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:
9
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:
Javascript
<script> // Javascript program to calculate range sum// queries for anticlockwise// rotations of array by K// Function to execute the queriesfunction rotatedSumQuery(arr, n, query, Q){ // Construct a new array // of size 2*N to store // prefix sum of every index let prefix = []; // Copy elements to the new array for(let i = 0; i < n; i++) { prefix[i] = arr[i]; prefix[i + n] = arr[i]; } // Calculate the prefix sum // for every index for(let i = 1; i < 2 * n; i++) prefix[i] += prefix[i - 1]; // Set start pointer as 0 let start = 0; for(let q = 0; q < Q; q++) { // Query to perform // anticlockwise rotation if (query[q][0] == 1) { let k = query[q][1]; start = (start + k) % n; } // Query to answer range sum else if (query[q][0] == 2) { let L, R; L = query[q][1]; R = query[q][2]; // If pointing to 1st index if (start + L == 0) // Display the sum upto start + R document.write(prefix[start + R] + "<br/>"); else // Subtract sum upto start + L - 1 // from sum upto start + R document.write(prefix[start + R] - prefix[start + L - 1] + "<br/>"); } }} // Driver code let arr = [ 1, 2, 3, 4, 5, 6 ]; // Number of query let Q = 5; // Store all the queries let query = [[ 2, 1, 3 ], [ 1, 3 ], [ 2, 0, 3 ], [ 1, 4 ], [ 2, 3, 5 ]]; let n = arr.length; rotatedSumQuery(arr, n, query, Q); // This code is contributed by susmitakundugoaldanga.</script> |
9 16 12
Time Complexity: O(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!
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