how to write a method that accepts two square matrices (nxn two dimensional arrays), and return the sum of the two. Both matrices being passed into the method will be of size nxn (square), containing only integers.
How to sum two matrices:
Take each cell [n][m] from the first matrix, and add it with the [n][m] cell from the second matrix. This will be cell [n][m] in the solution matrix.
like:
|1 2 3|
|3 2 1|
|1 1 1|
+
|2 2 1|
|3 2 3|
|1 1 3|
=
|3 4 4|
|6 4 4|
|2 2 4|
matrix_addition( [ [1, 2, 3], [3, 2, 1,], [1, 1, 1] ], [ [2, 2, 1], [3, 2, 3], [1, 1, 3] ] )
returns [ [3, 4, 4], [6, 4, 4], [2, 2, 4] ]
Even though it is possible to define method to do so, it is much easier to use ruby build in Matrix library for this:
require 'matrix'
m1 = Matrix[ [1, 2, 3], [3, 2, 1], [1, 1, 1] ]
m2 = Matrix[ [2, 2, 1], [3, 2, 3], [1, 1, 3] ]
sum = m1 + m2
Yes, certainly, use the Matrix class methods, but here is a way using recursion that might be of interest.
Code
def sum_arrays(a1, a2)
t = a1.zip(a2)
t.map { |e1,e2| (e1.is_a? Array) ? sum_arrays(e1,e2) : e1+e2 }
end
Examples
a1 = [1,2,3]
a2 = [4,5,6]
sum_arrays(a1, a2)
#=> [5, 7, 9]
a1 = [[1,2,3], [4,5]]
a2 = [[6,7,8], [9,10]]
sum_arrays(a1, a2)
#=> [[7, 9, 11], [13, 15]]
a1 = [[[ 1, 2, 3], [ 4, 5]],
[[ 6, 7], [ 8, 9, 10]]]
a2 = [[[11, 12, 13], [14, 15]],
[[16, 17], [18, 19, 20]]]
sum_arrays(a1, a2)
#=> [[[12, 14, 16], [18, 20]],
# [[22, 24], [26, 28, 30]]]
Generalization
You could make greater use of this method by passing an operator.
Code
def op_arrays(a1, a2, op)
t = a1.zip(a2)
t.map { |e1,e2| (e1.is_a? Array) ? op_arrays(e1,e2,op) : e1.send(op,e2) }
end
Examples
a1 = [[1,2,3], [4,5]]
a2 = [[6,7,8], [9,10]]
op_arrays(a1, a2, '+') #=> [[7, 9, 11], [13, 15]]
op_arrays(a1, a2, '-') #=> [[-5, -5, -5], [-5, -5]]
op_arrays(a1, a2, '*') #=> [[6, 14, 24], [36, 50]]
You could alternatively pass the operator as a symbol:
op_arrays(a1, a2, :+)
#=> [[7, 9, 11], [13, 15]]
Have you used ruby Matrix class?
It has #+ operator (mimic method).
Related
Let's say that we have the following list of lists:
[[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]]
How to transform it to a list containing sum of each element on its corresponding position so that in the end the result is
[5, 10, 15, 20] ?
There is unlikely a more succinct variant available, but one might avoid iterating lists several times and do everything in one pass (and without involving tuples and conversions) using recursion.
transpose = fn
[[x | xs] | xss], fun ->
[[x | Enum.map(xss, &hd/1)] | fun.([xs | Enum.map(xss, &tl/1)], fun)]
[[] | xss], fun -> fun.(xss, fun)
[], _ -> []
end
#⇒ #Function<43.97283095/2 in :erl_eval.expr/5>
transpose.(lists, transpose)
#⇒ [[1, 1, 1, 1, 1], [2, 2, 2, 2, 2], [3, 3, 3, 3, 3], [4, 4, 4, 4, 4]]
lists |> transpose.(transpose) |> Enum.map(&Enum.sum/1)
#⇒ [5, 10, 15, 20]
or, even simpler, avoiding an intermediate transpose:
sum = fn
[[] | _], _ -> []
xs, fun ->
[(xs |> Enum.map(&hd/1) |> Enum.sum()) |
fun.(Enum.map(xs, &tl/1), fun)]
end
sum.(lists, sum)
#⇒ [5, 10, 15, 20]
Given a set of distinct positive integers S we need to partition a set in such a way that the following function is maximize. Let S1, S2, ... Sn be the parition. n can be atleast 2.
F(S1, S2, ..., Sn) = AND(XOR(S1), XOR(S2), ..., XOR(Sn)))
where, AND is bitwise AND operation and XOR is bitwise XOR operation
We need to print the all such partitions possible.
I have tried the exponential approach as shown below.
I am looking for a solution with lesser complexity.
This problem is part of a homework, so only provide the hint.
from functools import reduce
from collections import defaultdict
def partition(collection):
if len(collection) == 1:
yield [ collection ]
return
first = collection[0]
for smaller in partition(collection[1:]):
# insert `first` in each of the subpartition's subsets
for n, subset in enumerate(smaller):
yield smaller[:n] + [[ first ] + subset] + smaller[n+1:]
# put `first` in its own subset
yield [ [ first ] ] + smaller
# print("END OF THE LOOP")
x = 4
initialAssum = [2, 4, 8, 16]
something = initialAssum
def andxor(xs):
def xorlist(xs):
return reduce(lambda i, j: i ^ j, xs)
tmp = [xorlist(x) for x in xs]
return reduce(lambda i, j: i & j, tmp)
ans = defaultdict(list)
for n, p in enumerate(partition(something), 1):
r = andxor(p)
if len(p) > 1:
ans[r].append(p)
m = max(ans.keys())
for a in ans[m]:
print(a)
#print(a, len(a))
print(f'{m}')
INPUT: the set itself
OUTPUT: max value possible followed by the all the partitions producing it
INPUT:
[2, 3, 4]
OUTPUT:
2
[[4, 2], [3]]
[[2], [4, 3]]
INPUT:
[2, 4, 6, 8]
OUTPUT:
0
[[2], [4, 8, 16]]
[[2, 4], [8, 16]]
[[4], [2, 8, 16]]
[[2], [4], [8, 16]]
[[2, 4, 8], [16]]
[[4, 8], [2, 16]]
[[2], [4, 8], [16]]
[[2, 8], [4, 16]]
[[8], [2, 4, 16]]
[[2], [8], [4, 16]]
[[2, 4], [8], [16]]
[[4], [2, 8], [16]]
[[4], [8], [2, 16]]
[[2], [4], [8], [16]]
This problem is part of a homework, so only provide the hint.
Hint: if we consider each bit separately from the highest to lowest, we can consider bit k as being set in the result if and only if that bit can appear an odd number of times in each part of the partition.
I have this array:
ary = [[1, 6, 7], [1, 4, 9], [1, 8, 3]]
I want to sort it by the first odd number, or the last number if they are all even, in each subarray.
Since the first element in each array is the same object 1 for this particular ary, I can solve this like this:
ary2 = ary.sort_by { |a, b, c| b.odd? ? b : c }
But when I try a more general one:
arr2 = ary.sort_by { |a, b, c| a.odd? ? a : b.odd? ? b : c }
ary2 comes back unsorted.
I tried removing the ternary operators like this:
ary2 = ary.sort_by do |a, b, c|
if a.odd?
a
elsif b.odd?
b
else
c
end
end
with the same effect (i.e., none).
Is there some reason that elsif can't be used in blocks passed to the sort_by method?
Edit: Axiac pointed out the problem with my logic. It looks like conditional logic has to deal with all of the possible permutations of odd and even values. This works:
arr2 = arr.sort_by do |a, b, c|
if a.odd?
if b.odd?
if c.odd?
[a, b, c]
else
[a, b]
end
elsif c.odd?
[a, c]
else
a
end
elsif b.odd?
if c.odd?
[b, c]
else
b
end
else
c
end
end
Maybe there's a more succinct and less brittle way to do it, but it's probably a good idea to do it this way instead:
arr2 = arr.sort_by do |sub_arr|
temp = sub_arr.select do |e|
e.odd?
end
temp.empty? ? Array(sub_arr.last) : temp
end
I'll see myself out.
Regarding your original question, just as axiac points out in the comment, the result of the sorting should be exactly the same as the input array because they are all sorted by the first odd element in each subarray, which is 1, and the sort method is stable in MRI.
Regarding your question after the edit, my answer would be:
ary.sort_by{|a| a[0...-1].select(&:odd?) << a.last}
# => [[1, 8, 3], [1, 6, 7], [1, 4, 9]]
I am pretty confident that this is what you wrote after the edit that you wanted, but I am not sure if this is what you wanted since the sorting mechanism looks strange to me.
I find the statement of the question ambiguous. I will give an answer that is consist with one interpretation. If that is not what you want, please clarify hte question.
def my_sort(arr)
arr.sort_by {|a| a.any?(&:odd?) ? a.map {|e| e.odd? ? e : Float::INFINITY} : [a.last]}
end
my_sort [[1, 6, 7], [1, 4, 9], [1, 2, 3]]
#=> [[1, ∞, 7], [1, ∞, 9], [1, ∞, 3]] (sort_by)
#=> [[1, 2, 3], [1, 6, 7], [1, 4, 9]]
my_sort [[3, 6, 7], [4, 1, 9], [5, 8, 1]]
#=> [[3, ∞, 7], [∞, 1, 9], [5, ∞, 1]] (sort_by)
#=> [[3, 6, 7], [5, 8, 1], [4, 1, 9]]
my_sort [[2, 6, 8], [4, 1, 4], [8, 6, 2]]
#=> [[8], [∞, 1, ∞], [2]] (sort_by)
#=> [[8, 6, 2], [2, 6, 8], [4, 1, 4]]
my_sort [[8, 6, 2], [5, 1, 1], [6, 8, 4]]
#=> [[2], [5, 1, 1], [4] (sort_by)
#=> [[8, 6, 2], [6, 8, 4], [5, 1, 1]]
For each example I've shown the arrays used by sort_by to produce the sort shown on the following line.
I'm working on the following algorithm from Leetcode:
Numbers can be regarded as product of its factors. For example,
8 = 2 x 2 x 2;
= 2 x 4.
Write a function that takes an integer n and return all possible combinations of its factors.
Note:
You may assume that n is always positive.
Factors should be greater than 1 and less than n.
Examples:
input: 1
output:
[]
input: 37
output:
[]
input: 12
output:
[
[2, 6],
[2, 2, 3],
[3, 4]
]
input: 32
output:
[
[2, 16],
[2, 2, 8],
[2, 2, 2, 4],
[2, 2, 2, 2, 2],
[2, 4, 4],
[4, 8]
]
Here's the code that I have thus far:
def get_factors(n)
factors = []
(2...n).each do |candidate|
if n % candidate == 0
factors << [candidate, (n/candidate)]
get_factors(n/candidate).each do |factor_set|
factors << [candidate] + factor_set
end
end
end
factors
end
This code works really well, but doesn't handle duplicates (e.g [3, 2, 2] will be inserted along with [2, 2, 3]). I tried using a Set with the following code,
def get_factors(n)
seen = Set.new
factors = []
(2...n).each do |candidate|
if n % candidate == 0 && !seen.include?(candidate)
factors << [candidate, (n/candidate)]
get_factors(n/candidate).each do |factor_set|
factors << [candidate] + factor_set
end
end
seen << (n/candidate)
end
factors
end
but that only works to solve some test cases and not others. I'm not sure how to go about ensuring no duplicates in an efficient way? The really inefficient way is to generate some sort of hash value for each array depending on it's elements (and not dependent on order), and while this would work, there definitely should be a better way. Any ideas?
I think always going forward is a good policy (i.e when checking, say, with 5, do not check with 2, 3, 4 etc). That way, searching for duplicates can be eliminated.
Since the algorithm already uses a lot of time, I don't see a problem sorting each answer and removing duplicates. This requires no proof to ensure it works, which the answer provided by mac does.
Code
require 'prime'
def get_factors(n)
primes, nbr = Prime.prime_division(n).transpose
powers = nbr.map { |m| (0..m).to_a }
powers.shift.
product(*powers).
map { |pows| primes.zip(pows).reduce(1) { |t,(pr,po)| t * (pr**po) } }.
sort
end
The array returned includes 1 and n (which are factors of n). If those values should be excluded, replace .sort with .sort - [1, n].
Examples
get_factors(24)
#=> [1, 2, 3, 4, 6, 8, 12, 24]
get_factors(64)
#=> [1, 2, 4, 8, 16, 32, 64]
get_factors(90)
#=> [1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90]
Explanation
Consider
n = 60
The steps are as follows.
a = Prime.prime_division(30)
#=> [[2, 2], [3, 1], [5, 1]]
Ergo, the primes of 30 are 2, 3 and 5, and
60 = 2**2 * 3**1 * 5**1
See Prime::prime_division. Continuing,
primes, nbr = a.transpose
#=> [[2, 3, 5], [2, 1, 1]]
primes
#=> [2, 3, 5]
nbr
#=> [2, 1, 1]
powers = nbr.map { |m| (0..m).to_a }
#=> [[0, 1, 2], [0, 1], [0, 1]]
This means that each factor will be the product of 0, 1 or 2 2's, 0 or 1 3's and 0 or 1 5's.
b = powers.shift
#=> [0, 1, 2]
powers
#=> [[0, 1], [0, 1]]
c = b.product(*powers)
#=> [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 1], [1, 0, 0], [1, 0, 1],
# [1, 1, 0], [1, 1, 1], [2, 0, 0], [2, 0, 1], [2, 1, 0], [2, 1, 1]]
d = c.map { |pows| primes.zip(pows).reduce(1) { |t,(pr,po)| t * (pr**po) } }
#=> [1, 5, 3, 15, 2, 10, 6, 30, 4, 20, 12, 60]
d.sort
#=> [1, 5, 3, 15, 2, 10, 6, 30, 4, 20, 12, 60]
Consider now the calculation of d. The 10th element of c that is passed to the block is [2, 0, 1]. The block calculation for that element is as follows.
pows = [2, 0, 1]
e = primes.zip(pows)
#=> [[2, 2], [3, 0], [5, 1]]
e.reduce(1) { |t,(pr,po)| t * (pr**po) }
#=> 20
The reduce calculation is equivalent to
2**2 * 3**0 * 5**1
#=> 4 * 1 * 5 => 20
The calculations for the other values of c passed to the block are similar.
A simple way is to replace the last line of your method with
factors.map(&:sort).uniq
which sorts all the subarrays and then eliminates duplicates.
I have a sparse array, for example:
rare = [[0,1], [2,3], [4,5], [7,8]]
I want to plot a chart with these data, each pair are point coordinates.
As you can see I don't have points for x=1, x=3 , x=5, x=6
I want to fill the array with the previous values, so for the above example I will get:
filled = [[0,1], [1,1], [2,3], [3,3], [4,5], [5,5], [6,5], [7,8]
As you can see, for calculating the y value, I simply take the last y value I used.
What is the best aproach to accomplish this ?
Range.new(*rare.transpose.first.sort.values_at(0,-1)).inject([]){|a,i|
a<<[i, Hash[rare][i] || a.last.last]
}
Step-by-step explanation:
rare.transpose.first.sort.values_at(0,-1) finds min and max x ([0,7] in your example)
Range.new() makes a range out of it (0..7)
inject iterates through the range and for every x returns pair [x,y], where y is:
y from input array, where defined
y from previously evaluated pair, where not
Note: here are some other ways of finding min and max x:
[:min,:max].map{|m| Hash[rare].keys.send m}
rare.map{|el| el.first}.minmax # Ruby 1.9, by steenslag
rare = [[0,1], [2,3], [4,5], [7,8]]
filled = rare.inject([]) do |filled, point|
extras = if filled.empty?
[]
else
(filled.last[0] + 1 ... point[0]).collect do |x|
[x, filled.last[1]]
end
end
filled + extras + [point]
end
p filled
# => [[0, 1], [1, 1], [2, 3], [3, 3], [4, 5], [5, 5], [6, 5], [7, 8]]
An inject solution:
filled = rare.inject([]) do |filled_acc, (pair_x, pair_y)|
padded_pairs = unless filled_acc.empty?
last_x, last_y = filled_acc.last
(last_x+1...pair_x).map { |x| [x, last_y] }
end || []
filled_acc + padded_pairs + [[pair_x, pair_y]]
end
More about Enumerable#inject and functional programming with Ruby here.
irb(main):001:0> rare = [[0,1], [2,3], [4,5], [7,8]]
=> [[0, 1], [2, 3], [4, 5], [7, 8]]
irb(main):002:0> r=rare.transpose
=> [[0, 2, 4, 7], [1, 3, 5, 8]]
irb(main):003:0> iv = (r[0][0]..r[0][-1]).to_a.select {|w| !r[0].include?(w) }
=> [1, 3, 5, 6]
irb(main):004:0> r[1][-1]=r[1][-2]
=> 5
irb(main):005:0> p (iv.zip(r[1]) + rare).sort
[[0, 1], [1, 1], [2, 3], [3, 3], [4, 5], [5, 5], [6, 5], [7, 8]]
=> [[0, 1], [1, 1], [2, 3], [3, 3], [4, 5], [5, 5], [6, 5], [7, 8]]