On 4/22/2012 9:07 PM, Nestor wrote:

The other day a colleague of mine submitted this challenge taken from some website to us coworkers:

This is more of a python-list post than a python-ideas post. So is my response.

Have the function ArrayAddition(arr) take the array of numbers stored in arr and print true if any combination of numbers in the array can be added up to equal the largest number in the array, otherwise print false. For example: if arr contains [4, 6, 23, 10, 1, 3] the output should print true because 4 + 6 + 10 + 3 = 23. The array will not be empty, will not contain all the same elements, and may contain negative numbers.

Since the order of the numbers is arbitrary and irrelevant to the problem, it should be formulated in term of a set of numbers. Non-empty means that max(set) exists. No duplicates means that max(set) is unique and there is no question of whether to remove one or all copies.

Examples: 5,7,16,1,2

False (5+7+1+2 == 15)

3,5,-1,8,12

True (8+5-1 == 12)

I proposed this solution:

from itertools import combinations, chain def array_test(arr): biggest = max(arr) arr.remove(biggest my_comb = chain(*(combinations(arr,i) for i in range(1,len(arr)+1)))

I believe the above works for sets as well as lists.

for one_comb in my_comb: if sum(one_comb) == biggest: return True, one_comb return False

The above is must clearer to me than the Haskell (or my equivalent) below, and I suspect that would be true even if I really knew Haskell. If you want something more like the Haskell version, try return any(filter(x == biggest, map(sum, my_comb))) To make it even more like a one-liner, replace my_comb with its expression.

But then somebody else submitted this Haskell solution:

import Data.List f :: (Ord a,Num a) => [a] -> Bool f lst = (\y -> elem y $ map sum $ subsequences $ [ x | x<- lst, x /= y ]) $ maximum lst

If you really want one logical line that I believe matches the above ;-) def sum_to_max(numbers): return ( (lambda num_max: (lambda nums: any(filter(lambda n: n == num_max, map(sum, chain(*(combinations(nums,i) for i in range(1,len(nums)+1)))))) ) (numbers - {num_max}) # because numbers.remove(num_max)is None ) (max(numbers)) ) print(sum_to_max({5,7,16,1,2}) == False, sum_to_max({3,5,-1,8,12}) == True) # sets because of numbers - {num_max} True, True Comment 1: debugging nested expressions is harder than debugging a sequence of statements because cannot insert print statements. Comment 2: the function should really return an iterator that yields the sets that add to the max. Then the user can decide whether or not to collapse the information to True/False and stop after the first.

I wonder if we should add a subsequences function to itertools or make the "r" parameter of combinations optional to return all combinations up to len(iterable).

I think not. The goal of itertools is to provide basic iterators that can be combined to produce specific iterators, just as you did. -- Terry Jan Reedy

Nestor wrote: [...]

But then somebody else submitted this Haskell solution:

import Data.List f :: (Ord a,Num a) => [a] -> Bool f lst = (\y -> elem y $ map sum $ subsequences $ [ x | x <- lst, x /= y ]) $ maximum lst

I wonder if we should add a subsequences function to itertools or make the "r" parameter of combinations optional to return all combinations up to len(iterable).

You really don't do your idea any favours by painting it as "Haskell envy". I have mixed ideas on this. On the one hand, subsequences is a natural function to include along with permutations and combinations in any combinatorics tool set. As you point out, Haskell has it. So does Mathematica, under the name "subsets". But on the other hand, itertools is arguably not the right place for it. If we add subsequences, will people then ask for partitions and derangements next? Where will it end? At some point the line needs to be drawn, with some functions declared "too specialised" for the general itertools module. (Perhaps there should be a separate combinatorics module.) And on the third hand, what you want is a simple two-liner, easy enough to write in place: from itertools import chain, combinations allcombs = chain(*(combinations(data, i) for i in range(len(data)+1))) which is close to what your code used. However, the discoverability of this solution is essentially zero (if you don't know how to do this, it's hard to find out), and it is hardly as self-documenting as from itertools import subsequences allcombs = subsequences(data) Overall, I would vote +0.5 on a subsequences function. -- Steven

Nestor wrote:

The other day a colleague of mine submitted this challenge taken from some website to us coworkers:

Have the function ArrayAddition(arr) take the array of numbers stored in arr and print true if any combination of numbers in the array can be added up to equal the largest number in the array, otherwise print false. For example: if arr contains [4, 6, 23, 10, 1, 3] the output should print true because 4 + 6 + 10 + 3 = 23. The array will not be empty, will not contain all the same elements, and may contain negative numbers.

By the way, your solution is wrong. Consider this sample data: -2, -5, 0, -1, -3 In this case, the Haskell solution should correctly print true, while yours will print false, because you skip the empty subset. The empty sum equals the maximum value of the set, 0. The ease at which people can get this wrong is an argument in favour of a standard solution. -- Steven