I'm very stuck on this (probably because I'm new to computer programming). I have the following code, from the question: [https://stackoverflow.com/questions/37616841/python-find-all-possible-combinations-of-parts-of-a-given-number/37617708?noredirect=1#comment62719215_37617708]
def sum_to_n(n, size, limit=None):
"""Produce all lists of `size` positive integers in decreasing order
that add up to `n`."""
if size == 1:
yield [n]
return
if limit is None:
limit = n
start = (n + size - 1) // size
stop = min(limit, n - size + 1) + 1
for i in range(start, stop):
for tail in sum_to_n(n - i, size - 1, i):
yield [i] + tail
for partition in sum_to_n(8, 3):
print (partition)
[6, 1, 1]
[5, 2, 1]
[4, 3, 1]
[4, 2, 2]
[3, 3, 2]
Is it very useful but I'm trying to modify it in order to set some options. Suppose I want to have only the results in which the first number of the list is 4 and the last of the list is 1. At the moment I use this solution:
def sum_to_n(n,first, last, size, limit=None):
if size == 1:
yield [n]
return
if limit is None:
limit = n
start = (n + size - 1) // size
stop = min(limit, n - size + 1) + 1
for i in range(start, stop):
if i <=first:
for tail in sum_to_n(n - i,first,last, size - 1, i):
ll=len(tail)
if tail[ll-1]==last:
yield [i] + tail
for i in sum_to_n(8,4,1,3):
if i[0]==4 and i[size-1]==1:
print(i)
if i[0]>4:
break
[4,3,1]
But with larger integers the program is doing a lot of unwanted work.
For example, the for i in range(start, stop): computes all the possible first numbers of the list and not only the "first" parameter needed and the function does not work without it.
Someone can suggest a better and faster solution to call the function giving the parameters needed in order to have only the requested computations?
Since you know the first number, you just need to solve if for the last one.
In your example, that would give something like:
for res in sum_to_n(n=8-4, last=1, size=3-1):
print([4] + res)