sum of prime numbers

Question

I have an exercise:

Write a program that takes the number n from the input and prints all cases of prime numbers whose sum is equal to n.

For example: input is n = 13 and output is:

2 2 2 2 2 3
2 2 2 2 5
2 2 2 7
2 2 3 3 3
2 3 3 5
2 11
3 3 7
3 5 5
13

The output is sorted by lexicographic method.

I just could code for finding the prime numbers between 1-n:

n = int(input())
lst = []
for i in range(2, n + 1):
    isPrime = True
    for j in range(2, i - 1):
        if i % j == 0:
            isPrime = False
    if isPrime:
        lst.append(i)

print(lst)

Asked By: Elio Baharan

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Source

Answer 1

Here is my take at the problem.

solution = []
primes_up_to_n = [2, 3, 5, 7, 11, 13]

def get_sums(primes, n, path):
    global solution # keep track of solutions found so far.
    if n < min(primes):
        return # no more solutions are possible at this point
    for prime in primes:
        if n == prime:
            solution.append(path+[prime])
        get_sums(primes, n-prime, path+[prime])

get_sums(primes_up_to_n , 13, [])

k = [sorted(x) for x in solution] # order the solutions
print([*map(list, {*map(tuple, k)})]) # remove the duplicates

Explanation:

we check if the current n is in the prime list. If it is, it means that path + [n] is a solution, so we append it.
we reccursively call get_sums to find further solutions.
The problem with this approach is that the algorithm doesn’t differentiate between [2, 2, 2, 2, 2, 3] and [2, 2, 2, 2, 3, 2] for instance. So we get rid of such duplicates in the last two lines.

The code outputs:

[[2, 2, 2, 2, 2, 3],
[2, 2, 2, 7],
[2, 3, 3, 5],
[13],
[3, 3, 7],
[2, 2, 3, 3, 3],
[3, 5, 5],
[2, 2, 2, 2, 5],
[2, 11]]

Answered By: nonlinear

sum of prime numbers

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