Ruby array subtraction without removing items more than once - ruby

The canonical Array difference example in Ruby is:
[ 1, 1, 2, 2, 3, 3, 4, 5 ] - [ 1, 2, 4 ] #=> [ 3, 3, 5 ]
What's the best way to get the following behavior instead?
[ 1, 1, 2, 2, 3, 3, 4, 5 ].subtract_once([ 1, 2, 4 ]) #=> [ 1, 2, 3, 3, 5 ]
That is, only the first instance of each matching item in the second array is removed from the first array.

Subtract values as many times as they appear in the other array, or any Enumerable:
class Array
# Subtract each passed value once:
# %w(1 2 3 1).subtract_once %w(1 1 2) # => ["3"]
# [ 1, 1, 2, 2, 3, 3, 4, 5 ].subtract_once([ 1, 2, 4 ]) => [1, 2, 3, 3, 5]
# Time complexity of O(n + m)
def subtract_once(values)
counts = values.inject(Hash.new(0)) { |h, v| h[v] += 1; h }
reject { |e| counts[e] -= 1 unless counts[e].zero? }
end
Subtract each unique value once:
require 'set'
class Array
# Subtract each unique value once:
# %w(1 2 2).subtract_once_uniq %w(1 2 2) # => [2]
# Time complexity of O((n + m) * log m)
def subtract_once_uniq(values)
# note that set is implemented
values_set = Set.new values.to_a
reject { |e| values_set.delete(e) if values_set.include?(e) }
end
end

class Array
def subtract_once(b)
h = b.inject({}) {|memo, v|
memo[v] ||= 0; memo[v] += 1; memo
}
reject { |e| h.include?(e) && (h[e] -= 1) >= 0 }
end
end
I believe this does what I want. Many thanks to #glebm

This is all I can think of so far:
[1, 2, 4].each { |x| ary.delete_at ary.index(x) }

Similar to #Jeremy Ruten's answer but accounting for the fact that some elements may not be present:
# remove each element of y from x exactly once
def array_difference(x, y)
ret = x.dup
y.each do |element|
if index = ret.index(element)
ret.delete_at(index)
end
end
ret
end
This answer also won't modify the original array as it operates, so:
x = [1,2,3]
y = [3,4,5]
z = array_difference(x, y) # => [1,2]
x == [1,2,3] # => [1,2,3]

Related

Reversed sequence in Ruby

How do I return an array of integers from n to 1 where n>0? I wrote this code:
def reverse_seq(num)
reverse_seq = []
[].reverse { |num| num > 0; num += 1 }
return []
end
Thanks!
You could create an enumerator via downto that goes from n down to 1 and turn that into an array:
n = 5
n.downto(1).to_a
#=> [5, 4, 3, 2, 1]
or you could call Array.new with a block and calculate each value based on its index:
n = 5
Array.new(n) { |i| n - i }
#=> [5, 4, 3, 2, 1]
or you could traverse a n..1 range by passing -1 to step:
n = 5
(n..1).step(-1).to_a
#=> [5, 4, 3, 2, 1]
Or
(1..5).to_a.reverse
#=> [5, 4, 3, 2, 1]
Or if you want to iterate over those elements in a next step anyway, use reverse_each
(1..5).reverse_each { |i| puts i }
#=> 5
4
3
2
1
As of 2.7 you can also use Enumerator#produce which is my new favorite way to create sequences.
For your use case:
def reverse_seq(num)
Enumerator.produce(num) {|prev| prev.positive? ? prev.pred : raise(StopIteration) }
end

Ruby how to reverse display order

I have code below:
def number_loop(n)
puts "#{n}"
while n != 1
if n >1
n -= 1
puts "#{n}"
else
n += 1
puts "#{n}"
end
end
end
number_loop(5)
when I ran the code, it displayed as below:
5
4
3
2
1
how to change the code so that it will display as:
1
2
3
4
5
Using a while loop is rare and almost never seen in Ruby.
When working with numbers use upto and downto methods or a range.
When working with objects use each and reverse_each.
Using Integer methods
1.upto(5).each { |n| puts n } # => 1, 2, 3, 4, 5
5.downto(1).each { |n| puts n } # => 5, 4, 3, 2, 1
1.step(5, 2).each { |n| puts n } # => 1, 3, 5
5.step(1, -2).each { |n| puts n } # => 5, 3, 1
5.times { |n| puts n } # => 0, 1, 2, 3, 4
Using a range
(1..5).each { |n| puts n } # => 1, 2, 3, 4, 5
And if you work with objects use
arr = ["a", "b", "c", "d", "e"]
arr.each { |str| puts str } # => a, b, c, d, e
arr.reverse_each { |str| puts str } # => e, d, c, b, a
And use map if you want to collect the results in an array
squares = (1..5).map { |n| n * n }
# => [1, 4, 9, 16, 25]
For more browse the methods of
Integer class
Enumerable module
And best install pry to explore these interactively with Pry's ls and ri commands.

Ruby Arrays - Find the sums of the diagonals

Haven't seen this one before, but I was wondering how you can find the sums of both diagonals of a 2D array in Ruby. Say you have a simple array, with 3 rows and 3 columns.
array = [1,2,3,4,5,6,7,8,9]
I can break it into groups of three by using
array.each_slice(3).to_a
Would now be
[1,2,3], [4,5,6], [7,8,9]
[1,2,3]
[4,5,6]
[7,8,9]
In this case, the diagonals are
1 + 5 + 9 = 15
3 + 5 + 7 = 15
So the total sum would be 15 + 15 = 30
I was thinking I could do something like
diagonal_sum = 0
for i in 0..2
for j in 0..2
diagonal_sum += array[i][j]
end
end
Here is my try :
array = [1,2,3,4,5,6,7,8,9]
sliced = array.each_slice(3).to_a
# As sliced size is 3, I took 2, i.e. 3 - 1
(0..2).map { |i| sliced[i][i] } #=> [1, 5, 9]
(0..2).map { |i| sliced[i][-i-1] } # => [3, 5, 7]
(0..2).map { |i| sliced[i][i] }.reduce :+
# => 15
(0..2).map { |i| sliced[i][-i-1] }.reduce :+
# => 15
As per the above observation it seems in one iteration you can do solve :
left_diagonal, right_diagoal = (0..2).each_with_object([[], []]) do |i, a|
a[0] << sliced[i][i]
a[1] << sliced[i][-i-1]
end
left_diagonal.reduce(:+) # => 15
right_diagonal.reduce(:+) # => 15
Added, OOP style of code :
class SquareMatrix
attr_reader :array, :order
def initialize array, n
#array = array.each_slice(n).to_a
#order = n
end
def collect_both_diagonal_elements
(0...order).collect_concat { |i| [ array[i][i], array[i][-i-1] ] }
end
def collect_left_diagonal_elements
(0...order).collect { |i| array[i][i] }
end
def collect_right_diagonal_elements
(0...order).collect { |i| array[i][-i-1] }
end
def sum_of_diagonal_elements type
case type
when :all then collect_both_diagonal_elements.reduce(0, :+)
when :right then collect_right_diagonal_elements.reduce(0, :+)
when :left then collect_left_diagonal_elements.reduce(0, :+)
end
end
end
array = [1,2,3,4,5,6,7,8,9]
sqm = SquareMatrix.new array, 3
sqm.collect_both_diagonal_elements # => [1, 3, 5, 5, 9, 7]
sqm.sum_of_diagonal_elements :all # => 30
sqm.collect_left_diagonal_elements # => [1, 5, 9]
sqm.sum_of_diagonal_elements :left # => 15
sqm.collect_right_diagonal_elements # => [3, 5, 7]
sqm.sum_of_diagonal_elements :right # => 15
The following is mostly for the academic discussion:
For the main diagonal, you are looking for the "Trace" function which is defined for the "Matrix" class. So the following will work (although it doesn't get you the other diagonal and I wouldn't bet on its efficiency):
require 'Matrix'
a = array.each_slice(3).to_a
Matrix[*a].trace
To get the other diagonal you have to somehow "flip" the matrix, so the following seems to work (Since the result of each_slice is an array of rows, reverse reverses the order of the row. Reversing the order of the columns is more difficult):
Matrix[*a.reverse].trace
I totally forgot about #map.with_index ...Thanks to #xlembouras , heres a one-liner
first_diagonal = array.map.with_index {|row, i| row[i]} .inject :+
inverted_diagonal = array.map.with_index {|row, i| row[-i-1]} .inject :+
It's possible to make it a one-liner:
first_diagonal, inverted_diagonal = (array.map.with_index {|row, i| row[i]} .inject :+) , (array.map.with_index {|row, i| row[-i-1]} .inject :+)
Original:
Here's a thought, which makes me think it would be great to have a #map_with_index method:
for a first to last diagonal:
i = -1
array.map { |row| row[i=i+1] }.inject :+
for the last to first diagonal (assuming a square array):
i = array.length
array.map { |row| row[i=i-1] }.inject :+
a = [1,2,3,4,5,6,7,8,9]
p a.values_at(0,2,4,4,6,8).inject(&:+) #=> 30
I would try iterating through the array and keep the values that I need according to the length of the (grouped) array
array = [[1,2,3], [4,5,6], [7,8,9]]
dimension = array.length
array.flatten.map.with_index do |x,i|
x if [0, dimension - 1].include?(i % dimension)
end.compact.inject(:+)
#=> 30
You don't need to first apply slice:
arr = [1,2,3,4,5,6,7,8,9]
We visualize arr as:
1 2 3
4 5 6
7 8 9
n = Math.sqrt(arr.size).round
#=> 3
For the main diagonal:
(0...arr.size).step(n+1).reduce(0) { |t,i| t+arr[i] }
#=> 15
For the off-diagonal:
(n-1..arr.size-n).step(n-1).reduce(0) { |t,i| t+arr[i] }
#=> 15
Another example:
arr = [1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6]
1 2 3 4
5 6 7 8
9 0 1 2
3 4 5 6
n = Math.sqrt(arr.size).round
#=> 4
(0...arr.size).step(n+1).reduce(0) { |t,i| t+arr[i] } +
(n-1..arr.size-n).step(n-1).reduce(0) { |t,i| t+arr[i] }
#=> 14 + 14 => 28
require 'Matrix'
arr = [[1, 3, 4], [2, 5, 7], [6, 7, 8]]
diag1 = Matrix[*arr].tr
diag2 = Matrix[*arr.reverse].tr
def diagonal(array)
single=array.flatten
new=[]
i=array.length-1
while i < single.length-2
new << single[i]
i+=array.length-1
end
new.sum
end
p diagonal([
[1, 2, 3],
[4, 5, 6],
[7, 9, 8],
])
OUTPUT
15
That is for finding the sum of right diagonal of a 2D array

Number of possible equations of K numbers whose sum is N in ruby

I have to create a program in ruby on rails so that it will take less time to solve the particular condition. Now i am to getting the less response time for k=4 but response time is more in case of k>5
Problem:
Problem is response time.
When value of k is more than 5 (k>5) response time is too late for given below equation.
Input: K, N (where 0 < N < ∞, 0 < K < ∞, and K <= N)
Output: Number of possible equations of K numbers whose sum is N.
Example Input:
N=10 K=3
Example Output:
Total unique equations = 8
1 + 1 + 8 = 10
1 + 2 + 7 = 10
1 + 3 + 6 = 10
1 + 4 + 5 = 10
2 + 2 + 6 = 10
2 + 3 + 5 = 10
2 + 4 + 4 = 10
3 + 3 + 4 = 10
For reference, N=100, K=3 should have a result of 833 unique sets
Here is my ruby code
module Combination
module Pairs
class Equation
def initialize(params)
#arr=[]
#n = params[:n]
#k = params[:k]
end
#To create possible equations
def create_equations
return "Please Enter value of n and k" if #k.blank? && #n.blank?
begin
Integer(#k)
rescue
return "Error: Please enter any +ve integer value of k"
end
begin
Integer(#n)
rescue
return "Error: Please enter any +ve integer value of n"
end
return "Please enter k < n" if #n < #k
create_equations_sum
end
def create_equations_sum
aar = []
#arr = []
#list_elements=(1..#n).to_a
(1..#k-1).each do |i|
aar << [*0..#n-1]
end
traverse([], aar, 0)
return #arr.uniq #return result
end
#To check sum
def generate_sum(*args)
new_elements = []
total= 0
args.flatten.each do |arg|
total += #list_elements[arg]
new_elements << #list_elements[arg]
end
if total < #n
new_elements << #n - total
#arr << new_elements.sort
else
return
end
end
def innerloop(arrayOfCurrentValues)
generate_sum(arrayOfCurrentValues)
end
#Recursive method to create dynamic nested loops.
def traverse(accumulated,params, index)
if (index==params.size)
return innerloop(accumulated)
end
currentParam = params[index]
currentParam.each do |currentElementOfCurrentParam|
traverse(accumulated+[currentElementOfCurrentParam],params, index+1)
end
end
end
end
end
run the code using
params = {:n =>100, :k =>4}
c = Combination::Pairs::Equation.new(params)
c.create_equations
Here are two ways to compute your answer. The first is simple but not very efficient; the second, which relies on an optimization technique, is much faster, but requires considerably more code.
Compact but Inefficient
This is a compact way to do the calculation, making use of the method Array#repeated_combination:
Code
def combos(n,k)
[*(1..n-k+1)].repeated_combination(3).select { |a| a.reduce(:+) == n }
end
Examples
combos(10,3)
#=> [[1, 1, 8], [1, 2, 7], [1, 3, 6], [1, 4, 5],
# [2, 2, 6], [2, 3, 5], [2, 4, 4], [3, 3, 4]]
combos(100,4).size
#=> 832
combos(1000,3).size
#=> 83333
Comment
The first two calculations take well under one second, but the third took a couple of minutes.
More efficient, but increased complexity
Code
def combos(n,k)
return nil if k.zero?
return [n] if k==1
return [1]*k if k==n
h = (1..k-1).each_with_object({}) { |i,h| h[i]=[[1]*i] }
(2..n-k+1).each do |i|
g = (1..[n/i,k].min).each_with_object(Hash.new {|h,k| h[k]=[]}) do |m,f|
im = [i]*m
mxi = m*i
if m==k
f[mxi].concat(im) if mxi==n
else
f[mxi] << im if mxi + (k-m)*(i+1) <= n
(1..[(i-1)*(k-m), n-mxi].min).each do |j|
h[j].each do |a|
f[mxi+j].concat([a+im]) if
((a.size==k-m && mxi+j==n) ||
(a.size<k-m && (mxi+j+(k-m-a.size)*(i+1))<=n))
end
end
end
end
g.update({ n=>[[i]*k] }) if i*k == n
h.update(g) { |k,ov,nv| ov+nv }
end
h[n]
end
Examples
p combos(10,3)
#=> [[3, 3, 4], [2, 4, 4], [2, 3, 5], [1, 4, 5],
# [2, 2, 6], [1, 3, 6], [1, 2, 7], [1, 1, 8]]
p combos(10,4)
#=> [[2, 2, 3, 3], [1, 3, 3, 3], [2, 2, 2, 4], [1, 2, 3, 4], [1, 1, 4, 4],
# [1, 2, 2, 5], [1, 1, 3, 5], [1, 1, 2, 6], [1, 1, 1, 7]]
puts "size=#{combos(100 ,3).size}" #=> 833
puts "size=#{combos(100 ,5).size}" #=> 38224
puts "size=#{combos(1000,3).size}" #=> 83333
Comment
The calculation combos(1000,3).size took about five seconds, the others were all well under one second.
Explanation
This method employs dynamic programming to compute a solution. The state variable is the largest positive integer used to compute arrays with sizes no more than k whose elements sum to no more than n. Begin with the largest integer equal to one. The next step is compute all combinations of k or fewer elements that include the numbers 1 and 2, then 1, 2 and 3, and so on, until we have all combinations of k or fewer elements that include the numbers 1 through n. We then select all combinations of k elements that sum to n from the last calculation.
Suppose
k => 3
n => 7
then
h = (1..k-1).each_with_object({}) { |i,h| h[i]=[[1]*i] }
#=> (1..2).each_with_object({}) { |i,h| h[i]=[[1]*i] }
#=> { 1=>[[1]], 2=>[[1,1]] }
This reads, using the only the number 1, [[1]] is the array of all arrays that sum to 1 and [[1,1]] is the array of all arrays that sum to 2.
Notice that this does not include the element 3=>[[1,1,1]]. That's because, already having k=3 elments, if cannot be combined with any other elements, and sums to 3 < 7.
We next execute:
enum = (2..n-k+1).each #=> #<Enumerator: 2..5:each>
We can convert this enumerator to an array to see what values it will pass into its block:
enum.to_a #=> [2, 3, 4, 5]
As n => 7 you may be wondering why this array ends at 5. That's because there are no arrays containing three positive integers, of which at least one is a 6 or a 7, whose elements sum to 7.
The first value enum passes into the block, which is represented by the block variable i, is 2. We will now compute a hash g that includes all arrays that sum to n => 7 or less, have at most k => 3 elements, include one or more 2's and zero or more 1's. (That's a bit of a mouthful, but it's still not precise, as I will explain.)
enum2 = (1..[n/i,k].min).each_with_object(Hash.new {|h,k| h[k]=[]})
#=> (1..[7/2,3].min).each_with_object(Hash.new {|h,k| h[k]=[]})
#=> (1..3).each_with_object(Hash.new {|h,k| h[k]=[]})
Enumerable#each_with_object creates an initially-empty hash that is represented by the block variable f. The default value of this hash is such that:
f[k] << o
is equivalent to
(f[k] |= []) << o
meaning that if f does not have a key k,
f[k] = []
is executed before
f[k] << o
is performed.
enum2 will pass the following elements into its block:
enum2.to_a #=> => [[1, {}], [2, {}], [3, {}]]
(though the hash may not be empty when elements after the first are passed into the block). The first element passed to the block is [1, {}], represented by the block variables:
m => 1
f => Hash.new {|h,k| h[k]=[]}
m => 1 means we will intially construct arrays that contain one (i=) 2.
im = [i]*m #=> [2]*1 => [2]
mxi = m*i #=> 2*1 => 2
As (m == k) #=> (1 == 3) => false, we next execute
f[mxi] << im if mxi + (k-m)*(i+1) <= n
#=> f[2] << [2] if 2 + (3-1)*(1+1) <= 7
#=> f[2] << [2] if 8 <= 7
This considers whether [2] should be added to f[2] without adding any integers j < i = 2. (We have yet to consider the combining of one 2 with integers less than 2 [i.e., 1].) As 8 <= 7, we do not add [2] to f[2]. The reason is that, for this to be part of an array of length k=3, it would be of the form [2,x,y], where x > 2 and y > 2, so 2+x+y >= 2+3+3 = 8 > n = 7. Clear as mud?
Next,
enum3 = (1..[(i-1)*(k-m), n-mxi].min).each
#=> = (1..[2,5].min).each
#=> = (1..2).each
#=> #<Enumerator: 1..2:each>
which passes the values
enum3.to_a #=> [1, 2]
into its block, represented by the block variable j, which is the key of the hash h. What we will be doing here is combine one 2 (m=1) with arrays of elements containing integers up to 1 (i.e., just 1) that sum to j, so the elements of the resulting array will sum to m * i + j => 1 * 2 + j => 2 + j.
The reason enum3 does not pass values of j greater than 2 into its block is that h[l] is empty for l > 2 (but its a little more complicated when i > 2).
For j => 1,
h[j] #=> [[1]]
enum4 = h[j].each #=> #<Enumerator: [[1]]:each>
enum4.to_a #=> [[1]]
a #=> [1]
so
f[mxi+j].concat([a+im]) if
((a.size==k-m && mxi+j==n) || (a.size<k-m && (mxi+j+(k-m-a.size)*(i+1))<=n))
#=> f[2+1].concat([[1]+[2]) if ((1==2 && 2+1==7) || (1<=3-1 && (2+1+(1)*(3)<=7))
#=> f[3].concat([1,2]) if ((false && false) || (1<=2 && (6<=7))
#=> f[3] = [] << [[1,2]] if (false || (true && true)
#=> f[3] = [[1,2]] if true
So the expression on the left is evaluated. Again, the conditional expressions are a little complex. Consider first:
a.size==k-m && mxi+j==n
which is equivalent to:
([2] + f[j]).size == k && ([2] + f[j]).reduce(:+) == n
That is, include the array [2] + f[j] if it has k elements that sum to n.
The second condition considers whether the array the arrays [2] + f[j] with fewer than k elements can be "completed" with integers l > i = 2 and have a sum of n or less.
Now, f #=> {3=>[[1, 2]]}.
We now increment j to 2 and consider arrays [2] + h[2], whose elements will total 4.
For j => 2,
h[j] #=> [[1, 1]]
enum4 = h[j].each #=> #<Enumerator: [[1, 1]]:each>
enum4.to_a #=> [[1, 1]]
a #=> [1, 1]
f[mxi+j].concat([a+im]) if
((a.size==k-m && mxi+j==n) || (a.size<k-m && (mxi+j+(k-m-a.size)*(i+1)<=n))
#=> f[4].concat([1, 1, 2]) if ((2==(3-1) && 2+2 == 7) || (2+2+(3-1-2)*(3)<=7))
#=> f[4].concat([1, 1, 2]) if (true && false) || (false && true))
#=> f[4].concat([1, 1, 2]) if false
so this operation is not performed (since [1,1,2].size => 3 = k and [1,1,2].reduce(:+) => 4 < 7 = n.
We now increment m to 2, meaning that we will construct arrays having two (i=) 2's. After doing so, we see that:
f={3=>[[1, 2]], 4=>[[2, 2]]}
and no other arrays are added when m => 3, so we have:
g #=> {3=>[[1, 2]], 4=>[[2, 2]]}
The statement
g.update({ n=>[i]*k }) if i*k == n
#=> g.update({ 7=>[2,2,2] }) if 6 == 7
adds the element 7=>[2,2,2] to the hash g if the sum of its elements equals n, which it does not.
We now fold g into h, using Hash#update (aka Hash#merge!):
h.update(g) { |k,ov,nv| ov+nv }
#=> {}.update({3=>[[1, 2]], 4=>[[2, 2]]} { |k,ov,nv| ov+nv }
#=> {1=>[[1]], 2=>[[1, 1]], 3=>[[1, 2]], 4=>[[2, 2]]}
Now h contains all the arrays (values) whose keys are the array totals, comprised of the integers 1 and 2, which have at most 3 elements and sum to at most 7, excluding those arrays with fewer than 3 elements which cannot sum to 7 when integers greater than two are added.
The operations performed are as follows:
i m j f
h #=> { 1=>[[1]], 2=>[[1,1]] }
2 1 1 {3=>[[1, 2]]}
2 1 2 {3=>[[1, 2]]}
2 2 1 {3=>[[1, 2]], 4=>[[2, 2]]}
{3=>[[1, 2]], 4=>[[2, 2]]}
3 1 1 {}
3 1 2 {}
3 1 3 {}
3 1 4 {7=>[[2, 2, 3]]}
3 2 1 {7=>[[2, 2, 3], [1, 3, 3]]}
g before g.update: {7=>[[2, 2, 3], [1, 3, 3]]}
g after g.update: {7=>[[2, 2, 3], [1, 3, 3]]}
h after h.update(g): {1=>[[1]],
2=>[[1, 1]],
3=>[[1, 2]],
4=>[[2, 2]],
7=>[[2, 2, 3], [1, 3, 3]]}
4 1 1 {}
4 1 2 {}
4 1 3 {7=>[[1, 2, 4]]}
g before g.update: {7=>[[1, 2, 4]]}
g after g.update: {7=>[[1, 2, 4]]}
h after h.update(g): {1=>[[1]],
2=>[[1, 1]],
3=>[[1, 2]],
4=>[[2, 2]],
7=>[[2, 2, 3], [1, 3, 3], [1, 2, 4]]}
5 1 1 {}
5 1 2 {7=>[[1, 1, 5]]}
g before g.update: {7=>[[1, 1, 5]]}
g after g.update: {7=>[[1, 1, 5]]}
h after h.update(g): {1=>[[1]],
2=>[[1, 1]],
3=>[[1, 2]],
4=>[[2, 2]],
7=>[[2, 2, 3], [1, 3, 3], [1, 2, 4], [1, 1, 5]]}
And lastly,
h[n].select { |a| a.size == k }
#=> h[7].select { |a| a.size == 3 }
#=> [[2, 2, 3], [1, 3, 3], [1, 2, 4], [1, 1, 5]]
#Cary's answer is very in-depth and impressive, but it appears to me that there is a much more naive solution, which proved to be much more efficient as well - good old recursion:
def combos(n,k)
if k == 1
return [n]
end
(1..n-1).flat_map do |i|
combos(n-i,k-1).map { |r| [i, *r].sort }
end.uniq
end
This solution simply reduces the problem each level by taking decreasing the target sum by each number between 1 and the previous target sum, while reducing k by one. Now make sure you don't have duplicates (by sort and uniq) - and you have your answer...
This is great for k < 5, and is much faster than Cary's solution, but as k gets larger, I found that it makes much too many iterations, sort and uniq took a very big toll on the calculation.
So I made sure that won't be needed, by making sure I get only sorted answers - each recursion should check only numbers larger than those already used:
def combos(n,k,min = 1)
if n < k || n < min
return []
end
if k == 1
return [n]
end
(min..n-1).flat_map do |i|
combos(n-i,k-1, i).map { |r| [i, *r] }
end
end
This solution is on par with Cary's on combos(100, 7):
user system total real
My Solution 2.570000 0.010000 2.580000 ( 2.695615)
Cary's 2.590000 0.000000 2.590000 ( 2.609374)
But we can do better: caching! This recursion does many calculations again and again, so caching stuff we already did will save us a lot of work when dealing with long sums:
def combos(n,k,min = 1, cache = {})
if n < k || n < min
return []
end
cache[[n,k,min]] ||= begin
if k == 1
return [n]
end
(min..n-1).flat_map do |i|
combos(n-i,k-1, i, cache).map { |r| [i, *r] }
end
end
end
This solution is mighty fast and passes Cary's solution for large n by light-years:
Benchmark.bm do |bm|
bm.report('Uri') { combos(1000, 3) }
bm.report('Cary') { combos_cary(1000, 3) }
end
user system total real
Uri 0.200000 0.000000 0.200000 ( 0.214080)
Cary 7.210000 0.000000 7.210000 ( 7.220085)
And is on par with k as high as 9, and I believe it is still less complicated than his solution.
You want the number of integer partitions of n into exactly k summands. There is a (computationally) somewhat ugly recurrence for that number.
The idea is this: let P(n,k) be the number of ways to partition n into k nonzero summands; then P(n,k) = P(n-1,k-1) + P(n-k,k). Proof: every partition either contains a 1 or it doesn't contain a 1 as one of the summands. The first case P(n-1,k-1) calculates the number of cases where there is a 1 in the sum; take that 1 away from the sum and partition the remaining n-1 into the now available k-1 summands. The second case P(n-k,k) considers the case where every summand is strictly greater than 1; to do that, reduce all of the k summands by 1 and recurse from there. Obviously, P(n,1) = 1 for all n > 0.
Here's a link that mentions that probably, no closed form is known for general k.

Removing elements from array Ruby

Let's say I am trying to remove elements from array a = [1,1,1,2,2,3]. If I perform the following:
b = a - [1,3]
Then I will get:
b = [2,2]
However, I want the result to be
b = [1,1,2,2]
i.e. I only remove one instance of each element in the subtracted vector not all cases. Is there a simple way in Ruby to do this?
You may do:
a= [1,1,1,2,2,3]
delete_list = [1,3]
delete_list.each do |del|
a.delete_at(a.index(del))
end
result : [1, 1, 2, 2]
[1,3].inject([1,1,1,2,2,3]) do |memo,element|
memo.tap do |memo|
i = memo.find_index(e)
memo.delete_at(i) if i
end
end
Not very simple but:
a = [1,1,1,2,2,3]
b = a.group_by {|n| n}.each {|k,v| v.pop [1,3].count(k)}.values.flatten
=> [1, 1, 2, 2]
Also handles the case for multiples in the 'subtrahend':
a = [1,1,1,2,2,3]
b = a.group_by {|n| n}.each {|k,v| v.pop [1,1,3].count(k)}.values.flatten
=> [1, 2, 2]
EDIT: this is more an enhancement combining Norm212 and my answer to make a "functional" solution.
b = [1,1,3].each.with_object( a ) { |del| a.delete_at( a.index( del ) ) }
Put it in a lambda if needed:
subtract = lambda do |minuend, subtrahend|
subtrahend.each.with_object( minuend ) { |del| minuend.delete_at( minuend.index( del ) ) }
end
then:
subtract.call a, [1,1,3]
A simple solution I frequently use:
arr = ['remove me',3,4,2,45]
arr[1..-1]
=> [3,4,2,45]
a = [1,1,1,2,2,3]
a.slice!(0) # remove first index
a.slice!(-1) # remove last index
# a = [1,1,2,2] as desired
For speed, I would do the following, which requires only one pass through each of the two arrays. This method preserves order. I will first present code that does not mutate the original array, then show how it can be easily modified to mutate.
arr = [1,1,1,2,2,3,1]
removals = [1,3,1]
h = removals.group_by(&:itself).transform_values(&:size)
#=> {1=>2, 3=>1}
arr.each_with_object([]) { |n,a|
h.key?(n) && h[n] > 0 ? (h[n] -= 1) : a << n }
#=> [1, 2, 2, 1]
arr
#=> [1, 1, 1, 2, 2, 3, 1]
To mutate arr write:
h = removals.group_by(&:itself).transform_values(&:count)
arr.replace(arr.each_with_object([]) { |n,a|
h.key?(n) && h[n] > 0 ? (h[n] -= 1) : a << n })
#=> [1, 2, 2, 1]
arr
#=> [1, 2, 2, 1]
This uses the 21st century method Hash#transform_values (new in MRI v2.4), but one could instead write:
h = Hash[removals.group_by(&:itself).map { |k,v| [k,v.size] }]
or
h = removals.each_with_object(Hash.new(0)) { | n,h| h[n] += 1 }

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