Provided the below values
start value = 1
End Value = 20
Interval = 5
I have been provided a number 6. I have to find the range of numbers in which the number 6 falls say now the answer is 6-10.
If the given number is greater than the end value then return the same number.
Is there any formula so that i can generate the range for the number?
UPDATE
I tried the below solution, But it is not working if the range interval is changed,
$end_value = $start_value + $range_interval;
// we blindly return the last term if value is greater than max value
if ($input_num > $end_value) {
return '>' . $end_value;
}
// we also find if its a first value
if ($input_num <= $end_value && $value >= $start_value) {
return $start_value . '-' . $end_value;
}
// logic to find the range for a given integer
$dived_value = $input_num/$end_value;
// round the value to get the exact match
$rounded_value = ceil($dived_value);
$upper_bound_range = $rounded_value*$end_value;
$lower_bound_range = $upper_bound_range - $end_value;
return $lower_bound_range . '-'. $upper_bound_range;
In (c-style) pseudocode:
// Integer division assumed
rangeNumber = (yourNumber - startValue) / rangeLength;
lower_bound_range = startValue + rangeNumber*rangeLength;
upper_bound_range = lower_bound_range + rangeLength-1;
For your input:
rangeNumber = (6-1)/5 = 1
lower_bound_range = 1 + 5*1 = 6
upper_bound_range = 10
and so range is [6, 10]
The answer depends on whether you talk about integers or floats. Since all your example numbers are integers, I assume you talk about those. I further assume that all your intervals contain the same number of integers, in your example 5, namely 1...5, 6...10, 11...15, and 16...20. Note that 0 is not contained in the 1st interval (otherwise the 1st interval had 6 numbers).
In this case the answer is easy.
Let be:
s the start value that is not contained in the 1st interval,
i the interval size, i.e. the number of integers that it contains,
p the provided number to which an interval should be assigned,
b the 1st integer in this interval, and
e the last integer in this interval.
Then:
b = s + (p-s-1)\i * i + 1 (here, "\" means integer division, i.e. without remainder)
e = b + i - 1
In your example:
s = 0, i = 5, p = 6, thus
b = 0 + (6-0-1)\5 * 5 + 1 = 6
e = 6 + 5 - 1 = 10
Related
I'd like to request help in form of pseudo-code for bouncing or "ping-ponging" a number in a range, by which I mean adding a number to another value in a range, where that number instead of exceeding the range or being clamped to it, is continuously bounced back into it.
Example
Consider the following variables:
Range: (-2, 2)
Starting value in the range: 1
Added value: 14
The number would start at 1 and go through 14 alterations, as following:
2
1
0
-1
-2
-1
0
1
2
1
0
-1
-2
-1
The code I am trying to write would only return the final number of this sequence, which is -1.
Specifications
— The code must not use a while loop.
— The code must be able to work with non-integer values.
— The code must be efficient and fail-proof.
Thank you in advance.
Just have a for loop that goes for the number of steps specified.
Inside the loop add to a running total the value of each step using a variable to hold the step value, and when you hit the limit multiply the step value by -1 to get it going in the other direction.
For the number of steps required
Add value to total
If total exceeds upper limit
Value *= -1
If value is less than lower limit
Value *= -1
Return the total when the loop ends
Edit: I'm on my phone and psedocode bit formatting got borked
First, compute cycle = 2 * (max - min) and find the largest integer n such that cycle * n is less than or equal to added value. One way to do this is to calculate full cycles = round_toward_zero(added value / cycle). We can immediately subtract from added value the value cycle * full cycles because moving by cycle returns you to where you started and headed in the same direction, so we only need to consider the portion of added value that is strictly greater than an even multiple of cycle. Let us define modified value = added value - cycle * full cycles.
Next, calculate position = starting position + modified value. Given that min <= starting position <= max, there are three cases for position:
position < min. In this case, modified value must have been negative, so we can simply "bounce right" by calculating position' = min + (min - position). There are two sub-cases now:
min <= position' <= max: simply return position' as the answer
max < position': we must "bounce back" again by calculating position'' = max - (position' - max). This time, position'' is guaranteed to be between min and max since modified value is guaranteed to to be between -2 * (max - min) and 0... so just return position''.
min <= position <= max. In this case, no additional bouncing is required, so just return position.
position > max. In this case, modified value must have been positive, so we can simply "bounce left" by calculating position' = max - (position - max). There are two sub-cases now:
position' < min: we must "bounce back" again by calculating position'' = min + (min - position'). This time, position'' is guaranteed to be between min and max since modified value is guaranteed to be between 0 and 2 * (max - min)... so just return position''.
min <= position' <= max: simply return position' as the answer
Example:
Range: (-2, 2)
Starting value in the range: 1
Added value: 14
min = -2
max = 2
starting position = 1
added value = 14
cycle = 2 * (max - min) = 2 * 4 = 8
full cycles = round_toward_zero(added value / cycle)
= round_toward_zero(14 / 8)
= round_toward_zero(1.75)
= 1
modified value = added value - cycle * full cycles
= 14 - 8 * 1
= 6
position = starting position + modified value
= 1 + 6
= 7
position = 7 > 2 = max
position' = max - (position - max)
= 2 - (7 - 2)
= 2 - 5
= -3
position' = -3 < -2 = min
position'' = min + (min - position')
= -2 + (-2 - -3)
= -2 + 1
= -1
Now, this might seem like a lot of calculations. For small numbers of steps, it might be faster just to do a loop. However, for large added values, this approach is significantly better.
I'm writing a diploma about vaccines. There is a region, its population and 12 month. There is an array of 12 values from 0 to 1 with step 0.01. It means which part of population should we vaccinate in every month.
For example if we have array = [0.1,0,0,0,0,0,0,0,0,0,0,0]. That means that we should vaccinate 0.1 of region population only in first month.
Another array = [0, 0.23,0,0,0,0,0,0, 0.02,0,0,0]. It means that we should vaccinate 0.23 of region population in second month and 0.02 of region population in 9th month.
So the question is: how to generate (using 3 loops) 12(months) * 12(times of vaccinating) * 100 (number of steps from 0 to 1) = 14_400 number of arrays that will contain every version of these combinations.
For now I have this code:
for(int month = 0;month<12;month++){
for (double step = 0;step<=1;step+=0.01){
double[] arr = new double[12];
arr[month] = step;
}
}
I need to add 3d loop that will vary number of vaccinating per year.
Have no idea how to write it.
Idk if it is understandable.
Hope u get it otherwise ask me, please.
You have 101 variants for the first month 0.00, 0.01..1.00
And 101 variants for the second month - same values.
And 101*101 possible combinations for two months.
Continuing - for all 12 months you have 101^12 variants ~ 10^24
It is not possible to generate and store so many combinations (at least in the current decade)
If step is larger than 0.01, then combination count might be reliable. General formula is P=N^M where N is number of variants per month, M is number of months
You can traverse all combinations representing all integers in range 0..P-1 in N-ric numeral system. Or make digit counter:
fill array D[12] with zeros
repeat
increment element at the last index by step value
if it reaches the limit, make it zero
and increment element at the next index
until the first element reaches the limit
It is similar to counting 08, 09, here we cannot increment 9, so make 10 and so on
s = 1
m = 3
mx = 3
l = [0]*m
i = 0
while i < m:
print([x/3 for x in l])
i = 0
l[i] += s
while (i < m) and l[i] > mx:
l[i] = 0
i += 1
if i < m:
l[i] += s
Python code prints 64 ((mx/s+1)^m=4^3) variants like [0.3333, 0.6666, 0.0]
I'm writing a VBScript that sends out a weekly email with client activity. Here is some sample data:
a b c d e f g
2,780 2,667 2,785 1,031 646 2,340 2,410
Since this is email, I don't want a chart with a trend line. I just need a simple function that returns "up", "down" or "stable" (though I doubt it will ever be perfectly stable).
I'm terrible with math so I don't even know where to begin. I've looked at a few other questions for Python or Excel but there's just not enough similarity, or I don't have the knowledge, to apply it to VBS.
My goal would be something as simple as this:
a b c d e f g trend
2,780 2,667 2,785 1,031 646 2,340 2,410 ↘
If there is some delta or percentage or other measurement I could display that would be helpful. I would also probably want to ignore outliers. For instance, the 646 above. Some of our clients are not open on the weekend.
First of all, your data is listed as
a b c d e f g
2,780 2,667 2,785 1,031 646 2,340 2,410
To get a trend line you need to assign a numerical values to the variables a, b, c, ...
To assign numerical values to it, you need to have little bit more info how data are taken. Suppose you took data a on 1st January, you can assign it any value like 0 or 1. Then you took data b ten days later, then you can assign value 10 or 11 to it. Then you took data c thirty days later, then you can assign value 30 or 31 to it. The numerical values of a, b, c, ... must be proportional to the time interval of the data taken to get the more accurate value of the trend line.
If they are taken in regular interval (which is most likely your case), lets say every 7 days, then you can assign it in regular intervals a, b, c, ... ~ 1, 2, 3, ... Beginning point is entirely your choice choose something that makes it very easy. It does not matter on your final calculation.
Then you need to calculate the slope of the linear regression which you can find on this url from which you need to calculate the value of b with the following table.
On first column from row 2 to row 8, I have my values of a,b,c,... which I put 1,2,3, ...
On second column, I have my data.
On third column, I multiplied each cell in first column to corresponding cell in second column.
On fourth column, I squared the value of cell of first column.
On row 10, I added up the values of the above columns.
Finally use the values of row 10.
total_number_of_data*C[10] - A[10]*B[10]
b = -------------------------------------------
total_number_of_data*D[10]-square_of(A[10])
the sign of b determines what you are looking for. If it's positive, then it's up, if it's negative, then it's down, and if it's zero then stable.
This was a huge help! Here it is as a function in python
def trend_value(nums: list):
summed_nums = sum(nums)
multiplied_data = 0
summed_index = 0
squared_index = 0
for index, num in enumerate(nums):
index += 1
multiplied_data += index * num
summed_index += index
squared_index += index**2
numerator = (len(nums) * multiplied_data) - (summed_nums * summed_index)
denominator = (len(nums) * squared_index) - summed_index**2
if denominator != 0:
return numerator/denominator
else:
return 0
val = trend_value([2781, 2667, 2785, 1031, 646, 2340, 2410])
print(val) # -139.5
in python:
def get_trend(numbers):
rows = []
total_numbers = len(numbers)
currentValueNumber = 1
n = 0
while n < len(numbers):
rows.append({'row': currentValueNumber, 'number': numbers[n]})
currentValueNumber += 1
n += 1
sumLines = 0
sumNumbers = 0
sumMix = 0
squareOfs = 0
for k in rows:
sumLines += k['row']
sumNumbers += k['number']
sumMix += k['row']*k['number']
squareOfs += k['row'] ** 2
a = (total_numbers * sumMix) - (sumLines * sumNumbers)
b = (total_numbers * squareOfs) - (sumLines ** 2)
c = a/b
return c
trendValue = get_trend([2781,2667,2785,1031,646,2340,2410])
print(trendValue) # output: -139.5
Using a random library with these functions:
randomChance(p) Returns true with the probability indicated by p.
randomInteger(low, high) Returns a random integer in the range low to high, inclusive.
what is the easiest way to implement a "random selector" that takes consideration of percentage, 1/4 or 1/3 etc... I got a array with key/value pairing. For example "a" migth have the value 2 and "b" have the value 2. 1/2 chance for both.
The max value will be the size of the array, cause it only contains unique items. The randomChance() function ranges between 0.0 - 1.0 where 1 = 100%. If my array size is, say 4. What is the best way of "letting 4 be 1".
Lets say you have:
a = 2, b = 2, c = 1, d = 3
now make it:
a = 2, b = 4, c = 5, d = 8
Create a random number from 1 to MaxVal (value of the last key, 8 in this example). Select the first Key where Value >= RandomNum
EDIT
I made a small VB.Net to show the algorithm and how it works. The code is not meant to be: Good, elegant, performant or readable.
Module Module1
Private Class Value
Public vOrg, vRecalc, HitCount As Integer
Public Key As String
Public Sub New(s, v1, v2, c)
Key = s : vOrg = v1 : vRecalc = v2 : HitCount = c
End Sub
End Class
Sub Main()
' set initial values
Dim KVP() As Value = {New Value("A", 2, 0, 0),
New Value("B", 2, 0, 0),
New Value("C", 1, 0, 0),
New Value("D", 3, 0, 0)}
' recalc values
For i = 0 To KVP.Length - 1
If i = 0 Then KVP(0).vRecalc = KVP(0).vOrg Else KVP(i).vRecalc = KVP(i).vOrg + KVP(i - 1).vRecalc
Next
' do test
Dim r As New Random
Dim runs As Integer = 1000 * 1000, maxval As Integer = KVP(KVP.Length - 1).vRecalc
For i = 1 To runs
Dim RandVal = r.Next(1, maxval + 1)
Dim chosen As Integer = (From j In Enumerable.Range(0, KVP.Length) Where KVP(j).vRecalc >= RandVal Take 1 Select j)(0)
KVP(chosen).HitCount += 1
Next
' ouput results
For Each kv In KVP
Console.WriteLine("{0} was chosen with {1:F3} propability, expected was {2:F3}", kv.Key, kv.HitCount / CDbl(runs), kv.vOrg / CDbl(maxval))
Next
Console.ReadLine()
End Sub
End Module
An output sample:
A was chosen with 0.250 propability, expected was 0.250
B was chosen with 0.251 propability, expected was 0.250
C was chosen with 0.124 propability, expected was 0.125
D was chosen with 0.375 propability, expected was 0.375
just multiply the randomChance() outcome and the array length together. It'll give you the index in the range [0,array_length-1] which you can use to access the array
array_index = (unsigned int)(randomChance(p) * (array_length - 1));
maybe you mean "letting 3 to be 1" (not 4) in your example. The last index of an array of length 4 is 3.
For ex.
double size = 10.35;
i should get
value = 1035;
exponent = -2;
so when i re calculate i will get 10.35.
i.e 1035 * 10^-2 = 10.35;
Please help me.
Thanks in advance
In general this is not possible since the fractional part of a double is stored in powers-of-2, and might or might not match powers-of-10.
For example: When looking at powers-of-2 vs powers-of-3: Just like 1/2 == 2^-1 == 5 * 10^-1 has a match, 1/3 == 3^-1 == ?? does not have a match.
However, you can approximate it.
It would have an answer if you would ask for powers-of-2. In that case you can just look at the double representation (see IEEE-754 here) and extract the right bits.
Very simplistically (in C#):
double size = 10.36;
int power = 0;
while (size != (int)size)
{
size *= 10.0;
power--;
}
Console.WriteLine("{0} * 10 to the {1}", size, power);
Though I'm sure with a bit more thought a more elegant solution can be found.
This doesn't go the other way where you've got a large number (103600 say) and want to get the smallest value to some power (1036 * 10^2).
I had to do something very similar. Here's a solution in Python (it hasn't been tested very well):
def normalize(value, fdigits=2):
"""
Convert a string representing a numerical value to value-digit/exponent form.
Round the fractional portion to the given number of digits.
value the value (string)
fdigits the number of digits to which to round the fractional
portion
"""
# if empty string, return error
if not value:
return None
# split value by decimal
v = value.split('.')
# if too many decimals, return error
if len(v) > 2:
return None
# add empty string for fractional portion if missing
elif len(v) == 1:
v.append('')
# assign whole and fractional portions
(w, f) = v
# pad fractional portion up to number of significant digits if necessary
if len(f) < fdigits:
f += ('0' * (fdigits - len(f)))
# if the number of digits in the fractional portion exceeds the
# number of digits allowed by fdigits
elif len(f) > fdigits:
# convert both portions to integers; use '0' for whole portion if missing
(wi, fi) = (int(w or '0'), int(f[:fdigits]))
# round up if first insignificant digit is gteq 5
if int(f[fdigits]) >= 5:
fi += 1
# roll whole value up if fractional portion rounds to a whole
if len(str(fi)) > fdigits:
wi += 1
fi = 0
# replace the whole and fractional strings
(w, f) = (str(wi), ("%0" + str(fdigits) + "d") % fi)
# derive value digits and exponent
n = w.lstrip() + f
l = len(n)
x = -fdigits
n = n.rstrip('0')
x += (l - len(n))
# return value digits and exponent
return (int(n), x)