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# C++ Program to Find Range sum queries for anticlockwise rotations of Array by K indices

Given an array arr consisting of N elements and Q queries of the following two types:

• 1 K: For this type of query, the array needs to be rotated by K indices anticlockwise from its current state.
• 2 L R: For this query, the sum of the array elements present in the indices [L, R] needs to be calculated.

Example:

Input: arr = { 1, 2, 3, 4, 5, 6 }, query = { {2, 1, 3}, {1, 3}, {2, 0, 3}, {1, 4}, {2, 3, 5} }
Output:

16
12
Explanation:
For the 1st query {2, 1, 3} -> Sum of the elements in the indices [1, 3] = 2 + 3 + 4 = 9.
For the 2nd query {1, 3} -> Modified array after anti-clockwise rotation by 3 places is { 4, 5, 6, 1, 2, 3 }
For the 3rd query {2, 0, 3} -> Sum of the elements in the indices [0, 3] = 4 + 5 + 6 + 1 = 16.
For the 4th query {1, 4} -> Modified array after anti-clockwise rotation by 4 places is { 2, 3, 4, 5, 6, 1 }
For the 5th query {2, 3, 5} -> Sum of the elements in the indices [3, 5] = 5 + 6 + 1 = 12.

Approach:

• Create a prefix array which is double the size of the arr and copy the element at the ith index of arr to ith and N + ith index of prefix for all i in [0, N).
• Precompute the prefix sum for every index of that array and store in prefix.
• Set the pointer start at 0 to denote the starting index of the initial array.
• For query of type 1, shift start to
`((start + K) % N)th position`
• For query of type 2, calculate

```prefix[start + R]
- prefix[start + L- 1 ]```
• if start + L >= 1 ,then print the value of

`prefix[start + R]`

Below code is the implementation of the above approach:

## C++

 `// C++ Program to calculate range sum``// queries for anticlockwise``// rotations of array by K`` ` `#include ``using` `namespace` `std;`` ` `// Function to execute the queries``void` `rotatedSumQuery(``    ``int` `arr[], ``int` `n,``    ``vector >& query,``    ``int` `Q)``{``    ``// Construct a new array``    ``// of size 2*N to store``    ``// prefix sum of every index``    ``int` `prefix[2 * n];`` ` `    ``// Copy elements to the new array``    ``for` `(``int` `i = 0; i < n; i++) {``        ``prefix[i] = arr[i];``        ``prefix[i + n] = arr[i];``    ``}`` ` `    ``// Calculate the prefix sum``    ``// for every index``    ``for` `(``int` `i = 1; i < 2 * n; i++)``        ``prefix[i] += prefix[i - 1];`` ` `    ``// Set start pointer as 0``    ``int` `start = 0;`` ` `    ``for` `(``int` `q = 0; q < Q; q++) {`` ` `        ``// Query to perform``        ``// anticlockwise rotation``        ``if` `(query[q] == 1) {``            ``int` `k = query[q];``            ``start = (start + k) % n;``        ``}`` ` `        ``// Query to answer range sum``        ``else` `if` `(query[q] == 2) {`` ` `            ``int` `L, R;``            ``L = query[q];``            ``R = query[q];`` ` `            ``// If pointing to 1st index``            ``if` `(start + L == 0)`` ` `                ``// Display the sum upto start + R``                ``cout << prefix[start + R] << endl;`` ` `            ``else`` ` `                ``// Subtract sum upto start + L - 1``                ``// from sum upto start + R``                ``cout << prefix[start + R]``                            ``- prefix[start + L - 1]``                     ``<< endl;``        ``}``    ``}``}`` ` `// Driver code``int` `main()``{`` ` `    ``int` `arr[] = { 1, 2, 3, 4, 5, 6 };`` ` `    ``// Number of query``    ``int` `Q = 5;`` ` `    ``// Store all the queries``    ``vector > query``        ``= { { 2, 1, 3 },``            ``{ 1, 3 },``            ``{ 2, 0, 3 },``            ``{ 1, 4 },``            ``{ 2, 3, 5 } };`` ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);``    ``rotatedSumQuery(arr, n, query, Q);`` ` `    ``return` `0;``}`

Output:

```9
16
12```

Time Complexity: O(N + Q), where Q is the number of queries, and as each query will cost O (1) time for Q queries time complexity would be O(Q).

Auxiliary Space: O(N), as we are using  extra space for prefix.

Please refer complete article on Range sum queries for anticlockwise rotations of Array by K indices for more details!