CLRS | : notebook : Solutions to Introduction to Algorithms | Machine Learning library
kandi X-RAY | CLRS Summary
kandi X-RAY | CLRS Summary
Solutions to Introduction to Algorithms by Charles E. Leiserson, Clifford Stein, Ronald Rivest, and Thomas H. Cormen (CLRS).
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CLRS Examples and Code Snippets
def find_optimal_binary_search_tree(nodes):
"""
This function calculates and prints the optimal binary search tree.
The dynamic programming algorithm below runs in O(n^2) time.
Implemented from CLRS (Introduction to Algorithms) book.
Community Discussions
Trending Discussions on CLRS
QUESTION
This is a continuation to my early complaints about CLRS(3rd edition) if you're looking to learn about algorithms, this is by far the worst book that you can ever use. All the pseudocode examples up to chapter 4 that I've seen so far have mistakes ranging from off by one, wrong/missing base cases for recursive functions, poor design choices that require complete redesign ex: the use of sentinel values in merge sort which is addressed in my other question I mentioned earlier. This book is overhyped and is plain garbage.
In the example shown below, the objective is to find a contiguous subarray with the largest sum.
ex: [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7]
sequence: 18, 20, -7, 12
: 43
ex: [4, 5]
sequence: 4, 5
: 9
ANSWER
Answered 2022-Mar-27 at 18:07The code given by the book treats low
and high
as inclusive indices. So firstly your call to the method should be
QUESTION
For example, given a List of Integer List list = Arrays.asList(5,4,5,2,2)
, how can I get a maxHeap
from this List in O(n)
time complexity?
The naive method:
...ANSWER
Answered 2021-Aug-28 at 15:09According to the java doc of PriorityQueue(PriorityQueue)
Creates a PriorityQueue containing the elements in the specified priority queue. This priority queue will be ordered according to the same ordering as the given priority queue.
So we can extend PriorityQueue
as CustomComparatorPriorityQueue
to hold the desired comparator and the Collection we need to heapify. Then call new PriorityQueue(PriorityQueue)
with an instance of CustomComparatorPriorityQueue
.
Below is tested to work in Java 15.
QUESTION
According to CLRS(3rd edition) ch2 pages 31-34, here's the pseudocode and respective code for merge
and merge_sort
.
ANSWER
Answered 2022-Mar-02 at 10:01There are multiple problem in the transposition from the pseudo code to python code:
in the pseudocode for i = 1 to n1, n1 is included, so you should use
range(1, n1 + 1)
same remark for for k = p to r, use
range(p, r + 1)
the algorithm uses infinite guard values (∞), a mathematical concept that does not fare well in code. If the list does contain infinite float values, the algorithm will fail. You should instead test index values in the merge loop and not rely on guard values.
list index values start at
0
in C and most programming languages, so the initial callmergesort(s, 1, size)
is inconsistent unless you subtract1
from all index values in subscripting expressions.
Algorithms are better formalized with 0
based loops with an excluded upper bound. The pseudo-code is confusing and the book is not practical for programmers. You should consider books that analyzes algorithms with a practical approach in the language of your choice.
Here is a modified version:
QUESTION
I am trying to implement the merge sort algorithm using sentinels in C#.
The array I am trying to sort:
...ANSWER
Answered 2022-Jan-10 at 11:01You have at least next several errors in the left
/right
array initialization:
- for
left
you should start fromlowerIndex
:
QUESTION
Well, at the beginning of the Implementation of ItemTouchHelper
, I chose to use only the Swipe function from it. Everything worked - with the help of Swipe I could delete items in RecyclerView
etc. But then I thought I'd add up-down movement so that the user could change the order in which the item appears in the list.
Then the problems began - the user can change the order in which items are displayed, but can no longer:
- Scroll
RecyclerView
(even if changing item up-down position is disabled) - Swipe functions have stopped working -
onSwiped
does not return the side (ItemTouchHelper.LEFT, ItemTouchHelper.RIGHT
) in which the item was swiped
I changed the View on which is trigger OnStartDragListener from _view to just ImageView and I can scroll now but there are now other problems:
- Swipe works on that ImageView too - I want to be able to swipe item whereever user click on item (_view)
- Swipe functions still doesn't work -
onSwiped
does not return the side (ItemTouchHelper.LEFT, ItemTouchHelper.RIGHT
) in which the item was swiped
FIXED
I Changed
...ANSWER
Answered 2021-Dec-25 at 15:17FIXED
I Changed
QUESTION
I am trying to implement a bottom up approach function to the rod cutting problem and I need to use this particular pseudo-code from the CLRS textbook. In it there two functions and one calls the other in this fashion
(r,s) = EXTENDED-BOTTOM-UP-CUT-ROD(p,n)
Where r and s are two different arrays. The function also returns two arrays. I am currently using C++ and I've tried things such as
...ANSWER
Answered 2021-Nov-12 at 20:27You can use tuples and "structured binding" in C++17 to return multiple values efficiently as below:
QUESTION
I'm having trouble widening the x axis of the forestplot. i.e. area inside the red box. I want to increase/zoom-in the plotted area(area inside the red box) without skipping any numbers. I want it to be wide enough for improved visibility. Any tips on how to expand the mean (95% CI) number lines would be greatly appreciated.
Can anyone help me?
Here are the r codes that I have used to create the above forestplot:
...ANSWER
Answered 2021-Oct-10 at 19:01Here is a potential solution to your problem. You can create the range of your x-axis
by doing this Tthis is just an example. I am not sure what values you want to use).
QUESTION
- This is my jsx code I am trying to create a color game but my main_color starts from undefined and then lags behind the main color array which I created and imported from another function . I need help fixing my code . Can anyone help me with it
ANSWER
Answered 2021-Sep-17 at 14:25Ok so if I understand what you want to do, this is your problem:
QUESTION
As CLRS book,page 260 stated,
I wouldn't have any problem if the author says the bound is eventually
or even
What kind of theories shall we apply to simplify the original result, i.e, cancelling the factor 1/n of a. Since n is one of inputs of the function, is it necessary to cancel it by treating it as a constant? What i've missed? is anyone got the same confusion T_T?
ANSWER
Answered 2021-Sep-14 at 08:47alpha/n
is asimptotically smaller (has lower order) being compared with alpha
, so it might be ignored. When n
(hashtable size, AFAIU) becomes larger, 1/n
value tends to zero.
Note - wiki table does not contain 1/n
function because it is evaluated as having zero impact
Alike situation - if time is Theta(n^2 + 100*n + 10000)
, dominating summand is quadratic, and
QUESTION
In the book "Introduction to Algorithms" by CLRS we are asked to find the time complexity of a recursive function:
4.4-8
Use a recursion tree to give an asymptotically tight solution to the recurrence T(n) = T(n - a) + T(a) + cn where a ≥ 1 and c > 0 are constants.
However, when T(a) is called, T(a) will be called again, which will call T(a) again, and so on. There will never be a base case for this branch. The function will therefore never end! How can this function then have a time complexity of O(n^2) when it actually will result in O(∞)?
...
ANSWER
Answered 2021-Aug-19 at 13:47When recurrence relations are given for the purpose of determining complexity, the base case(s) are often just left out.
Assuming that the program terminates, then if x is any constant, T(x) is also a constant. You can just replace it with a constant like "d", or remember that you don't have to expand it.
Since it doesn't matter what the constant is, it will often be written as O(1), even though that is formally incorrect, because O(1) is a set. It's also not appropriate for you, since you are looking for a tight bound.
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