Two sum algorithm with bsearch (Ruby) - ruby

I just started learning Ruby not too long ago and was confused with this two-sum algorithm. Basically, the algorithm will return true if there are any two integers in the array that add up to the sum, and false if not. I am familiar with the bsearch method in Ruby, but can't figure out why there is:
match_idx && match_idx != i
Shouldn't it just be:
match_idx != i
Code in question:
def okay_two_sum_b(arr, target)
arr = arr.sort
arr.each_with_index do |el, i|
match_idx = arr.bsearch_index { |el2| (target - el) <=> el2 }
return true if match_idx && match_idx != i
end
false
end
arr = [0, 1, 5, 7]
p bad_sum(arr, 6) # => should be true
p bad_sum(arr, 10) # => should be false
Thanks!

For a given value of el, match_idx will equal a non-negative integer (an index of arr) if there is an index el2 of arr such that arr[el] + arr[el2] == target, else match_idx will equal nil, so you have to make sure match_id is not nil before checking match_idx != i.
Let's see if we can make the method more efficient, considering that the time complexity of sorting is O(nlog(n)), where n is the size of the array.
require 'set'
def two_sum?(arr, target)
return true if target.even? && (arr.count(target/2) > 1)
st = arr.to_set
st.each do |e|
f = target-e
return true if e != f && st.include?(f)
end
false
end
two_sum?([0, 1, 5, 7], 6) #=> true
two_sum?([0, 1, 5, 7], 10) #=> false
If n is the size of arr, the time complexity to construct the set (effectively the same as that of constructing an underlying hash) is O(n) and the time complexity of determining if the set contains a given value is only slightly worse than O(n).

Related

Detect if nested array contains similar elements

I have a method that gets an array of arrays and detects if any sub array is occurs more than one time, regardless of its order:
def has_similar_content?(array)
array.each.with_index do |prop1, index1|
array.each.with_index do |prop2, index2|
next if index1 == index2
return true if prop1.sort == prop2.sort
end
end
false
end
> has_similar_content?([%w[white xl], %w[red xl]])
=> false
> has_similar_content?([%w[blue xl], %w[xl blue cotton]])
=> false
> has_similar_content?([%w[blue xl], %w[xl blue]])
=> true
> has_similar_content?([%w[xl green], %w[red xl], %w[green xl]])
=> true
My problem is the runtime of this method, it has a quadratic complexity and needs an additional sort of the arrays to detect if the elements are the same.
Is there a more efficient way to do this?
I have assumed the question is as stated in my comment on the question.
Code
def disregarding_order_any_dups?(arr)
arr.map do |a|
a.each_with_object(Hash.new(0)) do |k,h|
h[k] += 1
end
end.uniq.size < arr.size
end
Examples
disregarding_order_any_dups? [%w[white xl], %w[red xl]]
#=> false
disregarding_order_any_dups? [%w[blue xl],
%w[xl blue cotton]]
#=> false
disregarding_order_any_dups? [%w[blue xl], %w[xl blue]]
#=> true
disregarding_order_any_dups? [%w[xl green], %w[red xl],
%w[green xl]]
#=> true
disregarding_order_any_dups? [[1,2,3,2], [3,1,3,2],
[2,3,1,2]]
#=> true
Complexity
If n = arr.size and m = arr.map(&:size).max, the computational complexity is O(n*m). The single statement within map's block could be replaced with a.sort, but that would increase the computational complexity to O(n*m*log(m)).
Explanation
For the last example the steps are as follows.
arr = [[1,2,3,2], [3,1,3,2], [2,3,1,2]]
b = arr.map do |a|
a.each_with_object(Hash.new(0)) do |k,h|
h[k] += 1
end
end
#=> [{1=>1, 2=>2, 3=>1}, {3=>2, 1=>1, 2=>1},
# {2=>2, 3=>1, 1=>1}]
c = b.uniq
#=> [{1=>1, 2=>2, 3=>1}, {3=>2, 1=>1, 2=>1}]
d = c.size
#=> 2
e = arr.size
#=> 3
d < e
#=> true
The expression
h = Hash.new(0)
creates a counting hash. Ruby expands h[k] += 1 to
h[k] = h[k] + 1
The hash instance methods are :[]= on the left, :[] on the right. If h does not have a key k, h[k] on the right is replaced with h's default value, which has been defined to equal zero, resulting in:
h[k] = 0 + 1
If h has a key k, h[k] on the right, the value of k, is not replaced with h's default value. See the version of Hash::new which takes an argument equal to the hash's default value.
this way is simpler:
array.
group_by(&:sort).
transform_values(&:length).
values.any? { |count| count > 1 }
This is still quadratic but it is faster :
def has_similar_content?(array)
# sort subarray only once. O( n * m * log(m) )
sorted_array= array.map(&:sort)
# if you can change the input array, this prevent object allocation :
# array.map!(&:sort!)
# compare each pair only once O( n * n/2 )
nb_elements= sorted_array.size
0.upto(nb_elements - 1).each do |i|
(i + 1).upto(nb_elements - 1).each do |j|
return true if sorted_array[i] == sorted_array[j]
end
end
return false
end

Compare sums of elements in an array: Ruby

I need to check whether the sum of any 2 elements of an array equals to the given number. This is what I came up with, but it doesn't seem to do the comparison
def sum_comparison(int_array, x)
n = int_array.length
(0..n).each do |i|
(1..n).each do |j|
if ((int_array[i].to_i + int_array[j].to_i) == x)
return true
else
return false
end
end
end
end
Your solution seems overly complicated and strongly influenced by the programming style of low-level procedural languages like C. One apparent problem is that you write
n = int_array.length
(0..n).each do |i|
# use int_array[i].to_i inside the loop
end
Now inside the each loop, you will get the numbers i = 0, 1, 2, ..., n, for example for int_array = [3,4,5] you get i = 0, 1, 2, 3. Notice that there are four elements, because you started counting at zero (this is called an off by one error). This will eventually lead to an array access at n, which is one beyond the end of the array. This will again result in a nil coming back, which is probably why you use to_i to convert that back to an integer, because otherwise you would get a TypeError: nil can't be coerced into Fixnum whend doing the addition. What you probably wanted instead was simply:
int_array.each do |i|
# use i inside the loop
end
For the example array [3,4,5] this would actually result in i = 3, 4, 5. To get the combinations of an array in a more Ruby way, you can for example use Array#combination. Likewise, you can use Array#any? to detect if any of the combinations satisfy the specified condition:
def sum_comparison(array, x)
array.combination(2).any? do |a, b|
a + b == x
end
end
When your function compare first element, it's immediately returns false. You need to return only true when iterating and return false at the end if nothing were found, to avoid this issue:
def sum_comparison(int_array, x)
n = int_array.size
(0...n).each do |i|
(1...n).each do |j|
if (int_array[i].to_i + int_array[j].to_i) == x
return true
end
end
end
false
end
To simplify this you can use permutation or combination and any? methods as #p11y suggests. To get founded elements you could use find or detect.
def sum_comparison(a, x)
a.combination(2).any? { |i, j| i + j == x }
end
a.combination(2).detect { |i, j| i + j == x }
# sum_comparison([1,2,3, 4], 6) => [2, 4]
Using an enumerator:
#!/usr/bin/env ruby
def sum_comparison(int_array, x)
enum = int_array.to_enum
loop do
n = enum.next
enum.peek_values.each do |m|
return true if (n + m) == x
end
end
false
end
puts sum_comparison([1, 2, 3, 4], 5)
Output:
true
Problem
Your method is equivalent to:
def sum_comparison(int_array, x)
return int_array[0].to_i + int_array[1].to_i == x
end
Therefore,
int_array = [1,2,4,16,32,7,5,7,8,22,28]
sum_comparison(int_array, 3) #=> true, just lucky!
sum_comparison(int_array, 6) #=> false, wrong!
Alternative
Here is a relatively efficient implemention, certainly far more efficient than using Enumerable#combination.
Code
def sum_comparison(int_array, x)
sorted = int_array.sort
smallest = sorted.first
sorted_stub = sorted.take_while { |e| e+smallest <= x }
p "sorted_stub = #{sorted_stub}"
return false if sorted_stub.size < 2
loop do
return false if sorted_stub.size < 2
v = sorted_stub.shift
found = sorted_stub.find { |e| v+e >= x }
return true if found && v+found == x
end
false
end
Examples
sum_comparison([7,16,4,12,-2,5,8], 3)
# "sorted_stub = [-2, 4, 5]"
#=> true
sum_comparison([7,16,4,12,-2,5,8], 7)
# "sorted_stub = [-2, 4, 5, 7, 8]"
#=> false
sum_comparison([7,16,4,22,18,12,2,41,5,8,17,31], 9)
# "sorted_stub = [2, 4, 5, 7]"
#=> true
Notes
The line p "sorted_stub = #{sorted_stub}" is included merely to display the array sorted_stub in the examples.
If e+smallest > x for any elements f and g in sorted for which g >= e and f < g, f+g >= e+smallest > x. Ergo, sorted_stub.last is the largest value in sorted that need be considered.
For a given value v, the line found = sorted_stub.find { |e| v+e >= x } stops the search for a second value e for which v+e = x as soon as it finds e such that v+e >= x. The next line then determines if a match has been found.

Checking to see if 2 numbers in array sum to 0 in Ruby

I've been going at this problem for a few hours, and I can't see why I can't get it to run properly. The end game to this method is having 2 numbers in an array equaling zero when added together. Here is my code:
def two_sums(nums)
i = 0
j = -1
while i < nums.count
num_1 = nums[i]
while j < nums.count
num_2 = nums[j]
if num_1 + num_2 == 0
return "There are 2 numbers that sum to zero & they are #{num_1} and #{num_2}."
else
return "Nothing adds to zero."
end
end
i += 1
j -= 1
end
end
The problem I'm having is unless the first and last number in the array are the positive and negative of the same number, this will always return false.
For example, if I had an array that was [1, 4, 6, -1, 10], it should come back true. I'm sure my 2 while statement is the cause of this, but I can't think of a way to fix it. If someone could point me in the right direction, that would be helpful.
You can find the first pair that adds up to 0 like this:
nums.combination(2).find { |x, y| x + y == 0 }
#=> returns the first matching pair or nil
Or if you want to select all pairs that add up to 0:
nums.combination(2).select { |x, y| x + y == 0 }
#=> returns all matching pairs or an empty array
Therefore you can implement your method like this:
def two_sums(nums)
pair = nums.combination(2).find { |x, y| x + y == 0 }
if pair
"There are 2 numbers that sum to zero & they are #{pair.first} and #{pair.last}."
else
"Nothing adds to zero."
end
end
Or if you want to find all pairs:
def two_sums(nums)
pairs = nums.combination(2).select { |x, y| x + y == 0 }
if pairs.empty?
"Nothing adds to zero."
else
"The following pairs sum to zero: #{pairs}..."
end
end
Here's another way:
Code
def sum_to_zero(arr)
arr.group_by { |e| e.abs }
.values
.select { |a| (a.size > 1 && a.first == 0) || a.uniq.size > 1 }
end
Examples
sum_to_zero [1, 4, 6, -1, 10] #=> [[1, -1]]
sum_to_zero [1, 4, 1, -2, 10] #=> []
sum_to_zero [1, 0, 4, 1, 0, -1] #=> [[1, 1, -1], [0, 0]]
This method is relatively fast. Let's try it with an array of 200,000 elements, each a random number between -500,000 and 500,000.
require 'time'
t = Time.now
arr = Array.new(200_000) { rand(1_000_001) - 500_000 }
arr.size #=> 200000
sum_to_zero(arr).size #=> 16439
Time.now - t
#=> 0.23 (seconds)
sum_to_zero(arr).first(6)
#=> [[-98747, 98747],
# [157848, -157848],
# [-459650, 459650],
# [176655, 176655, -176655],
# [282101, -282101],
# [100886, 100886, -100886]]
If you wish to group the non-negative and negative values that sum to zero:
sum_to_zero(arr).map { |a| a.partition { |e| e >= 0 } }.first(6)
#=> [[[98747], [-98747]],
# [[157848], [-157848]],
# [[459650], [-459650]],
# [[176655, 176655], [-176655]],
# [[282101], [-282101]],
# [[100886, 100886], [-100886]]]
If you only want a single value for each group (a non-negative value, say):
sum_to_zero(arr).map { |a| a.first.abs }.first(6)
#=> [98747, 157848, 459650, 176655, 282101, 100886]
I think the most Ruby way would be:
nums.combination(2).any? { |x,y| (x+y).zero? }
Here's a way that should work well for large arrays. The methods above which go through every possible combination of two numbers are perfectly fine for small cases but will be very slow and memory hungry for arrays with lots of elements.
def two_sums nums
h = Hash.new
nums.each do |n|
return true if h[-n]
h[n] = true
end
false
end
Well, given it's tagged as #ruby, here's the most "ruby way" I could think of tackling this problem:
def two_sums(arr)
numbers = arr.combination(2).select { |a| a.reduce(:+) == 0 }.flatten
if numbers.empty?
"Nothing adds to zero."
else
"There are 2 numbers that sum to zero & they are #{numbers.first} and #{numbers.last}."
end
end
array.combination(2).select{|x|x[0] + x[1] == 0}

Finding the index of second smallest number in the list?

How can I find the second smallest number and return its index?
Another approach :
>> a = [1,3,5,6,2,4]
=> [1, 3, 5, 6, 2, 4]
>> a.index(a.sort[1])
=> 4
>>
I can see two options from the top of my head:
Delete the current min, so the new min will be the previous second min
arr = num.delete(num.min)
min_bis = arr.min
Loop through the array, using 2 variables to store the 2 lowest values.
This might be a little trickier but the complexity would only be O(n).
I don't know why you don't want to sort the array, but if it's a performance issue, it's probably one of the best options (to sort it) especially if the array is small.
(Below, Enumerable is a superset of Array, Hash and Range etc.)
Enumerable#sort returns a fresh array containing all the elements of the original object in a sorted order, so you can write a = num.sort[1] (provided that l > 1) to find the second smallest number, without modfying the original input nums.
Then you can feed it to Enumerable#find_index.
http://ruby-doc.org/core-1.9.3/Enumerable.html#method-i-sort
http://ruby-doc.org/core-1.9.3/Enumerable.html#method-i-find_index
By the way
while (index <l)
nums - gets.to_i
num[index] = nums
index +=1
end
can be written as
nums = (0...l).map{ gets.to_i }
I understand you don't want to sort the array before finding the second-lowest number. But are you willing to use a sorted clone/copy of that array?
If
nums = [1, 5, 1, 9, 3, 8]
Then:
# grab a sorted copy of nums
b = nums.sort
# b = [1, 1, 3, 5, 8, 9]
# delete the lowest number
b.delete(b.min)
# now b = [3, 5, 8, 9]
# so get the index from the original array
nums.index(b.first)
which should return 4 because nums[4] = 3. (You could also use nums.index(b[0]) since b is already sorted.)
If you don't mind being destructive to the original array:
a.delete(a.min)
a.index(a.min)
Here's an approach that does not use sort:
arr = [3,1,2,5,1]
If second_smallest(arr) => 2 is desired:
def second_smallest(arr)
return nil if arr.uniq.size < 2
mn, mx = arr.min, arr.max
arr.map! { |e| e == mn ? mx : e }
arr.index(arr.min)
end
If second_smallest(arr) => 4 is desired:
def second_smallest(arr)
return nil if arr.uniq.size < 2
i1 = arr.index(arr.min)
arr.delete_at(i1)
i2 = arr.index(arr.min)
i2 >= i1 ? i2 + 1 : i2
end
You don't want to use sort as it's O(nlogn). You want to iterate through the array only once (after getting the max):
arr = [123,35,12,34,5,32]
This is a straight forward way of solving the problem:
def second_min_index(arr)
max = arr.max
min, min_index, second_min, second_min_index = max, 0, max, 0
arr.each_with_index do |e, i|
# if something is less than min, second min should become what used to be min
if (e <= min)
second_min, second_min_index, min, min_index = min, min_index, e, i
# if something is less than second min (but not less than min)
# it becomes the second min
elsif (e < second_min)
second_min, second_min_index = e, i
end
end
second_min_index
end
second_min_index(arr)
=> 2
A better and more reusable way of doing this would be via a transform and conquer solution (just in case you get asked for the 3rd smallest number):
def min_index(arr)
min, min_index = arr[0], 0
arr.each_with_index { |e,i| min, min_index = e,i if e < min }
min_index
end
def min_index_excluding(arr, exclude_indexes)
min, min_index = arr[0], 0
arr.each_with_index { |e,i| min, min_index = e,i if (e < min && !exclude_indexes.include?(i)) }
min_index
end
def second_min_index(arr)
min_index_excluding(arr, [min_index(arr)])
end
second_min_index(arr)
=> 2
a_sorted = a.sort
second_min = a_sorted[1]
a.index(second_min)

Check to see if an array is already sorted?

I know how to put an array in order, but in this case I just want to see if it is in order. An array of strings would be the easiest, I imagine, and answers on that front are appreciated, but an answer that includes the ability to check for order based on some arbitrary parameter is optimal.
Here's an example dataset. The name of:
[["a", 3],["b",53],["c",2]]
Where the elements are themselves arrays containing several elements, the first of which is a string. I want to see if the elements are in alphabetical order based on this string.
It looks like a generic abstraction, let's open Enumerable:
module Enumerable
def sorted?
each_cons(2).all? { |a, b| (a <=> b) <= 0 }
end
end
[["a", 3], ["b", 53],["c", 2]].sorted? #=> true
Notice that we have to write (a <=> b) <= 0 instead of a <= b because there are classes that support <=> but not the comparator operators (i.e. Array), since they do not include the module Comparable.
You also said you'd like to have the ability "to check for order based on some arbitrary parameter":
module Enumerable
def sorted_by?
each_cons(2).all? { |a, b| ((yield a) <=> (yield b)) <= 0 }
end
end
[["a", 3], ["b", 1], ["c", 2]].sorted_by? { |k, v| v } #=> false
Using lazy enumerables (Ruby >= 2.1), we can reuse Enumerable#sorted?:
module Enumerable
def sorted_by?(&block)
lazy.map(&block).sorted?
end
end
You can compare them two by two:
[["a", 3],["b",53],["c",2]].each_cons(2).all?{|p, n| (p <=> n) != 1} # => true
reduce can compare each element to the one before, and stop when it finds one out of order:
array.reduce{|prev,l| break unless l[0] >= prev[0]; l}
If it turns out the array isn't sorted, will your next action always be to sort it? For that use case (though of course depending on the number of times the array will already be sorted), you may not want to check whether it is sorted, but instead simply choose to always sort the array. Sorting an already sorted array is pretty efficient with many algorithms and merely checking whether an array is already sorted is not much less work, making checking + sorting more work than simply always sorting.
def ascending? (array)
yes = true
array.reduce { |l, r| break unless yes &= (l[0] <= r[0]); l }
yes
end
def descending? (array)
yes = true
array.reduce { |l, r| break unless yes &= (l[0] >= r[0]); l }
yes
end
Iterate over the objects and make sure each following element is >= the current element (or previous is <=, obviously) the current element.
For this to work efficiently you will want to sort during insertion.
If you are dealing with unique items, a SortedSet is also an option.
For clarification, if we patch array to allow for a sorted insertion, then we can keep the array in a sorted state:
class Array
def add_sorted(o)
size = self.size
if size == 0
self << o
elsif self.last < o
self << o
elsif self.first > o
self.insert(0, o)
else
# This portion can be improved by using a binary search instead of linear
self.each_with_index {|n, i| if n > o; self.insert(i, o); break; end}
end
end
end
a = []
12.times{a.add_sorted(Random.rand(10))}
p a # => [1, 1, 2, 2, 3, 4, 5, 5, 5, 5, 7]
or to use the built in sort:
class Array
def add_sorted2(o)
self << o
self.sort
end
end
or, if you are dealing with unique items:
require "set"
b = SortedSet.new
12.times{b << Random.rand(10)}
p b # => #<SortedSet: {1, 3, 4, 5, 6, 7, 8, 9}>
These are all way too hard. You don't have to sort, but you can use sort to check. Scrambled array below for demonstration purposes.
arr = [["b",3],["a",53],["c",2]]
arr.sort == arr # => false
p arr.sort # => [["a",53],["b",3],["c",2]]

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