Sparse matrix subtraction - python

I need to write a function which gets a list of dictionaries (every dictionary represents a sparse matrix) and returns a dictionary of the subtraction matrix.
For example: for the list [{(1, 3): 2, (2, 7): 1}, {(1, 3): 6}] it needs to return {(1, 3): -4, (2, 7): 1} .
The matrices don't have to be the same size, the list can have more than two matrices and if the subtraction is 0 then it should not appear in the final dictionary.
I succeeded in getting the -4 but no matter what I write after defining x I get x == -6 and I can't tell why. I want to insert the -4 as the new value for the element.
lst = [{(1, 3): 2, (2, 7): 1}, {(1, 3): 6}]
def diff_sparse_matrices(lst):
result = {}
for dictionary in lst:
for element in dictionary:
if element not in result:
result[element] = dictionary[element]
if element in result:
x = result[element] - dictionary[element]

def diff_sparse_matrices(lst):
result = lst[0].copy()
for matrix in lst[1:]:
for coordinates, value in matrix.items():
result[coordinates] = result.get(coordinates, 0) - value
if result[coordinates] == 0:
del result[coordinates]
return result

def diff_sparse_matrices(lst):
result = lst[0].copy()
for d in lst[1:]:
for tup in d:
if tup in result:
result[tup] -= d[tup]
else:
result[tup] = -d[tup]
return result

Related

Index to closest coordinate

I have this function
A=[(1,2,3),(2,3,4)]
B=[(2,4,3),(1,8,1),(2,3,5),(1,5,3)]
def closestNew(A,B):
C = {}
for bp in B:
closestDist = -1
for ap in A:
dist = sum(((bp[0]-ap[0])**2, (bp[1]-ap[1])**2, (bp[2]-ap[2])**2))
if(closestDist > dist or closestDist == -1):
C[bp] = ap
closestDist = dist
return C
That will return the closest coordinate between the two lists.
Output:
{(1, 2, 3): (2, 4, 3), (2, 3, 4): (2, 3, 5)}
However, I want the index of array B (the points that matched with array A (check output)) as well in a seperate list, any ideas?
Return
idx=[0,2]
A=[(1,2,3),(2,3,4)]
B=[(2,4,3),(1,8,1),(2,3,5),(1,5,3)]
C={(1, 2, 3): (2, 4, 3), (2, 3, 4): (2, 3, 5)}
C is a dictionary where it values correspond to points on B.
idx=[] # an empty list
for x in C.values():
idx.append(B.index(x)) # index function to find the index of values in B
print(idx)
#[0, 2]
If you want to calcule the closest point to A, is better to have A as a outer loop and B as inside loop, in that way you can iterate for every A through all B's. Also you can use enumerate to know what index you are in the loop.
a = [(1,2,3),(2,3,4)]
b =[(2,4,3),(1,8,1),(2,3,5),(1,5,3)]
# store reference for the min index-point
index = []
C = {}
for indexA, ap in enumerate(a):
# Assume the max distance
closestDist = 1e9
for indexB,bp in enumerate(b):
dist = sum(((bp[0]-ap[0])**2, (bp[1]-ap[1])**2, (bp[2]-ap[2])**2))
if(dist < closestDist):
C[ap] = bp
closestDist = dist
# Initialize the list if not have value for the i-th of A
if indexA + 1 > len(index):
index.append(indexB)
else:
index[indexA] = indexB
print(index)
return C

Dictionary with multiple values per key via for loop

given a List in Python I want top create a dictionary that stores all possible two sums as keys and the corresponding indices as values, e.g.
list = [1,0,-1, 0]
Then I would to compute the dictionary {1:{0,1}, {0,3}, 0: {1,3},{0,2}, -1:{1,2}, {2,3}}.
I am having troubles finding out how to have a dictionary where one key corresponds to multiple values. If I use dict[sum]={i,j} I am always replacing the entries in my dictionary while instead I would like to add them.
Does anyone know if there exists a solution?
IIUC, use a dictionary with setdefault to add the results and itertools.combinations to generate the combinations of indices:
lst = [1,0,-1, 0]
from itertools import combinations
out = {}
for i,j in combinations(range(len(lst)), 2):
a = lst[i] # first value
b = lst[j] # second value
S = a+b # sum of values
# if the key is missing, add empty list
# append combination of indices as value
out.setdefault(S, []).append((i,j))
print(out)
Condensed variant:
out = {}
for i,j in combinations(range(len(lst)), 2):
out.setdefault(lst[i]+lst[j], []).append((i,j))
output:
{ 1: [(0, 1), (0, 3)],
0: [(0, 2), (1, 3)],
-1: [(1, 2), (2, 3)]}
Try this:
arr = [1, 0, -1, 0]
map = {}
for i in range(len(arr)):
for j in range(i + 1, len(arr)):
s = arr[i] + arr[j]
if s not in map:
map[s] = []
map[s].append((i, j))
print(map)

Given a list of numbers, how many different ways can you add them together to get a sum S?

Given a list of numbers, how many different ways can you add them together to get a sum S?
Example:
list = [1, 2]
S = 5
1) 1+1+1+1+1 = 5
2) 1+1+1+2 = 5
3) 1+2+2 = 5
4) 2+1+1+1 = 5
5) 2+2+1 = 5
6) 1+2+1+1 = 5
7) 1+1+2+1 = 5
8) 2+1+2 = 5
Answer = 8
This is what I've tried, but it only outputs 3 as the answer
lst = [1, 2]
i = 1
result = 0
while i <= 5:
s_list = [sum(comb) for comb in combinations_with_replacement(lst, i)]
for val in s_list:
if val == 5:
result += 1
i+= 1
print(result)
However, this outputs three. I believe it outputs three because it doesn't account for the different order you can add the numbers in. Any ideas on how to solve this.
The problem should work for much larger data: however, I give this simple example to give the general idea.
Using both itertools.combinations_with_replacement and permutations:
import itertools
l = [1,2]
s = 5
res = []
for i in range(1, s+1):
for tup in itertools.combinations_with_replacement(l, i):
if sum(tup) == s:
res.extend(list(itertools.permutations(tup, i)))
res = list(set(res))
print(res)
[(1, 2, 2),
(2, 2, 1),
(1, 1, 2, 1),
(1, 2, 1, 1),
(2, 1, 1, 1),
(1, 1, 1, 2),
(2, 1, 2),
(1, 1, 1, 1, 1)]
print(len(res))
# 8
How about using dynamic programming? I believe it's more easy to understand and can be implemented easily.
def cal(target, choices, record):
min_choice = min(choices)
if min_choice > target:
return False
for i in range(0, target+1):
if i == 0:
record.append(1)
elif i < min_choice:
record.append(0)
elif i == min_choice:
record.append(1)
else:
num_solution = 0
j = 0
while j < len(choices) and i-choices[j] >= 0:
num_solution += record[i-choices[j]]
j += 1
record.append(num_solution)
choices = [1, 2]
record = []
cal(5, choices, record)
print(record)
print(f"Answer:{record[-1]}")
The core idea here is using an extra record array to record how many ways can be found to get current num, e.g. record[2] = 2 means we can use to ways to get a sum of 2 (1+1 or 2).
And we have record[target] = sum(record[target-choices[i]]) where i iterates over choices. Try to think, the way of getting sum=5 must be related with the way of getting sum=4 and so on.
Use Dynamic Programming.
We suppose that your list consists of [1,2,5] so we have this recursive function :
f(n,[1,2,5]) = f(n-1,[1,2,5]) + f(n-2,[1,2,5]) + f(n-5,[1,2,5])
Because if the first number in sum is 1 then you have f(n-1,[1,2,5]) options for the rest and if it is 2 you have f(n-2,[1,2,5]) option for the rest and so on ...
so start from f(1) and work your way up with Dynamic programming. this solution in the worst case is O(n^2) and this happens when your list has O(n) items.
Solution would be something like this:
answers = []
lst = [1,2]
number = 5
def f(target):
val = 0
for i in lst: #O(lst.count())
current = target - i
if current > 0:
val += answers[current-1]
if lst.__contains__(target): #O(lst.count())
val += 1
answers.insert(target,val)
j = 1;
while j<=number: #O(n) for while loop
f(j)
j+=1
print(answers[number-1])
here is a working version.
You'd want to use recursion to traverse through each possibility for each stage of addition, and pass back the numbers used once you've reached a number that is equal to the expected.
def find_addend_combinations(sum_value, addend_choices, base=0, history=None):
if history is None: history = []
if base == sum_value:
return tuple(history)
elif base > sum_value:
return None
else:
results = []
for v in addend_choices:
r = find_addend_combinations(sum_value, addend_choices, base + v,
history + [v])
if isinstance(r, tuple):
results.append(r)
elif isinstance(r, list):
results.extend(r)
return results
You could write the last part a list comprehension but I think this way is clearer.
Combinations with the elements in a different order are considered to equivalent. For example, #3 and #5 from your list of summations are considered equivalent if you are only talking about combinations.
In contrast, permutations consider the two collections unique if they are comprised of the same elements in a different order.
To get the answer you are looking for you need to combine both concepts.
First, use your technique to find combinations that meet your criteria
Next, permute the collection of number from the combination
Finally, collect the generated permutations in a set to remove duplicates.
[ins] In [01]: def combination_generator(numbers, k, target):
...: assert k > 0, "Must be a positive number; 'k = {}".format(k)
...: assert len(numbers) > 0, "List of numbers must have at least one element"
...:
...: for candidate in (
...: {'numbers': combination, 'sum': sum(combination)}
...: for num_elements in range(1, k + 1)
...: for combination in itertools.combinations_with_replacement(numbers, num_elements)
...: ):
...: if candidate['sum'] != target:
...: continue
...: for permuted_candidate in itertools.permutations(candidate['numbers']):
...: yield permuted_candidate
...:
[ins] In [02]: {candidate for candidate in combination_generator([1, 2], 5, 5)}
Out[02]:
{(1, 1, 1, 1, 1),
(1, 1, 1, 2),
(1, 1, 2, 1),
(1, 2, 1, 1),
(1, 2, 2),
(2, 1, 1, 1),
(2, 1, 2),
(2, 2, 1)}

Better ways to find pairs that sum to N

Is there a faster way to write this, the function takes a list and a value to find the pairs of numeric values in that list that sum to N without duplicates I tried to make it faster by using sets instead of using the list itself (however I used count() which I know is is linear time) any suggestions I know there is probably a way
def pairsum_n(list1, value):
set1 = set(list1)
solution = {(min(i, value - i) , max(i, value - i)) for i in set1 if value - i in set1}
solution.remove((value/2,value/2)) if list1.count(value/2) < 2 else None
return solution
"""
Example: value = 10, list1 = [1,2,3,4,5,6,7,8,9]
pairsum_n = { (1,9), (2,8), (3,7), (4,6) }
Example: value = 10, list2 = [5,6,7,5,7,5,3]
pairsum_n = { (5,5), (3,7) }
"""
Your approach is quite good, it just needs a few tweaks to make it more efficient. itertools is convenient, but it's not really suitable for this task because it produces so many unwanted pairs. It's ok if the input list is small, but it's too slow if the input list is large.
We can avoid producing duplicates by looping over the numbers in order, stopping when i >= value/2, after using a set to get rid of dupes.
def pairsum_n(list1, value):
set1 = set(list1)
list1 = sorted(set1)
solution = []
maxi = value / 2
for i in list1:
if i >= maxi:
break
j = value - i
if j in set1:
solution.append((i, j))
return solution
Note that the original list1 is not modified. The assignment in this function creates a new local list1. If you do actually want (value/2, value/2) in the output, just change the break condition.
Here's a slightly more compact version.
def pairsum_n(list1, value):
set1 = set(list1)
solution = []
for i in sorted(set1):
j = value - i
if i >= j:
break
if j in set1:
solution.append((i, j))
return solution
It's possible to condense this further, eg using itertools.takewhile, but it will be harder to read and there won't be any improvement in efficiency.
Try this, running time O(nlogn):
v = [1, 2, 3, 4, 5, 6, 7, 8, 9]
l = 0
r = len(v)-1
def myFunc(v, value):
ans = []
% this block search for the pair (value//2, value//2)
if value % 2 == 0:
c = [i for i in v if i == value // 2]
if len(c) >= 2:
ans.append((c[0], c[1]))
v = list(set(v))
l = 0
r = len(v)-1
v.sort()
while l<len(v) and r >= 0 and l < r:
if v[l] + v[r] == value:
ans.append((v[l], v[r]))
l += 1
r -= 1
elif v[l] + v[r] < value:
l += 1
else:
r -= 1
return list(set(ans))
It is called the Two pointers technique and it works as follows. First of all, sort the array. This imposes a minimum running time of O(nlogn). Then set two pointers, one pointing at the start of the array l and other pointing at its last element r (pointers name are for left and right).
Now, look at the list. If the sum of the values returned at position l and r is lower than the value we are looking for, then we need to increment l. If it's greater, we need to decrement r.
If v[l] + v[r] == value than we can increment/decrement both l or r since in any case we want to skip the combination of values (v[l], v[r]) as we don't want duplicates.
Timings: this is actually slower then the other 2 solutions. Due to the amount of combinations produced but not actually needed it gets worse the bigger the lists are.
You can use itertools.combinations to produce the 2-tuple-combinations for you.
Put them into a set if they match your value, then return as set/list:
from itertools import combinations
def pairsum_n(list1, value):
"""Returns the unique list of pairs of combinations of numbers from
list1 that sum up `value`. Reorders the values to (min_value,max_value)."""
result = set()
for n in combinations(list1, 2):
if sum(n) == value:
result.add( (min(n),max(n)) )
return list(result)
# more ugly one-liner:
# return list(set(((min(n),max(n)) for n in combinations(list1,2) if sum(n)==value)))
data = [1,2,3,4,5,6,6,5,4,3,2,1]
print(pairsum_n(data,7))
Output:
[(1, 6), (2, 5), (3, 4)]
Fun little thing, with some sorting overhead you can get all at once:
def pairsum_n2(data, count_nums=2):
"""Generate a dict with all count_nums-tuples from data. Key into the
dict is the sum of all tuple-values."""
d = {}
for n in (tuple(sorted(p)) for p in combinations(data,count_nums)):
d.setdefault(sum(n),set()).add(n)
return d
get_all = pairsum_n2(data,2) # 2 == number of numbers to combine
for k in get_all:
print(k," -> ", get_all[k])
Output:
3 -> {(1, 2)}
4 -> {(1, 3), (2, 2)}
5 -> {(2, 3), (1, 4)}
6 -> {(1, 5), (2, 4), (3, 3)}
7 -> {(3, 4), (2, 5), (1, 6)}
2 -> {(1, 1)}
8 -> {(2, 6), (4, 4), (3, 5)}
9 -> {(4, 5), (3, 6)}
10 -> {(5, 5), (4, 6)}
11 -> {(5, 6)}
12 -> {(6, 6)}
And then just access the one you need via:
print(get_all.get(7,"Not possible")) # {(3, 4), (2, 5), (1, 6)}
print(get_all.get(17,"Not possible")) # Not possible
Have another solution, it's alot faster then the one I just wrote, not as fast as #PM 2Ring's answer:
def pairsum_n(list1, value):
set1 = set(list1)
if list1.count(value/2) < 2:
set1.remove(value/2)
return set((min(x, value - x) , max(x, value - x)) for x in filterfalse(lambda x: (value - x) not in set1, set1))

top n keys with highest values in dictionary with tuples as keys

I want to get the top n keys of a dictionary with tuples as keys, where the first value of the tuple is a particular number (1 in the example below):
a = {}
a[1,2] = 3
a[1,0] =4
a[1,5] = 1
a[2,3] = 9
I want [1,0] and [1,2] to be returned, where the first element of the tuple/key = 1
this
import heapq
k = heapq.nlargest(2, a, key=a.get(1,))
returns [1,4] and [1,3], the highest keys/tuples with first element = 1, though if I make it
k = heapq.nlargest(2, a, key=a.get(2,))
it returns the same thing?
First you should take only the keys with first coordinate 1. Otherwise, there is the chance if there are a few elements with 1 as first coordinate, to get other tuples also. Then you can use heapq normally. For example:
a = {
(1, 2): 3,
(1, 0): 4,
(1, 5): 1,
(2, 3): 9
}
import heapq
print heapq.nlargest(2, (k for k in a if k[0] == 1), key=lambda k: a[k])
print heapq.nlargest(2, (k for k in a if k[0] == 2), key=lambda k: a[k])
Output:
[(1, 0), (1, 2)]
[(2, 3)]
The key parameter should be a function. But you are passing in a.get(1,). What this does is calling a.get(1,) which is the same as a.get(1) which is the same as a.get(1, None).
The dictionary doesn't have a 1 key so it returns None which means you are doing the equivalent of passing key=None which is the same as not passing a key at all: you are using the identity function as key.
Then heapq.nlargest returns the top 2 elements which are, correctly, [1, 4] and [1, 3].
This explains why using a.get(1,) and a.get(2,) does the same thing. The above reasoning works for both values and you end up with key=None in both cases.
To achieve what you want use something like:
key=lambda x: (x[0] == 1, a[x])
If you find yourself using this kind of keys often you can create a key maker function:
def make_key(value, container):
def key(x):
return x[0] == value, container[x]
return key
using it as:
nlargest(2, a, key=make_key(1, a))
nlargest(2, a, key=make_key(2, a))

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