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Constant time range add operation on an array
• Difficulty Level : Medium
• Last Updated : 05 Oct, 2020

Given an array of size N which is initialized with all zeros. We are given many ranges add queries, which should be applied to this array. We need to print the final updated array as our result.

Examples:

```N = 6
Arr = [0, 0, 0, 0, 0, 0]
rangeUpdate1 [0, 2], add 100
Arr = [100, 100, 100, 0, 0, 0]
rangeUpdate1 [1, 5], add 100
Arr = [100, 200, 200, 100, 100, 100]
rangeUpdate1 [2, 3], add 100
Arr = [100, 200, 300, 200, 100, 100]
Which is the final updated array.
```

This problem can be solved using segment tree with lazy updates in O(log N) time per query but we can do better here, as update operation is not given. We can process each query in constant time using this logic when a query to add V is given in range [a, b] we will add V to arr[a] and –V to arr[b+1] now if we want to get the actual values of the array we will convert the above array into prefix sum array.

See below example to understand:

```Arr = [0, 0, 0, 0, 0, 0]

rangeUpdate1 [0, 2], add 100
Arr = [100, 0, 0, -100, 0, 0]

rangeUpdate1 [1, 5], add 100.
Arr = [100, 100, 0, -100, 0, 0]
Note: You can not add -100 at 6th index because array length is 6.

rangeUpdate1 [2, 3], add 100
Arr = [100, 100, 100, -100, -100, 0]

Now we will convert above operation array to prefix sum array as shown below,
Arr = [100, 200, 300, 200, 100, 100]

Which is the final updated array.
```

So in effect, when we add a value V to specific index of the array, It represents adding V to all elements right to this index, that is why we add –V after range to remove its effect after its range of add query.
Please note in below code, if range spans till the last index, the addition of –V is omitted to be in memory limit of the array.

## C++

 `//  C++ program to get updated array after many array range``// add operation``#include ``using` `namespace` `std;` `//  Utility method to add value val, to range [lo, hi]``void` `add(``int` `arr[], ``int` `N, ``int` `lo, ``int` `hi, ``int` `val)``{``    ``arr[lo] += val;``    ``if` `(hi != N - 1)``       ``arr[hi + 1] -= val;``}` `//  Utility method to get actual array from operation array``void` `updateArray(``int` `arr[], ``int` `N)``{``    ``//  convert array into prefix sum array``    ``for` `(``int` `i = 1; i < N; i++)``        ``arr[i] += arr[i - 1];``}` `//  method to print final updated array``void` `printArr(``int` `arr[], ``int` `N)``{``    ``updateArray(arr, N);``    ``for` `(``int` `i = 0; i < N; i++)``        ``cout << arr[i] << ``" "``;``    ``cout << endl;``}` `//  Driver code``int` `main()``{``    ``int` `N = 6;` `    ``int` `arr[N] = {0};` `    ``//  Range add Queries``    ``add(arr, N, 0, 2, 100);``    ``add(arr, N, 1, 5, 100);``    ``add(arr, N, 2, 3, 100);` `    ``printArr(arr, N);``    ``return` `0;``}`

## Java

 `// Java program to get updated array after``// many array range add operation``import` `java.io.*;` `class` `GFG {``    ``// Utility method to add value val,``    ``// to range [lo, hi]``    ``static` `void` `add(``int` `arr[], ``int` `N, ``int` `lo, ``int` `hi,``                    ``int` `val)``    ``{``        ``arr[lo] += val;``        ``if` `(hi != N - ``1``)``            ``arr[hi + ``1``] -= val;``    ``}` `    ``// Utility method to get actual array from``    ``// operation array``    ``static` `void` `updateArray(``int` `arr[], ``int` `N)``    ``{``        ``// convert array into prefix sum array``        ``for` `(``int` `i = ``1``; i < N; i++)``            ``arr[i] += arr[i - ``1``];``    ``}` `    ``// method to print final updated array``    ``static` `void` `printArr(``int` `arr[], ``int` `N)``    ``{``        ``updateArray(arr, N);``        ``for` `(``int` `i = ``0``; i < N; i++)``            ``System.out.print(``""` `+ arr[i] + ``" "``);``        ``System.out.print(``"\n"``);``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `N = ``6``;` `        ``int` `arr[] = ``new` `int``[N];` `        ``// Range add Queries``        ``add(arr, N, ``0``, ``2``, ``100``);``        ``add(arr, N, ``1``, ``5``, ``100``);``        ``add(arr, N, ``2``, ``3``, ``100``);` `        ``printArr(arr, N);``    ``}``}` `// This code is contributed by Prakriti Gupta`

## Python3

 `# Python3 program to get updated array``# after many array range add operation` `# Utility method to add value``# val, to range [lo, hi]`  `def` `add(arr, N, lo, hi, val):` `    ``arr[lo] ``+``=` `val``    ``if` `(hi !``=` `N ``-` `1``):``        ``arr[hi ``+` `1``] ``-``=` `val` `# Utility method to get actual``# array from operation array`  `def` `updateArray(arr, N):` `    ``# convert array into prefix sum array``    ``for` `i ``in` `range``(``1``, N):``        ``arr[i] ``+``=` `arr[i ``-` `1``]` `# method to print final updated array`  `def` `printArr(arr, N):` `    ``updateArray(arr, N)``    ``for` `i ``in` `range``(N):``        ``print``(arr[i], end``=``" "``)``    ``print``()`  `# Driver code``N ``=` `6``arr ``=` `[``0` `for` `i ``in` `range``(N)]` `# Range add Queries``add(arr, N, ``0``, ``2``, ``100``)``add(arr, N, ``1``, ``5``, ``100``)``add(arr, N, ``2``, ``3``, ``100``)` `printArr(arr, N)` `# This code is contributed by Anant Agarwal.`

## C#

 `// C# program to get updated array after``// many array range add operation``using` `System;` `class` `GFG {` `    ``// Utility method to add value val,``    ``// to range [lo, hi]``    ``static` `void` `add(``int``[] arr, ``int` `N, ``int` `lo, ``int` `hi,``                    ``int` `val)``    ``{``        ``arr[lo] += val;``        ``if` `(hi != N - 1)``            ``arr[hi + 1] -= val;``    ``}` `    ``// Utility method to get actual``    ``// array from operation array``    ``static` `void` `updateArray(``int``[] arr, ``int` `N)``    ``{``        ``// convert array into``        ``// prefix sum array``        ``for` `(``int` `i = 1; i < N; i++)``            ``arr[i] += arr[i - 1];``    ``}` `    ``// method to print final updated array``    ``static` `void` `printArr(``int``[] arr, ``int` `N)``    ``{``        ``updateArray(arr, N);``        ``for` `(``int` `i = 0; i < N; i++)``            ``Console.Write(``""` `+ arr[i] + ``" "``);``        ``Console.Write(``"\n"``);``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `N = 6;` `        ``int``[] arr = ``new` `int``[N];` `        ``// Range add Queries``        ``add(arr, N, 0, 2, 100);``        ``add(arr, N, 1, 5, 100);``        ``add(arr, N, 2, 3, 100);` `        ``printArr(arr, N);``    ``}``}` `// This code is contributed by Nitin Mittal.`

## PHP

 ``
Output
```100 200 300 200 100 100
```

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