Okay, so honestly this is a homework question, but I really did my best to find the solution, and I think I partially did.
The question:
We are given a series of cities whose positions are symbolized with only one coordinate and we are supposed to implement a given number of hospitals to cities so that the sum of each cities' distance to nearest hospital will be minimum.
That is, if we are given the cities at 1, 3, 5, 7, 9, 11, 13 and if we are going to put 3 hospitals, the hospitals will be at 3, 7, 11 (actually there could be multiple best solutions for this one, did not check).
We are advised to use dynamic programming and first check the case in which we implement only one hospital.
I've figured out finding the subsequent hospital's location. I create a table, and of cities. Then to each cell, I put either the city of the current rows' distance to closest hospital that already build or city's distance to city of the corresponding column.
For example, if we already implemented a hospital to 1, it would be like:
*-1-3-5-7-9-11-13
1|0|0|0|0|0|0||0|
3|2|0|2|2|2|2|2|
5|4|2|0|2|4|4|4|
..............
then sum the columns and find the next hospital.
The problem is, I cannot figure out the first hospital that I'm supposed to build!!
When I manually add one of the element of the actual solution, I can get the right answer so my partial solution should be true.
BTW complexity should be O(CityNum^2), hospitalNum is a constant. So I can't use bruteforce.
An example input and output (from the homework assg):
Input:
10 5 (10 is city num, 5 is hospital num)
1 2 3 6 7 9 11 22 44 50 (coordinates)
Output:
9 (sum of minimum distances)
Related
I have a range of cells in excel. How to increment numbers when meeting data validation from three different columns?
I tried using formula COUNTIF($A$2:A2,A2) which creates a number sequence. But I have other data to validate from another column for it to return the correct number sequence.
First validation: count the emp no in column range A1:A5 which return a result under Hierarchy column.
Second validation: check the % value under column L as per below level of hierarchy in which the problem comes from.
1 - 0.25
2 - 0.25
3 - 0.5
4 - 0.5
5 - 1
Third validation: check the type of Relation (see Relation column) that needs to check when returning number of sequence too. Below is the Relation Level table.
I don't know on how to join these three conditions for the result to be as below.
My really problem here is on how will i get a sequence number if a person does have 3 children and should be tagged as 2,3,4 (next to spouse which is 1) then the next relation which is parent will be tagged then as next number sequence from the last count of child wherein will be 5 given that as per relation table, Parent level is 3 but it will be adjusted as per count of relations a person has. And for this specific instance, if Parent count will be 5, it still should have 0.5 EE % (see relation table level vs % hierarchy level) even though the count of number is 5. I hope this will make sense. But let me know if you have any questions.
Hope someone could help me on this coz I am not that expert when it comes to excel formula. Thank you!
For a project we are making an Excel file for the WK in Russia.
So I need the following things (if its possible only nesting):
TOTO: the home team wins = 1, away team wins = 2, its equal = 3
This is what I have right now for these:
IF(F5<H5;"2";IF(F5>H5;"1";IF(F5;"3";IF(H5;"3";""))))
This works but if I set the score 0-0 then I get 0 back in stead of 3.
Then the next one:
If they gambled that the home team score is correct they get 2 points,
If they gambled that the away team score is correct they get 2 points
If they gambled that the TOTO is correct: 5 points
If all is correct: 1 bonus point
What i mean with the second thing is if somebody says that the score is 2-1 and the game ends on 0-1 then i get 2 points (one for the TOTO and 1 point for the team that scored 0-1).
E.g. Belgium-Tunis (player1) on 2-1 with TOTO = 1. Game ends on 0-1. Player1 gets 2 points in total because he predict the goals of Tunis correct.
Last but not least:
IF the teams are going to the quarter finals,... are coming a few lines on it:
Country good: 10 points
European champ correct: 25 points
Total yellow: 20 points
TOtal red: 20 points.
I believe the formula you want for the first of your questions (the home team wins = 1, away team wins = 2, its equal = 3) is:
=IF(F5<H5,"2",IF(F5>H5,"1",IF(F5=H5,"3","")))
Not sure why you have the numbers in speech marks (have left as is in the above) you could have:
=IF(F5<H5,2,IF(F5>H5,1,IF(F5=H5,3,"")))
Which would probably be easier if you want to do any maths with the values.
It's not entirely clear what you're asking with the rest of the question(s).
The following pseudocode finds the smallest number of coins needed to sum upto S using DP. Vj is the value of coin and min represents m as described in the following line.
For each coin j, Vj≤i, look at the minimum number of coins found for the i-Vjsum (we have already found it previously). Let this number be m. If m+1 is less than the minimum number of coins already found for current sum i, then we write the new result for it.
1 Set Min[i] equal to Infinity for all of i
2 Min[0]=0
3
4 For i = 1 to S
5 For j = 0 to N - 1
6 If (Vj<=i AND Min[i-Vj]+1<Min[i])
7 Then Min[i]=Min[i-Vj]+1
8
9 Output Min[S]
Can someone explain the significance of the "+1 " in line 6? Thanks
The +1 is because you need one extra coin. So for example, if you have:
Vj = 5
Min[17] = 4
And you want to know the number of coins it will take to get 22, then the answer isn't 4, but 5. It takes 4 coins to get to 17 (according to the previously calculated result Min[17]=4), and an additional one coin (of value Vj = 5) to get to 22.
EDIT
As requested, an overview explanation of the algorithm.
To start, imagine that somebody told you you had access to coins of value 5, 7 and 17, and needed to find the size of the smallest combination of coins which added to 1000. You could probably work out an approach to doing this, but it's certainly not trivial.
So now let's say in addition to the above, you're also given a list of all the values below 1000, and the smallest number of coins it takes to get those values. What would your approach be now?
Well, you only have coins of value 5, 7, and 23. So go back one step- the only options you have are a combination which adds to 995 + an extra 5-value coin, a combination which adds to 993 + an extra 7-value, or a combination up to 977 + an extra 23-value.
So let's say the list has this:
...
977: 53 coins
...
993: 50 coins
...
995: 54 coins
(Those examples were off the top of my head, I'm sure they're not right, and probably don't make sense, but assume they're correct for now).
So from there, you can see pretty easily that the lowest number of coins it will take to get 1000 is 51 coins, which you do by taking the same combination as the one in the list which got 993, then adding a single extra 7-coin.
This is, more or less, what your algorithm does- except instead of aiming just to calculate the number for 1000, it's aim would be to calculate every number up to 1000. And instead of being passed the list for lower numbers in from somewhere external, it would keep track of the values it had already calculated.
I'm trying to design an excel formula for some golf game scores. Golfers get points based on a random number (0-9) and the last digit of their score. So, if the random number is 0 and the golfers score ends in 0, they get 10 points. Still with a 0 random number, if the golfers score ends in a 1, they get 9 points. 8 points for a last digit of 2. 7 for 3. 6 for 4. 10 for 5. 9 for 6. 8 for 7. 7 for 8. 6 for 9.
Score ends in: Points:
0 10
1 9
2 8
3 7
4 6
5 10
6 9
7 8
8 7
9 6
As long as I come up with one formula for the random number of 0, I can adjust it for the remaining 9 random numbers.
The way I was hoping for this to work was to just be able to enter the scores into one column and then have the points calculated in a separate column. There will also have to be a cell where I enter the random number.
Any help is appreciated!
You can use something like this to get the score if the random number is 0:
=IF(A1=0,10-MOD(RIGHT(B1),5))
This will give the points you mentioned provided:
A1 is the cell containing the random number
B1 is the cell containing the points of the golfer.
The main formula here is:
10-MOD(RIGHT(B1),5)
RIGHT() takes the last digit of the points. MOD(,5) will get the remainder when this digit is divided by 5.
When you have 0, you get no remainder, hence 0.
When you have 1, you get a remainder of 1, hence 1.
When you have 2, you get a remainder of 2, hence 2.
When you have 6, you get a remainder of 1, hence 1 again.
Then 10 minus that remainder gives you the points you're looking for.
You could certainly use =RAND()*10to get a random value in excel. Or to get a value without commas use = ROUNDDOWN(RAND()*10;0)
Then you add something a VLOOKUPto get a value to each players score. RIGHT(A1;1)gives you the last value of a field.
VLOOKUPrequires you to have a table somewhere with the values for each score as you described.
edit: the MOD solution looks even better. Please note that RANDOM gets a fresh value everytime you refresh the XLS sheet. so probably use it to get a value and put that into another field manually.
Need to try and get a result based on possible 3 lookups in Excel.
I have a price for a certain size hire vehicle and need to check to see if I want to add in a supplement or not based on entry into a cell in another sheet.
I have a sheet called Keys that has the criteria I base my calculations on and a second sheet I have the rates loaded for all the vehicle sizes available, cars to coaches. I would like to calculate the supplement for customers of the move to a larger vehicle or even a reduction dependent on what I choose.
Keys data is:
Vehicle Sizes
Range # Seats Rate Column Supplement Range to work on
1 4 R N
2 7 S Y 1
3 16 T N
4 24 U Y 5
5 29 V N
6 35 W N
7 45 X N
So for example if the I have chosen to calculate the supplement on the 7 seater then I want to calculate the difference between the 7 seater and 4 seater and that is my supplement. I have also chosen to calculate the reduction between the 29 and 24 seater vehicles.
Am trying to figure out how to combine multiple IF and LOOKUP, if they are correct or not.
So basically IF I have a Y in the supplement column on Keys then calculate the difference in the rates based on the Rate Column based on the Range to work on.
Any suggestions or help appreciated
Sorry think I forgot about the actual rates. They are stored on another sheet as per below. the charges are per service, like an airport transfer etc., they are in VN Dong so thats why they are in the 100,000 + range.
R S T U V W X
Rate with Surcharge
4 7 16 24 29 35 45
340000 373000 394000 735000 780000 1050000 1210000
I have tried to tweak the answer from pnuts but getting a bit lost, note sure if I need the MATCH in the formula of not.
I doubt this will suit but it may help to clarify your requirements:
=IF($D2="N","",INDEX(Sheet2!$Q$2:$X$4,MATCH(F$1,Sheet2!$Q$2:$Q$4,0),CODE($C2)-80)-INDEX(Sheet2!$Q$2:$X$4,MATCH(F$1,Sheet2!$Q$2:$Q$4,0),CODE($C2)+$E2-$A1-81))
in F2 copied across and down to suit.