Otherwise, find the sum of array elements in the range [L, R] using segment tree and print the obtained sum multiplying by -1.

Below is the implementation of the above approach :

## C++

 `// C++  program to implement``// the above approach` `#include ``using` `namespace` `std;` `// Function to build the segment tree``void` `build(``int` `tree[], ``int` `arr[], ``int` `start,``           ``int` `end, ``int` `index)``{` `    ``// If current node is a leaf node``    ``// of the segment tree``    ``if` `(start == end) {` `        ``if` `(start % 2 == 0) {` `            ``// Update tree[index]``            ``tree[index] = arr[start];``        ``}` `        ``else` `{` `            ``// Update tree[index]``            ``tree[index] = -arr[start];``        ``}``        ``return``;``    ``}` `    ``// Divide the segment tree``    ``int` `mid = start + (end - start) / 2;` `    ``// Update on L segment tree``    ``build(tree, arr, start, mid,``          ``2 * index + 1);` `    ``// Update on R segment tree``    ``build(tree, arr, mid + 1, end,``          ``2 * index + 2);` `    ``// Find the sum from L subtree``    ``// and R subtree``    ``tree[index] = tree[2 * index + 1] + tree[2 * index + 2];``}` `// Function to update elements at index pos``// by val in the segment tree``void` `update(``int` `tree[], ``int` `index, ``int` `start,``            ``int` `end, ``int` `pos, ``int` `val)``{` `    ``// If current node is a leaf node``    ``if` `(start == end) {` `        ``// If current index is even``        ``if` `(start % 2 == 0) {` `            ``// Update tree[index]``            ``tree[index] = val;``        ``}` `        ``else` `{` `            ``// Update tree[index]``            ``tree[index] = -val;``        ``}``        ``return``;``    ``}` `    ``// Divide the segment tree elements``    ``// into L and R subtree``    ``int` `mid = start + (end - start) / 2;` `    ``// If element lies in L subtree``    ``if` `(mid >= pos) {` `        ``update(tree, 2 * index + 1, start,``               ``mid, pos, val);``    ``}``    ``else` `{``        ``update(tree, 2 * index + 2, mid + 1,``               ``end, pos, val);``    ``}` `    ``// Update tree[index]``    ``tree[index]``        ``= tree[2 * index + 1] + tree[2 * index + 2];``}` `// Function to find the sum of array elements``// in the range [L, R]``int` `FindSum(``int` `tree[], ``int` `start, ``int` `end,``            ``int` `L, ``int` `R, ``int` `index)``{` `    ``// If start and end not lies in``    ``// the range [L, R]``    ``if` `(L > end || R < start) {``        ``return` `0;``    ``}` `    ``// If start and end comleately lies``    ``// in the range [L, R]``    ``if` `(L <= start && R >= end) {` `        ``return` `tree[index];``    ``}``    ``int` `mid = start + (end - start) / 2;` `    ``// Stores sum from left subtree``    ``int` `X = FindSum(tree, start, mid, L,``                    ``R, 2 * index + 1);` `    ``// Stores sum from right subtree``    ``int` `Y = FindSum(tree, mid + 1, end, L,``                    ``R, 2 * index + 2);` `    ``return` `X + Y;``}` `int` `main()``{` `    ``int` `arr[] = { 1, 2, 3, 4 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``int` `tree[4 * N + 5] = { 0 };``    ``build(tree, arr, 0, N - 1, 0);` `    ``int` `Q[][3] = { { 2, 0, 3 }, { 1, 1, 5 }, { 2, 1, 2 } };` `    ``int` `cntQuey = 3;``    ``for` `(``int` `i = 0; i < cntQuey; i++) {` `        ``if` `(Q[i][0] == 1) {` `            ``update(tree, 0, 0, N - 1,``                   ``Q[i][1], Q[i][2]);``        ``}` `        ``else` `{` `            ``if` `(Q[i][1] % 2 == 0) {` `                ``cout << FindSum(tree, 0, N - 1,``                                ``Q[i][1], Q[i][2], 0)``                     ``<< ``" "``;``            ``}``            ``else` `{` `                ``cout << -FindSum(tree, 0, N - 1,``                                 ``Q[i][1], Q[i][2], 0)``                     ``<< ``" "``;``            ``}``        ``}``    ``}``}`

## Java

 `// Java program to implement``// the above approach``import` `java.util.*;`` ` `class` `GFG{`` ` `// Function to build the segment tree``static` `void` `build(``int` `tree[], ``int` `arr[], ``int` `start,``           ``int` `end, ``int` `index)``{` `    ``// If current node is a leaf node``    ``// of the segment tree``    ``if` `(start == end) {` `        ``if` `(start % ``2` `== ``0``) {` `            ``// Update tree[index]``            ``tree[index] = arr[start];``        ``}` `        ``else` `{` `            ``// Update tree[index]``            ``tree[index] = -arr[start];``        ``}``        ``return``;``    ``}` `    ``// Divide the segment tree``    ``int` `mid = start + (end - start) / ``2``;` `    ``// Update on L segment tree``    ``build(tree, arr, start, mid,``          ``2` `* index + ``1``);` `    ``// Update on R segment tree``    ``build(tree, arr, mid + ``1``, end,``          ``2` `* index + ``2``);` `    ``// Find the sum from L subtree``    ``// and R subtree``    ``tree[index] = tree[``2` `* index + ``1``] + tree[``2` `* index + ``2``];``}` `// Function to update elements at index pos``// by val in the segment tree``static` `void` `update(``int` `tree[], ``int` `index, ``int` `start,``            ``int` `end, ``int` `pos, ``int` `val)``{` `    ``// If current node is a leaf node``    ``if` `(start == end) {` `        ``// If current index is even``        ``if` `(start % ``2` `== ``0``) {` `            ``// Update tree[index]``            ``tree[index] = val;``        ``}` `        ``else` `{` `            ``// Update tree[index]``            ``tree[index] = -val;``        ``}``        ``return``;``    ``}` `    ``// Divide the segment tree elements``    ``// into L and R subtree``    ``int` `mid = start + (end - start) / ``2``;` `    ``// If element lies in L subtree``    ``if` `(mid >= pos)``    ``{``        ``update(tree, ``2` `* index + ``1``, start,``               ``mid, pos, val);``    ``}``    ``else``    ``{``        ``update(tree, ``2` `* index + ``2``, mid + ``1``,``               ``end, pos, val);``    ``}` `    ``// Update tree[index]``    ``tree[index]``        ``= tree[``2` `* index + ``1``] + tree[``2` `* index + ``2``];``}` `// Function to find the sum of array elements``// in the range [L, R]``static` `int` `FindSum(``int` `tree[], ``int` `start, ``int` `end,``            ``int` `L, ``int` `R, ``int` `index)``{` `    ``// If start and end not lies in``    ``// the range [L, R]``    ``if` `(L > end || R < start)``    ``{``        ``return` `0``;``    ``}` `    ``// If start and end comleately lies``    ``// in the range [L, R]``    ``if` `(L <= start && R >= end)``    ``{``        ``return` `tree[index];``    ``}``    ``int` `mid = start + (end - start) / ``2``;` `    ``// Stores sum from left subtree``    ``int` `X = FindSum(tree, start, mid, L,``                    ``R, ``2` `* index + ``1``);` `    ``// Stores sum from right subtree``    ``int` `Y = FindSum(tree, mid + ``1``, end, L,``                    ``R, ``2` `* index + ``2``);``    ``return` `X + Y;``}`` ` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``1``, ``2``, ``3``, ``4` `};``    ``int` `N = arr.length;``    ``int` `tree[] = ``new` `int``[``4` `* N + ``5``];``    ``Arrays.fill(tree, ``0``);``    ``build(tree, arr, ``0``, N - ``1``, ``0``);``    ``int` `Q[][] = { { ``2``, ``0``, ``3` `}, { ``1``, ``1``, ``5` `}, { ``2``, ``1``, ``2` `} };``    ``int` `cntQuey = ``3``;``    ``for` `(``int` `i = ``0``; i < cntQuey; i++)``    ``{``        ``if` `(Q[i][``0``] == ``1``)``        ``{``            ``update(tree, ``0``, ``0``, N - ``1``,``                   ``Q[i][``1``], Q[i][``2``]);``        ``}``        ``else` `{``            ``if` `(Q[i][``1``] % ``2` `== ``0``)``            ``{``                ``System.out.print(FindSum(tree, ``0``, N - ``1``,``                                ``Q[i][``1``], Q[i][``2``], ``0``) + ``" "``);``            ``}``            ``else``            ``{``                ``System.out.print(-FindSum(tree, ``0``, N - ``1``,``                                 ``Q[i][``1``], Q[i][``2``], ``0``)+ ``" "``);``            ``}``        ``}``    ``}``}``}` `// This code is contributed by code_hunt.`

## Python3

 `# Python3  program to implement``# the above approach` `# Function to build the segment tree``def` `build(tree, arr, start, end, index):` `    ``# If current node is a leaf node``    ``# of the segment tree``    ``if` `(start ``=``=` `end):``        ``if` `(start ``%` `2` `=``=` `0``):` `            ``# Update tree[index]``            ``tree[index] ``=` `arr[start]``        ``else``:` `            ``# Update tree[index]``            ``tree[index] ``=` `-``arr[start]``        ``return` `    ``# Divide the segment tree``    ``mid ``=` `start ``+` `(end ``-` `start) ``/``/` `2` `    ``# Update on L segment tree``    ``build(tree, arr, start, mid, ``2` `*` `index ``+` `1``)` `    ``# Update on R segment tree``    ``build(tree, arr, mid ``+` `1``, end, ``2` `*` `index ``+` `2``)` `    ``# Find the sum from L subtree``    ``# and R subtree``    ``tree[index] ``=` `tree[``2` `*` `index ``+` `1``] ``+` `tree[``2` `*` `index ``+` `2``]` `# Function to update elements at index pos``# by val in the segment tree``def` `update(tree, index, start, end, pos, val):` `    ``# If current node is a leaf node``    ``if` `(start ``=``=` `end):` `        ``# If current index is even``        ``if` `(start ``%` `2` `=``=` `0``):` `            ``# Update tree[index]``            ``tree[index] ``=` `val``        ``else``:` `            ``# Update tree[index]``            ``tree[index] ``=` `-``val``        ``return` `    ``# Divide the segment tree elements``    ``# into L and R subtree``    ``mid ``=` `start ``+` `(end ``-` `start) ``/``/` `2` `    ``# If element lies in L subtree``    ``if` `(mid >``=` `pos):``        ``update(tree, ``2` `*` `index ``+` `1``, start, mid, pos, val)``    ``else``:``        ``update(tree, ``2` `*` `index ``+` `2``, mid ``+` `1``, end, pos, val)` `    ``# Update tree[index]``    ``tree[index] ``=` `tree[``2` `*` `index ``+` `1``] ``+` `tree[``2` `*` `index ``+` `2``]` `# Function to find the sum of array elements``# in the range [L, R]``def` `FindSum(tree, start, end, L, R, index):` `    ``# If start and end not lies in``    ``# the range [L, R]``    ``if` `(L > end ``or` `R < start):``        ``return` `0` `    ``#If start and end comleately lies``    ``#in the range [L, R]``    ``if` `(L <``=` `start ``and` `R >``=` `end):``        ``return` `tree[index]``    ``mid ``=` `start ``+` `(end ``-` `start) ``/``/` `2` `    ``# Stores sum from left subtree``    ``X ``=` `FindSum(tree, start, mid, L, R, ``2` `*` `index ``+` `1``)` `    ``# Stores sum from right subtree``    ``Y ``=` `FindSum(tree, mid ``+` `1``, end, L, R, ``2` `*` `index ``+` `2``)` `    ``return` `X ``+` `Y` `  ``# Driver code``if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``1``, ``2``, ``3``, ``4``]``    ``N ``=` `len``(arr)``    ``tree ``=` `[``0` `for` `i ``in` `range``(``4` `*` `N ``+` `5``)]``    ``build(tree, arr, ``0``, N ``-` `1``, ``0``)``    ``Q ``=` `[ [ ``2``, ``0``, ``3` `], [ ``1``, ``1``, ``5` `], [ ``2``, ``1``, ``2` `] ]``    ``cntQuey ``=` `3``    ``for` `i ``in` `range``(cntQuey):``        ``if` `(Q[i][``0``] ``=``=` `1``):``            ``update(tree, ``0``, ``0``, N ``-` `1``, Q[i][``1``], Q[i][``2``])``        ``else``:``            ``if` `(Q[i][``1``] ``%` `2` `=``=` `0``):``                ``print``(FindSum(tree, ``0``, N ``-` `1``, Q[i][``1``], Q[i][``2``], ``0``),end``=``" "``)``            ``else``:``                ``print``(``-``FindSum(tree, ``0``, N ``-` `1``, Q[i][``1``], Q[i][``2``], ``0``),end``=``" "``)``                ` `# This code is contributed by mohit kumar 29`

## C#

 `// C#  program to implement``// the above approach``using` `System;``class` `GFG``{``    ` `    ``// Function to build the segment tree``    ``static` `void` `build(``int``[] tree, ``int``[] arr, ``int` `start,``               ``int` `end, ``int` `index)``    ``{``     ` `        ``// If current node is a leaf node``        ``// of the segment tree``        ``if` `(start == end)``        ``{  ``            ``if` `(start % 2 == 0)``            ``{``     ` `                ``// Update tree[index]``                ``tree[index] = arr[start];``            ``}``     ` `            ``else``            ``{``     ` `                ``// Update tree[index]``                ``tree[index] = -arr[start];``            ``}``            ``return``;``        ``}``     ` `        ``// Divide the segment tree``        ``int` `mid = start + (end - start) / 2;``     ` `        ``// Update on L segment tree``        ``build(tree, arr, start, mid,``              ``2 * index + 1);``     ` `        ``// Update on R segment tree``        ``build(tree, arr, mid + 1, end,``              ``2 * index + 2);``     ` `        ``// Find the sum from L subtree``        ``// and R subtree``        ``tree[index] = tree[2 * index + 1] + tree[2 * index + 2];``    ``}``     ` `    ``// Function to update elements at index pos``    ``// by val in the segment tree``    ``static` `void` `update(``int``[] tree, ``int` `index, ``int` `start,``                ``int` `end, ``int` `pos, ``int` `val)``    ``{``     ` `        ``// If current node is a leaf node``        ``if` `(start == end)``        ``{``     ` `            ``// If current index is even``            ``if` `(start % 2 == 0)``            ``{``     ` `                ``// Update tree[index]``                ``tree[index] = val;``            ``}``     ` `            ``else``            ``{``     ` `                ``// Update tree[index]``                ``tree[index] = -val;``            ``}``            ``return``;``        ``}``     ` `        ``// Divide the segment tree elements``        ``// into L and R subtree``        ``int` `mid = start + (end - start) / 2;``     ` `        ``// If element lies in L subtree``        ``if` `(mid >= pos)``        ``{``     ` `            ``update(tree, 2 * index + 1, start,``                   ``mid, pos, val);``        ``}``        ``else``        ``{``            ``update(tree, 2 * index + 2, mid + 1,``                   ``end, pos, val);``        ``}``     ` `        ``// Update tree[index]``        ``tree[index]``            ``= tree[2 * index + 1] + tree[2 * index + 2];``    ``}``     ` `    ``// Function to find the sum of array elements``    ``// in the range [L, R]``    ``static` `int` `FindSum(``int``[] tree, ``int` `start, ``int` `end,``                ``int` `L, ``int` `R, ``int` `index)``    ``{``     ` `        ``// If start and end not lies in``        ``// the range [L, R]``        ``if` `(L > end || R < start)``        ``{``            ``return` `0;``        ``}``     ` `        ``// If start and end comleately lies``        ``// in the range [L, R]``        ``if` `(L <= start && R >= end)``        ``{``     ` `            ``return` `tree[index];``        ``}``        ``int` `mid = start + (end - start) / 2;``     ` `        ``// Stores sum from left subtree``        ``int` `X = FindSum(tree, start, mid, L,``                        ``R, 2 * index + 1);``     ` `        ``// Stores sum from right subtree``        ``int` `Y = FindSum(tree, mid + 1, end, L,``                        ``R, 2 * index + 2);``     ` `        ``return` `X + Y;``    ``}` `  ``// Driver code``  ``static` `void` `Main()``  ``{``    ``int``[] arr = { 1, 2, 3, 4 };``    ``int` `N = arr.Length;``    ``int``[] tree = ``new` `int``[4 * N + 5];``    ``build(tree, arr, 0, N - 1, 0);`` ` `    ``int``[,] Q = { { 2, 0, 3 }, { 1, 1, 5 }, { 2, 1, 2 } };`` ` `    ``int` `cntQuey = 3;``    ``for` `(``int` `i = 0; i < cntQuey; i++)``    ``{``        ``if` `(Q[i, 0] == 1)``        ``{``            ``update(tree, 0, 0, N - 1,``                   ``Q[i, 1], Q[i, 2]);``        ``}`` ` `        ``else``        ``{``            ``if` `(Q[i, 1] % 2 == 0)``            ``{``                ``Console.Write(FindSum(tree, 0, N - 1,``                                      ``Q[i, 1], Q[i, 2], 0) + ``" "``);``            ``}``            ``else``            ``{``                ``Console.Write(-FindSum(tree, 0, N - 1,``                                       ``Q[i, 1], Q[i, 2], 0) + ``" "``);``            ``}``        ``}``    ``}``  ``}``}` `// This code is contributed by divyesh072019.`

## Javascript

 ``
Output:
`-2 2`

Time Complexity: O(|Q| * log(N))
Auxiliary Space: O(N)

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