Create a data structure to perform inverse queries and report queries in poly-logarithmic time

Question

Given a sequence of n numbers, {a ₁ , a ₂ , a ₃ , ..., a _{nsub>}. Create a data structure so that the following operations are performed during polyling.}

• Inverse (i, j):

  Flip all the elements in the range from i to j, as shown below:
    Original sequence: <... a _i-1 , _i , a _{i + 1} , ..., a _j-1 , a _j , a _{j + 1} , ...>
    Sequence after swap: <... a _i-1 , _j , a _j-1 , ..., a _i-1 , _i , a _{j + 1} , ...>

• Report (i):

  Report the i-th element in the sequence, i.e. _i .

Here poly-logn means some degree of log n. how log (n) · log (n) may be acceptable.

[Note: thanks prof. Baswan for asking this question.]

Answer 1

node, Left & Right .

• Left, ,
• Else ( Right), ,

Report : O(log n)

Revert , , .

, "" , ( ). [a..b] [i..j]

• , ( )
• Revert [a..i-1] [j+1..b]

, :/

:) , , .

, - , , .

Answer 2

Splay trees + O (log n), . , , , O (log n) node, .

(: , , .)