Check if numbers summed in array match input parameter - ruby

Question

I'm following Ruby practice problem from a website and I'm completely stuck on figuring out a solution to this problem. Basically, given a function has_sum?(val, arr), return true if any combination of numbers in the array (second parameter) can be added together to equal the first parameter, otherwise return false. So:
has_sum?(5, [1, 2, 3, 4]) # true
has_sum?(5, [1, 2, 6]) # false
I'm completely stuck and not quite sure how to accomplish this... Here's what I have so far.
def has_sum?(val, arr)
arr.each_with_index do |idx, v|
# ??? no idea what to do here except add the current num to the next in the list
end
end
Any help would be greatly appreciated - thanks!

Answer 1

An array can produce a sum when there is a subset of any length that adds up to that sum:
def has_sum?(val, arr)
(arr.size + 1).times
.flat_map { |i| arr.combination(i).to_a }
.any? { |s| s.inject(:+) == val }
end
has_sum?(5, [5])
# => true
has_sum?(5, [1, 2, 3])
# => true
has_sum?(5, [1, 1, 1, 1, 1, 1])
# => true
has_sum?(5, [1, 2, 7])
# => false
This is not very efficient as it generates all the possibilities before testing. This should terminate sooner:
def has_sum?(val, arr)
(arr.size + 1).times.any? { |i|
arr.combination(i).any? { |s| s.inject(:+) == val }
}
end
Even more efficiently, a recursive implementation, with the idea that a sum of an empty array is zero (and has_sum(nonzero, []) should return false); for a larger array, we pop off its head, and see if the sum of the rest of the array is okay if we count, or don't count, the head element. Here, we don't do the useless summing of the whole array over and over again:
def has_sum?(val, arr)
if arr.empty?
val.zero?
else
first, *rest = arr
has_sum?(val, rest) || has_sum?(val - first, rest)
end
end

Answer 2

This solution employs dynamic programming. I assume that zeroes have been removed from the array. If all numbers in the array are positive, we can also remove elements that are larger than the target sum.
Code
def sum_to_target(arr, target)
h = arr.each_index.with_object({}) do |i,h|
v = arr[i]
h.keys.each do |n|
unless h.key?(n+v) # || (n+v > target)
h[n+v] = v
return reconstruct(h, target) if n+v == target
end
end
h[v] = v unless h.key?(v)
return reconstruct(h, target) if v == target
end
nil
end
def reconstruct(h, target)
a = []
loop do
i = h[target]
a.unshift i
target -= i
return a if target == 0
end
a
end
Additional efficiency improvements are possible if arr contains only postive values.1
Examples
#1
sum_to_target [2,4,7,2], 8
#=> [2, 4, 2]
#2
arr = [64, 18, 64, 6, 39, 51, 87, 62, 78, 62, 49, 86, 35, 57, 40, 15, 74, 10, 8, 7]
a = sum_to_target(arr, 461)
#=> [64, 18, 39, 51, 87, 62, 78, 62]
Let's check that.
a.reduce(:+)
#=> 461
#3
a = sum_to_target([-64, 18, 64, -6, 39, 51, -87, 62, -78, 62, 49, 86, 35, 57,
40, 15, -74, 10, -8, -7], 190)
#=> [18, 64, -6, 39, 51, -87, 62, 49]
a.reduce(:+)
#=> 190
#4
arr = 1_000.times.map { rand 1..5_000 }
#=> [3471, 1891, 4257, 2265, 832, 1060, 3961, 875, 614, 2308, 2240, 3286,
# ...
# 521, 1316, 1986, 4099, 1398, 3803, 4498, 4607, 2262, 3941, 4367]
arr is an array of 1,000 elements, each a random number between 1 and 5,000.
answer = arr.sample(500)
#=> [3469, 2957, 1542, 950, 4765, 3126, 3602, 755, 4132, 4281, 2374,
# ...
# 427, 4238, 4397, 2717, 912, 1690, 3626, 169, 3607, 4084, 3161]
answer is an array of 500 elements from arr, sampled without replacement.
target = answer.reduce(:+)
#=> 1_226_020
target is the sum of the elements of answer. We will now search arr for a collection of elements that sum to 1,226,020 (answer being one such collection).
require 'time'
t = Time.now
#=> 2016-12-12 23:00:51 -0800
a = sum_to_target(arr, target)
#=> [3471, 1891, 4257, 2265, 832, 1060, 3961, 875, 614, 2308, 2240, 3286,
# ...
# 3616, 4150, 3222, 3896, 631, 2806, 1932, 3244, 2430, 1443, 1452]
Notice that a != answer (which is not surprising).
a.reduce(:+)
#=> 1226020
(Time.now-t).to_i
#=> 60 seconds
For this last example, methods that use Array#combination would have to wade though as many as
(1..arr.size).reduce(0) { |t,i| t + arr.combination(i).size }.to_f
#~> 1.07+301
combinations.
Explanation
Let
arr = [2,4,7,2]
target = 8
Suppose we temporarily redefine reconstruct to return the hash passed to it.
def reconstruct(h, target)
h
end
We then obtain the following:
h = sum_to_target(arr, target)
#=> {2=>2, 6=>4, 4=>4, 9=>7, 13=>7, 11=>7, 7=>7, 8=>2}
h is defined as follows.
Given an array of non-zero integers arr and a number n, if n is a key of h there exists an array a containing elements from arr, in the same order, such that the elements of a sum to n and the last element of a equals h[n].
which, admittedly, is a mouthful.
We now use the reconstruct (as defined in the "Code" section) to construct an array answer that will contain elements from arr (without repeating elements) that sum to target.
reconstruct(h, target) #=> [2, 4, 2]
Initially, reconstruct initializes the array answer, which it will build and return:
answer = []
h will always contain a key equal to target (8). As h[8] #=> 2 we conclude that the last element of answer equals 2, so we execute
answer.unshift(2) #=> [2]
The problem is now to find an array of elements from arr that sum to 8 - 2 #=> 6. As h[6] #=> 4, we conclude that the element in answer that precedes the 2 we just added is 4:
answer.unshift(4) #=> [4, 2]
We now need 8-2-4 #=> 2 more to total target. As h[2] #=> 2 we execute
answer.unshift(2) #=> [2, 4, 2]
Since 8-2-4-2 #=> 0 we are finished and therefore return answer.
Notice that 4 precedes the last 2 in arr and the first 2 precedes the 4 in arr. The way h is constructed ensures the elements of answer will always be ordered in this way.
Now consider how h is constructed. First,
h = {}
As arr[0] #=> 2, we conclude that, using only the first element of arr, all we can conclude is:
h[2] = 2
h #=> {2=>2}
h has no key equal to target (8), so we continue. Now consider arr[1] #=> 4. Using only the first two elements of arr we can conclude the following:
h[2+4] = 4
h #=> {2=>2, 6=>4}
and since h has no key 4,
h[4] = 4
h #=> {2=>2, 6=>4, 4=>4}
h still has no key equal to target (8), so we press on and examine arr[2] #=> 7. Using only the first three elements of arr we conclude the following:
h[2+7] = 7
h[6+7] = 7
h[4+7] = 7
h #=> {2=>2, 6=>4, 4=>4, 9=>7, 13=>7, 11=>7}
and since h has no key 7:
h[7] = 7
h #=> {2=>2, 6=>4, 4=>4, 9=>7, 13=>7, 11=>7, 7=>7}
We added four elements to h, but since arr contains only positive numbers, those with keys 9, 13 and 11 are of no interest.
Since h still does not have a key equal to target (8), we examine the next element in arr: arr[3] #=> 2. Using only the first four elements of arr we conclude the following:
h[4+2] = 2
h[6+2] = 2
Here we stop, since 6+2 == target #=> true.
h #=> {2=>2, 6=>2, 4=>4, 9=>7, 13=>7, 11=>7, 7=>7, 8=>2}
Notice that we did not compute h[2+2] = 2 since h already has a key 4. Further, had arr contained additional elements we still would have terminated the construction of the hash at this point.
Had we modified the code to take advantage of the fact that arr contains only positive values, the final hash would have been:
h #=> {2=>2, 6=>2, 4=>4, 7=>7, 8=>2}
If this is still not clear, it might be helpful to run the code for this example with included puts statements (e.g., puts "i=#{i}, h=#{h}, v=#{v}" after the line v = arr[i] in sum_to_target, and so on).
1 The line unless h.key?(n+v) can be changed to unless h.key?(n+v) || (n+v > target) if it is known that the array contains no negative elements. (Doing so reduced the solution time for example #4 by 4 seconds.) One could also compute #all_positive = arr.all?(&:positive?) and then make that line conditional on #all_positive.

Answer 3

I would do nested loops.
for x = 0 to length of array
for y = x + 1 to length of array
if number at x + number at y = sum return true
return false
Basically it will check the sum of each number with each of the numbers after it.
EDIT: this will only sum 2 numbers at a time. If you want to be able to sum any amount of numbers this wont work.