What is the average performance of Quicksort assuming
every input permutation is equally likely? Prove it.
Hint: In this case pivot(split) element very likely to
provide good balance during partition.
A bag contains 2 apples, 3 oranges, and 4 bananas. The number of ways in which 3 fruits can be selected if atleast one banana is always in the combination (Assume fruits of same species to be alike) is
Let P = (p1,...,pn) be a permutation of [n]. We say a
number i is a fixed point of p, if pi = i.
(a) Determine the number of permutations of [6] with at most three
fixed points.
(b) Determine the number of 9-derangements of [9] so that each even
number is in an even position.
(c) Use the following relationship (not proven here, but relatively
easy to see) for the Rencontre numbers:
Dn =(n-1)-(Dn-1 +Dn-2) (∗)
to perform an...
Prove that (((p v ~q) ⊕ p) v ~p) ⊕ (p v ~q) ⊕ (p ⊕ q) is
equivalent to p ^ q. Please show your work and name all the logical
equivalence laws for each step. ( v = or, ~ = not, ⊕ = XOR)
Thank you
Suppose a is a positive integer and p is a prime/ Prove that p|a
if and only if the prime factorization of a contains p.
Can someone please show a full proof to this, thank you.
C#
Palindrome Permutation: Given a string, write a
function to check if it is a permutation of a palindrome. A
palindrome is a word or phrase that is the same forwards and
backwards. A permutation is a rearrangement of letters. The
palindrome does not need to be limited to just dictionary
words.
Input: Tact Coa
Output: True (permutations: "taco cat", "atco cta", etc.)
Comment your code to explain it.