DFA which accepts either even number of 1s or odd number of 0s. ex- 0,11,10,01,110,011,000,101 etc
we can make four different cases that are
and corresponding the table we will have three final states that are acceptable cases. let the states be:
q0 for even even
q1 for odd even
q2 for even odd
and q3 for odd odd
so the transition graph would be given by
i think below DFA will full fill requirements...i made in paint so,not looking pretty.
State O 1
->q0* q1 q2
q1* q0 q3
q2 q3 q0
q3* q2 q1
q0 is the initial state and q0,q1,q3 are the final states.
Create 4 states like below
+-------------+
| 0s | 1s |
+-------------------+
| q0* | even | even |
+-------------------+
| q1 | even | odd |
+-------------------+
| q2* | odd | even |
+-------------------+
| q3* | odd | odd |
+-------------------+
See that your accepting states are q0, q2 and q3
Your state transition table will be like this
+----+----+
| 0 | 1 |
+---------------+
| q0* | q2 | q1 |
+---------------+
| q1 | q3 | q0 |
+---------------+
| q2* | q0 | q3 |
+---------------+
| q3* | q1 | q4 |
+-----+----+----+
Related
Goal: Use SUMIFS to get the sum of value if color is Red or Yellow. Outcome should be 3.
+---+--------+-------+---+-----------+
| | A | B | C | D |
+---+--------+-------+---+-----------+
| 1 | Key | Value | | Condition |
| 2 | Red | 1 | | Red |
| 3 | Yellow | 2 | | Yellow |
| 4 | Green | 3 | | |
+---+--------+-------+---+-----------+
Problem:
It works if I hardcode the condition {"Red","Yellow"}. The result is 3.
=SUM(SUMIFS(B2:B4, A2:A4, {"Red","Yellow"}))
But if I reference the condition by cell D2:D3, I get 0.
=SUM(SUMIFS(B2:B4, A2:A4, D2:D3))
Question: How do I reference the condition dynamically by cell and make it work?
Use SUMPRODUCT() instead of SUM():
=SUMPRODUCT(SUMIFS(B2:B4,A2:A4,D2:D3))
One note:
This variation allows the expansion of the lists without the need to reapply the ranges:
=SUMPRODUCT(SUMIFS(B:B,A:A,D2:INDEX(D:D,MATCH("zzz",D:D))))
Alternatively, you can use SUMIF() together:
=SUMIF(A2:A4,"Red",B2:B4)+SUMIF(A2:A4,"Yellow",B2:B4)
Or make sure you're using CTRL+SHIFT+ENTER with your current formula attempt.
I am looking for a little help in making a formula based dynamic array in excel.
KPI | Tgt | number | Weight
FCR | 0% | 1 | 45%
FCR | 60% | 2 | 45%
FCR | 80% | 3 | 45%
Leads | 45% | 4 | 25%
Leads | 50% | 5 | 25%
Leads | 200% | 6 | 25%
Attrition | 8% | 7 | 10%
Attrition | 12% | 8 | 10%
Attrition | 100% | 9 | 10%
Abandon | 1% | 10 | 20%
Abandon | 5% | 11 | 20%
Abandon | 200% | 12 | 20%
So if i have a Leads score in cell E2 as 3%, then i want output in F2 as Number 4 which is <45% hence 4.
PS: I have a spreadsheet but don't know how to attach it.
Try this in F2:
=INDEX(C:C,AGGREGATE(15,6,ROW(B:B)/((B:B>=E2)*(A:A="Leads")),1))
This will only return matches for rows with "Leads" in column A. This can be made into another reference if you have or want to put that into another cell instead.
EDIT:
Based on you're comment below, this formula works as well if entered as an array (CTRL + SHIFT + ENTER):
=INDEX(C:C,MATCH(1,(A:A="Leads")*(B:B>=E2),0))
EDIT 2:
We can cover our bases for an unsorted list in column B by combining the two solution:
{=INDEX(C:C,MATCH(1,(A:A="Leads")*(B:B=AGGREGATE(15,6,B:B/((B:B>=E2)*(A:A="Leads")),1)),0))}
Say that I gain +5 coins from every room I complete. What I'm trying to do is to make a formula in Excel that gets the total coins I've gotten from the first room to the 100th room.
With C++, I guess it would be something like:
while (lastRoom > 0)
{
totalCoins = lastRoom*5;
lastRoom--;
}
totalCoins, being an array so that you can just output the sum of the array.
So if ever, how do you put this code in excel and get it to work? Or is there any other way to get the total coins?
The are infinite solutions.
One is to build a table like this:
+---+----------+---------------+
| | A | B |
+---+----------+---------------+
| 1 | UserID | RoomCompleted |
| 2 | User 001 | Room 1 |
| 3 | User 002 | Room 1 |
| 4 | User 002 | Room 2 |
| 5 | User 002 | Room 3 |
+---+----------+---------------+
them pivot the spreadsheet to get the following:
+---+----------+-----------------------+
| | A | B |
+---+----------+-----------------------+
| 1 | User | Total Rooms completed |
| 2 | User 001 | 1 |
| 3 | User 002 | 3 |
+---+----------+-----------------------+
where you have the number of completed rooms for each users. You can now multiplicate the number per 5 as a simple formula or (better) as a calculated filed of the pivot.
If I understand you correctly you shouldn't need any special code, just a formula:
=(C2-A2+1)*B2
Where C2 = Nth room, A2 = Previous Room, and B2 = coin reward. You can change A2, B2, or C2 and the formula in D2 will output the result.
You can use the formula for sum of integers less than n: (n - 1)*(n / 2), then multiply it by coin count so you will get something like: 5 * (n - 1)*(n / 2). Then you just hook it up to your table.
Hope it helps
We are working on an application where millions of users will be entering information at the same time. Suppose the application allows people to rate geographic regions on where they would like to live. Each participant is allowed to rate each region using a decimal value from 0-10. Each person belongs to one or more groups based upon attributes such as gender, and people that consider themselves active, or enjoy culture.
Every time a rating is made, we need to have a view which shows us the average rating for each region/group. I'm aware that most DB's have an "average" function, but for our purposes we need to be able to use our own function as we may use a the geometric mean instead of the arithmetic mean.
Below are some tables which might be used. Note: I did not include the relationship table PeopleGroups which map which groups a person is a member of for brevity purposes.
Regions People Groups RegionScoresByPerson
+-----+------------+ +-----+-------+ +-----+----------+ +-----+-----+-------+
| RID | NAME | | PID | Name | | GID | Name | | RID | PID | Score |
+-----+------------+ +-----+-------+ +-----+----------+ +-----+-----+-------+
| 1 | Flordia | | P1 | Alice | | G0 | Everyone | | 1 | P1 | 6 |
| 2 | California | | P2 | Bob | | G1 | Women | | 1 | P2 | 8 |
+-----+------------+ | P3 | Frank | | G2 | Men | | 1 | P3 | 3 |
| P4 | Mary | | G3 | Active | | 1 | P4 | 2 |
+-----+-------+ | G4 | Culture | | 1 | P1 | 7 |
+-----+----------+ | 1 | P2 | 5 |
| 1 | P3 | 8 |
| 1 | P4 | 2 |
+-----+-----+-------+
Our current implementation uses a similar set of tables for storing ratings, but we don't calculate averages real-time. Anytime we need the results (e.g. show me the average score California for women), we have to pull all the information into memory and run the calculations manually.
I was wondering how I leverage database technologies such as views, triggers, stored procedures, etc. to present to me a simple table that will allow me to get scores by for people and groups so we don't have to manually run calculations.
I would like some table like the following, where everything is handled by the DB. Any insert,update,delete actions on the RegionScoresByPerson or Groups tables would automatically be reflected in this table. If it is not apparent, the rows marked with * calculated rows. In this case I'm using a simple arithmetic average, but I the design should allow for any type of function.
EID stands for entity ID (a person or group)
Besides deciding how to build such a view, I'm unsure of what sort of datatypes to use (and index) for People and Groups. I suppose I'd like the index to be integers, but that would prevent me from creating the table below because I couldn't distinguish between Person 1 and Group 1 -- Would having ID's such as P1 and G1 be a performance hit? I'm obviously concerned about the design being scalable.
ScoreView
+-----------+-----+-------+
| RID | EID | Score |
| 1 | P1 | 6 |
| 1 | P2 | 8 |
| 1 | P3 | 3 |
| 1 | P4 | 2 |
| 1 | P1 | 7 |
| 1 | P2 | 5 |
| 1 | P3 | 8 |
| 1 | P4 | 2 |
| 1 | G0 | 4.75 |*
| 1 | G1 | 4 |*
| 1 | G2 | … |*
| 1 | G3 | … |*
+-----------+-----+-------+
Apache Flume is the open source tool designed to solve this kind of problem. Also have a look at Google Cloud Dataflow.
https://flume.apache.org/
I have "components" which can be assembled in different ways into a "system". I want my database to hold all these "components", their type specific data and define how they are connected to each other to form a "system".
The systems are typically gearboxes and they can have rather complex branched designs. Let's start with an easy example:
This system is built up out of Masses (horizontal lines) and Stiffnesses (vertical lines). Gears and clutches are types of masses and come in pairs. Colors represent different branch speeds due to gear ratios. Here's a (bad) example of how I could store everything from this particular illustration:
ID | Type | Clutch | Ends | DrivenBy | NoOfTeeth| Mass | Stiffness
--- | ---- | ------ | ---- | --------- | -------- | ---- | ---------
1 | Mass | | Input1 | | | 5 |
2 | Stiffness | | | | | | 15
3 | Mass | 1.1 | | | | 2 |
4 | Mass | 1.2 | | | | 3 |
5 | Stiffness | | | | | | 20
6 | Gear | | | | 10 | 4 |
7 | Stiffness | | | | | | 30
8 | Gear | | | | 4 | 5 |
9 | Gear | | | 8 | 7 | 2 |
10 | Stiffness | | | | | | 40
11 | Mass | | | | | 4 |
12 | Stiffness | | Output1 | | | | 10
13 | Gear | | | 6 | 5 | 4 |
14 | Stiffness | | | | | | 20
15 | Mass | 2.1 | | | | 4 |
16 | Mass | 2.2 | | | | 3
17 | Stiffness | | | | | | 30
18 | Mass | | Output2 | | | 2 |
Obviously, this is not a very good way to store the data. This design pattern resembles somewhat of a "Repeated attributes" since each component type has a different attribute to be filled. I could create a table for each type of component, but things become more complex when looking at other examples, such as this 2-stage gearbox:
There are also examples with more than 1 input and several outputs, but I can't post more links due to low reputation.
Eitherway, you will see that the usual hierarchical data storage doesn't apply here because the data is not purely "tree-shaped" where everything branches off from 1 main branch.
I think that even though I could store data in the above mentioned way, I will get huge difficulties when it comes to the programming stage.
To add to the complexity, these gearboxes are actually sub-systems to a much bigger system.
So, any suggestions on a good way to store this type of data?*
Perhaps this is a possible way of doing it?
Here you will see that there is a "main" table called GearboxBranch, keeping track of all elements in the gearbox, giving them an id and to identify in which branch the element exists.
Then for the elements themselves, masses are defined in their dedicated table, so are stiffnesses. Gears and Clutches (which are types of masses) are then defined in their perspective tables. A recursive relationship is existing in the gear table, since one gear has to be driven by at least one other gear.
Furthermore, the table with Shaft Ends defines which of the elements in the gearbox are input or output and what number they have.
I can't seem to see any problems with this method, but I'm a little unsure how to get data out of the database. There will be considerable coding involved I'm afraid.