An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is ______.

There are n unsorted arrays: A₁, A₂, ..., A_n. Assume that n is odd. Each of A₁, A₂, ..., A_n contains n distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of A₁, A₂, ..., A_n is

Consider a sequence of 14 elements: A = [-5, -10, 6, 3, -1, -2, 13, 4, -9, -1, 4, 12, -3, 0]. The subsequence sum $$S\left( {i,j} \right) = \sum\limits_{k = 1}^j {A\left[ k \right]} $$. Determine the maximum of S(i, j), where 0 ≤ i ≤ j < 14. (Divide and conquer approach may be used)

Answer : ________.

Consider the augmented grammar given below :

S' → S
S → 〈L〉 | id
L → L,S | S

Let I₀ = CLOSURE ({[S' → ●S]}). The number of items in the set GOTO (I₀ , 〈 ) is: _____.