Select less frequent elements from list - arrays

I would appreciate some help with this problem. I have a list with multiple elements and I want to select de element with the lowest frequency. If multiple elements have the lowest frequency, I have to return them all.
For example:
list1 = [1,2,2,2,3]
I have to return 1 and 3
I tried using min(list1, key = list1.count)) but this return 1 only
I am using Python 3.10
Edit: I am not allowed to use import

I think this question can be answered with more google research by yourself. But let me help you in some understanding.
If you really need any help from the Algorithm side, then there are multiple approaches like using a Hashmap to find the elements in O(n) time and space. You can also sort the array to perform the operation in O(nlgn) time but in constant space.
If you are trying to find some python oneliner, then I would say don't because most these one liners are deceiving. They tend to very clean but cost time in the background.
In your case max or min is designed to get a single element. Hence you get only one result. However you can build upon the following code
sorted(list1, key=list1.count)
Edit 1: What do you mean that you are not allowed to use import. Is it some kind of interview/homework question? You shouldn't ask for homework solutions in total at SO.

Related

Excel calculate smallest of X columns within Y columns, ignoring zeros

I'm trying to calculate the sum of best segments in a run. For example, each Km gives a list as such:
5:40 6:00 5:45 5:55 6:21 6 :30
I'm trying to gather the best segments of 2km/3km/4km etc and would like a simple code to do it. At the moment, I'm using the formula
=Min(If(B1=0,9:9:9,sum(A1:B1),If(C1=0,9:9:9,sum(B1:C1))
but this goes all the way to 50km, meaning a very long formulae that I then have to repeat slightly differently at 3km, then 4km, then 5km etc. Surely there must me a way of
generating an array of summed columns of every n column, then iterating over that to find the min while ignoring values of 0?
I can do it manually for now, but what if I want to go over 50km? I might want to incorporate bike rides/car drives in the future just for some data analysis so I figured it best finding an ideal formulae now.
It's frustrating as I could code it and I want to avoid VBA ideally and stick to formulae in Excel.
Here is a draft of the case where there aren't any zeroes just for groups of 2Km. I decided the simplest approach initially was to add a couple of helper rows containing the running total of times (and for later use counts) and use a formula like this to subtract them in pairs:
=MIN(INDEX(A2:J2,SEQUENCE(1,9,2))-IF(SEQUENCE(1,9,0)=0,0,INDEX(A2:J2,SEQUENCE(1,9,0))))
but if you have access to recent additions to Excel 365 like Scan you can do it without helper rows.
Here is a more realistic scenario with a couple of zeroes thrown in
=LET(runningSum,Y$4:AP$4,runningCount,Y$5:AP$5,cols,COLUMNS(runningSum),leg,X7,
seqEnd,SEQUENCE(1,cols-leg+1,leg),seqStart,SEQUENCE(1,cols-leg+1,0),
times,INDEX(runningSum,seqEnd)-IF(seqStart=0,0,INDEX(runningSum,seqStart)),
counts,INDEX(runningCount,seqEnd)-IF(seqStart=0,0,INDEX(runningCount,seqStart)),
MIN(IF(counts=leg,times)))
Note that there are no runs of more than seven consecutive legs that don't contain a zero so 8, 9, 10 etc. just work out to 0.
As mentioned you could dispense with the helper rows by using Scan, but not everyone has access to this so I will add it separately:
=LET(data,Y$3:AP$3,runningSum,SCAN(0,data,LAMBDA(a,b,a+b)),
runningCount,SCAN(0,data,LAMBDA(a,b,a+(b>0))),leg,X7,cols,COLUMNS(data),
seqEnd,SEQUENCE(1,cols-leg+1,leg),seqStart,SEQUENCE(1,cols-leg+1,0),
times,INDEX(runningSum,seqEnd)-IF(seqStart=0,0,INDEX(runningSum,seqStart)),
counts,INDEX(runningCount,seqEnd)-IF(seqStart=0,0,INDEX(runningCount,seqStart)),
MIN(IF(counts=leg,times)))
Tom that worked! I learnt a few things on the way too and using the indexing method alongside sequence and columns is something I had not thought of. I'd never heard of the LET command before and I can already see that this is going to really help with some of the bigger calculations in the future.
Thank you so much, I'd like to show you how it now looks. Row 3087 is my old formula, row 3088 is a copy of the same data using the new formula, as you can see I've gotten exactly the same results so it's clear that it works perfectly and it is can be easily duplicated.

Looping and selectig different value in each line

I have a problem that I think would be solved relatively quickly with a loop. I have to work with SPSS and I think it can only be solved in syntax.
Unfortunately I am not good with loops, so I hope that one of you can help me.
I have done a study on reasons for abortions. Now I would like to present the distribution of reasons.
The problem is that each person was first asked about all their pregnancies (because this is also relevant for the later analysis), then the pregnancy was determined to which the questionnaire will further refer.
So the further questionnaire was only about one of the pregnancies, whereas the first questions (f.ex. year of pregnancy, reason for abortion) were answered for each pregnancy. For the reasons I only need the information that refers to the pregnancy that was also used for the further questionnaire.
I have an index variable that determines the loop at which pass the relevant pregnancy is asked ("index"). Then I have the variable "Loop_1_R" to "Loop_5_R" which queries the reasons for each up to 5 abortions (of course, for each woman, only the number of pregnancies that she also indicated). In between there are some missing data, for ex. it could be that a woman said that she had 5 pregnancies, but only two of them were abortions (f.ex. the third and fifth). So then she would only give reasons for an abortion in loop3 and loop5.
Now I want to create a new variable which contains only the reason which refers to the relevant pregnancy. So for each woman only one value. I was thinking, you could build a loop in the sense of calculate new variable in such a way that loop i is taken at index i.
I could of course do it by hand, but with a VPN count of over 3000 it will obviously take considerably longer.
I hope someone can help me! This is an example dataset with less loops and VPN:
You can use do repeat to loop and catch the value you need this way:
do repeat vr=Loop_1_R to Loop_5_R/vl=1 to 5.
if Index=vl reason=vr.
end repeat.

Optimizing People Placement - Large Data Set

I'm trying to figure out the best method / program to handle this computation to get the most people happy, ie the highest value for each person while still having all values be almost equal.
There are 24 people, 100 days and 4 people need to be selected for each day. All days must be full, ie the 24 people must be spread over 400 the slots with each person getting about 8 slots.
How can I create a program / algorithm that will allow the people to rank all 100 days in order of preference as well as the top 5 people they would prefer to be selected with. I was thinking that each day and each of the preferred people would get some sort of point value. Then the algorithm would run through the data set and find the combination that would yield the highest amount of people the happiest while still making everyone roughly even.
Is this easily possible using something like excel?
Thanks
Read up on "The Assignment Problem"; this is a well studied class of problems. Off the top of my head, the Hungarian Assignment method and the Stable Marriage/Stable Roommate method might be relevant.
You can solve this problem as a MILP using Solver as shown in this video and many others like it, but I am afraid that the build-in Solver may not allow enough binary variables for it to work. Get a feeling for how the problem work on a small scale and then download a nicer solver.

large test data for knapsack problem

i am researcher student. I am searching large data for knapsack problem. I wanted test my algorithm for knapsack problem. But i couldn't find large data. I need data has 1000 item and capacity is no matter. The point is item as much as huge it's good for my algorithm. Is there any huge data available in internet. Does anybody know please guys i need urgent.
You can quite easily generate your own data. Just use a random number generator and generate lots and lots of values. To test that your algorithm gives the correct results, compare it to the results from another known working algorithm.
I have the same requirement.
Obviously only Brute force will give the optimal answer and that won't work for large problems.
However we could pitch our algorithms against each other...
To be clear, my algorithm works for 0-1 problems (i.e. 0 or 1 of each item), Integer or decimal data.
I also have a version that works for 2 dimensions (e.g. Volume and Weight vs. Value).
My file reader uses a simple CSV format (Item-name, weight, value):
X229257,9,286
X509192,11,272
X847469,5,184
X457095,4,88
etc....
If I recall correctly, I've tested mine on 1000 items too.
Regards.
PS:
I ran my algorithm again the problem on Rosette Code that Mark highlighted (thank you). I got the same result but my solution is much more scalable than the dynamic programming / LP solutions and will work on much bigger problems

How do you solve the 15-puzzle with A-Star or Dijkstra's Algorithm?

I've read in one of my AI books that popular algorithms (A-Star, Dijkstra) for path-finding in simulation or games is also used to solve the well-known "15-puzzle".
Can anyone give me some pointers on how I would reduce the 15-puzzle to a graph of nodes and edges so that I could apply one of these algorithms?
If I were to treat each node in the graph as a game state then wouldn't that tree become quite large? Or is that just the way to do it?
A good heuristic for A-Star with the 15 puzzle is the number of squares that are in the wrong location. Because you need at least 1 move per square that is out of place, the number of squares out of place is guaranteed to be less than or equal to the number of moves required to solve the puzzle, making it an appropriate heuristic for A-Star.
A quick Google search turns up a couple papers that cover this in some detail: one on Parallel Combinatorial Search, and one on External-Memory Graph Search
General rule of thumb when it comes to algorithmic problems: someone has likely done it before you, and published their findings.
This is an assignment for the 8-puzzle problem talked about using the A* algorithm in some detail, but also fairly straightforward:
http://www.cs.princeton.edu/courses/archive/spring09/cos226/assignments/8puzzle.html
The graph theoretic way to solve the problem is to imagine every configuration of the board as a vertex of the graph and then use a breath-first search with pruning based on something like the Manhatten Distance of the board to derive a shortest path from the starting configuration to the solution.
One problem with this approach is that for any n x n board where n > 3 the game space becomes so large that it is not clear how you can efficiently mark the visited vertices. In other words there is no obvious way to assess if the current configuration of the board is identical to one that has previously been discovered through traversing some other path. Another problem is that the graph size grows so quickly with n (it's approximately (n^2)!) that it is just not suitable for a brue-force attack as the number of paths becomes computationally infeasible to traverse.
This paper by Ian Parberry A Real-Time Algorithm for the (n^2 − 1) - Puzzle describes a simple greedy algorithm that iteritively arrives at a solution by completing the first row, then the first column, then the second row... It arrives at a solution almost immediately, however the solution is far from optimal; essentially it solves the problem the way a human would without leveraging any computational muscle.
This problem is closely related to that of solving the Rubik's cube. The graph of all game states it too large to solve by brue force, but there is a fairly simple 7 step method that can be used to solve any cube in about 1 ~ 2 minutes by a dextrous human. This path is of course non-optimal. By learning to recognise patterns that define sequences of moves the speed can be brought down to 17 seconds. However, this feat by Jiri is somewhat superhuman!
The method Parberry describes moves only one tile at a time; one imagines that the algorithm could be made better up by employing Jiri's dexterity and moving multiple tiles at one time. This would not, as Parberry proves, reduce the path length from n^3, but it would reduce the coefficient of the leading term.
Remember that A* will search through the problem space proceeding down the most likely path to goal as defined by your heurestic.
Only in the worst case will it end up having to flood fill the entire problem space, this tends to happen when there is no actual solution to your problem.
Just use the game tree. Remember that a tree is a special form of graph.
In your case the leaves of each node will be the game position after you make one of the moves that is available at the current node.
Here you go http://www.heyes-jones.com/astar.html
Also. be mindful that with the A-Star algorithm, at least, you will need to figure out a admissible heuristic to determine whether a possible next step is closer to the finished route than another step.
For my current experience, on how to solve an 8 puzzle.
it is required to create nodes. keep track of each step taken
and get the manhattan distance from each following steps, taking/going to the one with the shortest distance.
update the nodes, and continue until reaches the goal

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