Range sum query using Sparse Table

We have an array arr[]. We need to find the sum of all the elements in the range L and R where 0 <= L <= R <= n-1. Consider a situation when there are many range queries.

Examples:

Input : 3 7 2 5 8 9
query(0, 5)
query(3, 5)
query(2, 4)
Output : 34
22
15

Note : array is 0 based indexed
 and queries too.

Since there are no updates/modifications, we use the Sparse table to answer queries efficiently. In a sparse table, we break queries in powers of 2.  

Suppose we are asked to compute sum of elements from arr[i] to arr[i+12]. We do the following:

// Use sum of 8 (or 2³) elements
table[i][3] = sum(arr[i], arr[i + 1], ...arr[i + 7]).

// Use sum of 4 elements
table[i+8][2] = sum(arr[i+8], arr[i+9], ..arr[i+11]).

// Use sum of single element
table[i + 12][0] = sum(arr[i + 12]).

Our result is sum of above values.

Notice that it took only 4 actions to compute the result over a subarray of size 13. 

Output:

34
22
15

This algorithm for answering queries with Sparse Table works in O(k), which is O(log(n)) because we choose minimal k such that 2^k+1 > n.
Time complexity of sparse table construction : Outer loop runs in O(k), inner loop runs in O(n). Thus, in total we get O(n * k) = O(n * log(n)) 

Auxiliary Space: O(n*k), since n*k extra space has been taken.