Given a set of S elements, how many unique combination of k elements can I find without any ripetition of the same pairs of elements?
The wording of your question is a bit confusing. But I think that perhaps you are looking for something like this: https://math.stackexchange.com/questions/240762/all-unique-combinations-of-n-numbers
Edit: Basically, you will have 2^k - 1 unique combinations of elements, given that k is the number of elements in the set.
Related
My goal is to get a two-column array of all the possible unique pairs of N items (so N*(N-1)/2 pairs).
I have done this in the past using extra calculation columns, but with the advent of LET() I was wondering if I can get a single function call.
This is my example data:
In the end I came up with this, which is a little unwieldy but does the job:
=LET(x,B2:B5,INDEX(x,LET(n,ROWS(x),s,(1+SEQUENCE((n*n*2),2))/2,r,INT((s-1)/n)+1,LET(a,IF(INT(s)=s,r,INT(s)-((r-1)*n)),FILTER(a,INDEX(a,,1)<INDEX(a,,2))))))
How would you efficiently solve this problem
Suppose we were given a list of words [“apple”, “banana”, “mango”]
If we are given a word in the list that is one typo away,
“Dpple”
“Adple”
“Appld”
We output true
If there is more than one typo, we output false.
For optimizations, I’ve tried storing the list in a hashtable containing the number of letters of each word and looking for the same number of letters upon the given input to reduce the size in which we look for our input. Is there a faster optimization we can make to this problem?
One possible optimisation would be to generate all one-typo words for the given list and put them in a map (or some better string lookup structure). Then lookup the given words - if found output true, else false. The total number of one-typo words is: 25*L, where L is the total number of letters in the input list (assuming case does not matter).
We are given with a string and an integer. We have to tell what character would be at that integer position in the string if the characters were to be placed into sort order.
For Example
String = LALIT
Index = 3
Sorted string AILLT and the character at position 3 is L
Is it possible to solve this problem without sorting?
if yes then can someone provide a pseudo code.
Yes, it's possible to do this. You're looking for something called a selection algorithm which, given a list of elements and a number k, returns what element would be in position k if the elements were to be in sorted order. Amazingly enough, it's possible to do this without sorting the entire list!
The simplest non-sorting algorithm for selection is called quickselect, which runs in expected time O(n) and, provided you're allowed to modify the original array, uses only O(1) auxiliary storage space. The idea behind quickselect is to do a single step of quicksort - pick a pivot element, partition the elements into elements less than the pivot, elements equal to the pivot, and elements greater than the pivot - then to see what happens based on that. If the pivot element ends up in position k after this step, then you're done - that's the element that would be at position k in the final sequence. If the pivot is at a position higher than k, recursively look to the left of the pivot (the kth smallest element is somewhere in there), and if the pivot is at a position lower than k, recursively look to the right of the pivot (the kth smallest element is somewhere in there).
Other approaches exist as well, such as the median-of-medians algorithm that always runs in worst-case O(n) time but is a classic "tricky algorithm to wrap your head around."
So I have a tiny problem. I got help here a while ago about sorting a dictionary with keys that have a list to each key according to the value of things in the list. The keys with lists with the least amount of values on the left and to the right the keys with lists with the most amount of values. That worked great. Now I know how to sort dictionary keys alphabetically but I cant get it to work combined with the above..
I'm trying to sort the dictionary below according to first how many values the key list contains... and then alphabetically if the key list contains the same amount of values as a previous key list.
so before I would have this:
Dict = {"anna":[1,2,3],"billy":[1,2],"cilla":[1,2,3,4],"cecillia":[1,2,3,4],"dan":[1]}
And after if everything goes well I would like to have...
Dict = {"dan":[1],"billy":[1,2],"anna":[1,2,3],"cecillia":[1,2,3,4],"cilla":[1,2,3,4]}
As you see in the above, cecillia comes before cilla since they both have 4 values in their lists... and dan comes in first since he has the least amount of values in his list. I hope this makes sense. What I have right now to get the below result is:
ascending = sorted(Dict, key =lambda x: len(Dict[x]))
this gives me for example:
{"dan":[1],"billy":[1,2],"anna":[1,2,3],"cilla":[1,2,3,4],"cecillia":[1,2,3,4]}
So it works but only for the values in the list.. now when I go
ascending.sort()
it sorts the dictionary alphabetically but then the order of values from least to greatest is gone. Anyone know how to to combine the two things? I would greatly appreciate it.
You cannot keep dictionaries sorted so you must convert it to a list of tuples:
D = [ (x, Dict[x]) for x in Dict]
ascending = sorted(D, key = lambda x: x[1])
ascending.sort()
See http://wiki.python.org/moin/HowTo/Sorting . BTW the feature you are relying on is in fact because the sorting algorithm is stable (which apparently was not the case when I was programming in Python).
I have one question to ask on Algorithms. I have been asked to write the algorithm on this: Not asking you to write the algo for me, but just let me know the efficient process what I need to do:
There is an array of n elements like the book or contents of Bible, and Suppose you have inserted a input string "Gaurav Agarwal" in that. What you want to do you need to fetch unique elements that are present in the array for that String. Just an algorithm how you will proceed further (unsorted)
If you did not understand then let me know and I will try to help on this.
One good way to find duplicates in an unsorted array is to sort it based on the string elements, therefore the algorithm for your homework question would be:
Sort the array
check your array for existence of "Gaurav Agarwal". Since it is sorted, neighboring elements would be the same string, and what you need to do then is to keep a counter and increment it until you find the first array element that is not equal to the string you're looking for
it will take some time to sort the string array and then to parse it. I would recommend just to parse the array of string and verify if length of your string is the same as the length of the string from the current position of the array. If the length is the same, compare the 2 strings
I dont think sorting and searching is the most efficient solution to your problem.
Sorting itself has nlogn complexity.
Just doing a bruteforce search of array is more efficient(has a complexity of n)
This is the case if you are finding unique elements for one string or a few strings.
If you are trying to find unique elements for a lot of input strings instead of one only then sorting makes sense.
I would proceed in the following steps:
I would use a hash table with chaining, using a hash function that
works well for strings.
find the hash of the new string and search the linked list of the
slot corresponding that hash for duplicates.