# Daily Challenge #63- Two Sum

Write a function that takes an array of numbers (integers for the tests) and a target number. It should find two different items in the array that, when added together, give the target value. The indices of these items should then be returned in a tuple like so: (index1, index2).

For the purposes of this kata, some tests may have multiple answers; any valid solutions will be accepted.

The input will always be valid (numbers will be an array of length 2 or greater, and all of the items will be numbers; target will always be the sum of two different items from that array).

twoSum [1, 2, 3] 4 === (0, 2)


Thank you to wthit56 and CodeWars, who has licensed redistribution of this challenge under the 2-Clause BSD License!

Want to propose a challenge idea for a future post? Email yo+challenge@dev.to with your suggestions!

Posted on by:

### dev.to staff

The hardworking team behind dev.to ❤️

### Discussion

F#

The other solutions posted so far were O(n2 ), I opted for an O(n) solution with a map and a recursive nested helper instead. I also didn't want to trust the input list, so went for a (int * int) option return type.

module TwoSum

let twoSum l n =
let rec twoSum' l i n m =
match l with
| [] -> None
| (x :: xs) ->
let diff = n - x
match Map.tryFind diff m with
| Some(j) -> Some(j, i)
| _ -> twoSum' xs (i + 1) n (Map.add x i m)
twoSum' l 0 n Map.empty


Tests:

module TwoSumTest

open FsUnit.Xunit
open Xunit
open TwoSum

[<Fact>]
let finding a sum in 3 element array () =
twoSum [1; 2; 3] 4 |> should equal (Some (0, 2))

[<Fact>]
let finding a sum in 2 element array () =
twoSum [4; 5] 9 |> should equal (Some (0, 1))

[<Fact>]
let finding a sum in bigger array () =
twoSum [4; 5; 6; 7; 8; 9] 17 |> should equal (Some (4, 5))

[<Fact>]
let too short array () =
twoSum [1] 2 |> should equal None

[<Fact>]
let no sum () =
twoSum [1; 2; 3;] 7 |> should equal None



A recursive solution that checks for each item x in the list if there is an item in the rest of the list that, added to x, results in the target value.

import Data.List (findIndex)

twoSum :: [Int] -> Int -> (Int, Int)
twoSum xs n = findSum (head xs) 0 (tail xs)
where
findSum x curr ys = case findIndex (isSum x) ys of
Just(i) -> (curr, i + curr + 1)
Nothing -> findSum (head ys) (curr + 1) (tail ys)

isSum x y = x + y == n


The input will always be valid that's even worst than premature optimizations.

However, for the purpose of this challenge, I'll take that assumption, because while super important, input validation is boring.

C#, with comments on every line, so that everyone can understand it even if they don't speak the language:

The simple, O(n2) solution - using a nested loop.


(int Index1, int Index2) TwoSum(int[] array, int target)
{
// iterate the array from 0 to length -2
for (var i = 0; i < array.Length - 1; i++)
{
// iterate the array from i+1 to length -1
for (var j = i + 1; j < array.Length; j++)
{
// if sum found
if (array[i] + array[j] == target)
{
// return both indexes
return (i, j);
}
}
}
// indicate no match found, required by the c# compier.
return (-1, -1);
}


The sophisticated, O(n) solution - using a single loop and a helper hash map.

    int Index1, int Index2) TwoSumImproved(int[] array, int target)
{
// In .Net, A dictionary is basically a hash map. here the keys and values are both ints
var map = new Dictionary<int, int>();

// iterate the full length of the array.
for (var i = 0; i < array.Length; i++)
{
// calculate the value needed to add to the current value to get the target sum
var valueNeeded = target - array[i];

// check if the map contains the value needed as it's key, If it does, return true and populate the int j
// The TryGetValue time complexity is approaching O(1)
if (map.TryGetValue(valueNeeded, out int j))
{
// return both indexes
return (j, i);
}
// add to the map, where the key is the array value and the value is the index.
}
return (-1, -1); // indicate no match found
}



Try it online

Inspired by Michael Kohl's solution in F# (O(n) rules!), I did the same thing in Rust. All the credit to him :)

fn two_sum(ns: &[i32], sum: i32) -> Option<(usize, usize)> {
let mut map = HashMap::new();
for (i, &n) in ns.iter().enumerate() {
let diff = sum - n;
if let Some(&j) = map.get(&diff) {
return Some((j, i));
}
map.insert(n, i);
}
None
}



global sum_value
sum_value = int(input("Enter the sum value :"))
arr = [ int(i) for i in input("Enter array elements :" ).split( )]
def two_sum (arr) :
for i in range(len(arr)) :
for j in  range(i+1 , len(arr)) :
if arr[j] + arr[i] == sum_value :
return (i , j)
return "NO SUCH PAIRS FOUND"

print (two_sum(arr))



Another one

global sum_value
sum_value = int(input("Enter the sum value :"))
arr = [ int(i) for i in input("Enter array elements :" ).split( )]
def two_sum (arr) :
for i in range(len(arr)) :
second_num = sum_value - arr[i]
if second_num in arr :
return (i , arr.index(second_num))
return "NO SUCH PAIRS FOUND"
print (two_sum(arr))


Here is the Python solution:

def two_sum(numbers, target):
num_index = 0
for number in numbers:
index = 1
while index < len(numbers):
if number + numbers[index] == target:
return [num_index, index]
index += 1
num_index += 1

return [0, len(numbers)-1]


In Python, written with a O(n) solution with the given assumptions using a dictionary and enumeration to generate an index.

def twoSum(arr: list, target: int) -> (int, int):
num_dict = dict()
for index, num in enumerate(arr):
diff = target - num
if diff in num_dict:
return (min(index, num_dict[diff]), max(index, num_dict[diff]))
num_dict[num] = index

raise IndexError


In gwion:

fun <~int, int~>Tuple twosum(int data[], int total) {
for(int i; i < data.size(); ++i) {
for(i + 1 => int j; j < data.size(); ++j) {
if((data[i]+data[j]) == total)
return <(i, j);
}
}
return null;
}

([1, 2, 3], 4) => twosum @=> >(index0, index1);
<<< index0, " ", index1 >>>;


The fun thing is that it undercovered a (now fixed) bug on tuple unpacking. 🍾

Ruby

The initial solution comes to mind which obviously could be improved in performance purposes having more time

  def two_sum(array, target)
array.each_with_index do |item, i|
(i + 1).upto(array.size - 1) do |j|
return [i, j] if item + array[j] == target
end
end

nil
end


import Control.Applicative
import Data.List (find)

twoSum :: (Eq a, Num a) => [a] -> a -> Maybe (Int, Int)
twoSum xs target = let withId = zip xs [0..]
sums = (\(x,a) (y,b) -> (x+y, (a, b))) <$> withId <*> withId in find ((==target) . fst) sums >>= (return . snd)  I know the question said the input is always good, but I didn't want to ignore possible errors in when using the function... I'm not sure of the speed of this code either. My guess is it only evaluates combinations until it finds a correct one? But I'm not an expert on lazy evaluation and I'm pretty sure this could be faster. My guess is it only evaluates combinations until it finds a correct one? Yes, Data.List.find will return the first list item satisfying the predicate. JavaScript Recursive solution. "use strict"; const addWith = target => current => target + current; const equalsTo = target => current => target === current; function twoSum(numbers, sum, index = 0) { if (numbers.length === 0) { return null; } const [first, ...rest] = numbers; const foundIndex = numbers.map(addWith(first)).findIndex(equalsTo(sum)); if (foundIndex > 0) { return [index, foundIndex + index]; } return twoSum(rest, sum, index + 1); } console.log(twoSum([18, 7, 1, 6, 0, 15, 3, 12, 111, 1111], 4)); // [2, 6]  reduce is good for this one. Here's a JS quickie with O(n) complexity. twoSum = (numbers, target) => numbers.reduce(([result, partials], num, i) => ([ result || (num in partials && [partials[num], i]), Object.assign(partials, {[target - num]: i}) ]), [undefined, {}])[0]  The partials map maps the index of each value to the value required to bring it up to the target. This can then be picked up by a later value to the get the answer. Perl solution. Walk the array, for each element, store the expected counterpart into a hash. If the element already exists in the hash, we have the pair. #!/usr/bin/perl use warnings; use strict; sub two_sum { my ($arr, $sum) = @_; my %expect; for my$i (0 .. $#$arr) {
return [ $expect{$sum - $arr->[$i] }, $i ] if exists$expect{ $sum -$arr->[$i] };$expect{ $arr->[$i] } = $i; } } use Test::More tests => 2; is_deeply two_sum([1, 2, 3], 4), [0, 2]; is_deeply two_sum([1 .. 99], 197), [97, 98];  const twoSum = (a,b) => { for (var x=0; x<a.length; x++) for (var y=x+1; y<a.length; y++) { if (a[x] + a[y] == b) return [x,y]; } }  Swift Solution class Solution { static func twosum(numbers: [Double], target: Double) -> [Int] { let result = numbers.filter({ return numbers.contains( target -$0 ) })

return [numbers.firstIndex(of: result[0])! , numbers.lastIndex(of: result [result.count - 1 ] )!] }
}

class Solution {
static func twosum(numbers: [Double], target: Double) -> [Int] {
let result = numbers.filter({ return numbers.contains( target - \$0 ) })

return [numbers.firstIndex(of: result[0])! , numbers.lastIndex(of: result [result.count - 1 ] )!] }
}

def twoSum(arr,target):
for i in range(len(arr)-1):
for j in range(i+1,len(arr)):
if(arr[i]+arr[j]==target):
return([i,j])
else:
return("no indices found with that sum")
if __name__=="__main__":
arr=list(map(int,input().split()))
target=int(input())
print(twoSum(arr,target))


The target example is given as:

twoSum [1, 2, 3] 4 === (0, 2)


But I believe that should be something like:

twoSum [1, 2, 3] 4 === (1, 3)


correct?

No, because it returns the indices, not the values.

The indices of these items should then be returned in a tuple like so: (index1, index2).

OH! missed that :) Thanks!