8/11/2019 Cheet Sheet

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THE RUNNING TIMES

2013 Mid-Term

A. Deleting an element from a map with n elements: O(log(n))

B. Constructing a heap from a vector with n elements: O(n)

C. Performing union()on a disjoint set instance with n elements: O(1)

D. Performing find()on a disjoint set instance with n elements: O((n))

E. Performing upper_bound()on a map with n elements: O(log(n))

F.

Inserting an element into a map with n elements: O(log(n))G. Performing pop()on a heap with n elements: O(log(n))

H. Performing push()on a heap with n elements: O(log(n))

2012 Mid-Term

A.

Sorting a vector using insertion sort. O(n2)

B.

Sorting a vector using heap sort. O(n log n)

C. Calling Push() on a heap. O(log n)

D. Creating a heap from a random vector. O(n)

E.

Calling Pop() on a heap. O(log n)

F.

Printing all elements of a map in order. O(n)G.

Printing all subsets of a set. O(2n)

H.

Calling Union() on a disjoint set. O(1)

I.

Deleting an element from a map. O(log n)

J.

Printing all pairs of elements in a vector of integers. O(n2)

K.

Inserting an element into a map. O(log n)

L.

Sorting a vector using selection sort. O(n2)

M.

Sorting a vector using bubble sort. O(n2)

N.

Calling Find() on a disjoint set. O((n))

O.

Sorting a vector using STL multisets. O(n log n)

P.

Enumerating all 2-disk failures in an n-disk system. O(n2)

2009 Mid-Term

A. Inserting an element into a map. Same as a balanced binary tree: O(log2(n)).

B. Creating a heap from a vector. This is where a heap excels over a set or map, because you can create a heap

from a vector in linear time: O(n).

C.

Finding the minimum element of a priority queue. The minimum element is at the root of the heap: O(1).

D.

Inserting an element into a priority queue. Add the new element to the back of the vector and percolate up:

O(log2(n)).

E. Appending an element to a vector. This is a constant time operation: O(1).

F.

Counting the number of unique elements of a multiset. You need to traverse the multiset with an iterator: O(G. Creating a sorted vector from a multiset that has n elements. Again, this simply requires traversing the multis

with an iterator: O(n).

H. Sorting a nearly sorted vector using selection sort. There is no advantage to having the vector nearly sorted --

selection sort still takes O(n2) operations.

I.

Deleting an element from a list: O(1).

J.

Sorting a nearly sorted vector using insertion sort. This is where insertion sort does well: O(n).