How to conditionally sort a list in python with respect to two lists

Question:

Is there a simple way to sort a list X in python using two other lists Y,Z like so?

before sorting:

X = ["a", "b", "c", "d"]
Y = [ 10,   1,   2,   16 ] #positive list
Z = [  5,  6,   7,  10 ] #negative list

creating list W to assist with understanding

W = [  5,  -5,  -5,  6 ] # create new list total (Y-Z) positive - negative values.

This is what I have done so far, sorted X according to W the total of Y,Z (Y-Z) in descending

  • Sort X based on W (total) in descending order
W, X = zip(*sorted(zip(W, X),reverse=True))
X = ["d", "a", "b", "c"]
W = [  6,  5,  -5,  -5 ]

What I would like to do further is conditionally sort
if values of W are equal, I’d like to sort based on highest value in list Y, lowest value in list Z and choosing the maximum.

X = ["a", "b", "c", "d"]
Y = [ 10,   1,   2,   16 ] #positive list
Z = [  5,  6,   7,  10 ] #negative list
W = [  5,  -5,  -5,  6 ] # create new list total (Y-Z) positive - negative values.

here, indexes 1,2 are tied in W because W[1]==W[2]=-5
so we compare k1=max(Y[1],Y[2])=max(1,2)=2 and k2=min(Z[1],Z[2])=min(6,7)=6

  • since k2>k1, we prioritize ordering of X based on Z
  • if k1>k2 we should prioritize ordering of X based on Y.
    final result must be,
X = ["d", "a", "b", "c"]

How could we do this as simple as possible even for huge lists with n number of same values in the list W?

Asked By: Gargee Suresh

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Answers:

Not sure I understand the details of your sort logic because I get a different result, but the general idea is to define your sort criteria clearly as a function and then pass it to sort on your data as a list of tuples.

X = ["a", "b", "c", "d"]
Y = [ 10,   1,   2,   16 ] #positive list
Z = [  5,  6,   7,  10 ] #negative list

data = list(zip(X, Y, Z))

def sort_criteria(x):
    return x[1] - x[2], max(x[1], -x[2])

data.sort(key=sort_criteria)
print(data)
result = [item[0] for item in data]
[('b', 1, 6), ('c', 2, 7), ('a', 10, 5), ('d', 16, 10)]
Answered By: Bill

In Python 3 you could use functools.cmp_to_key to sort a list based on a custom comparator. In a custom corporator you could implement whatever complex logic you may think of.

def comparator(item1, item2):
    # compares two tuples item1=(x1,y1,z1) and item2=(x2,y2,z2)
    # returns:
    #     1 if item1 > item2, 
    #    -1 if item1 < item2, 
    #     0 if item1 = item2
    if (item1[1] - item1[2]) > (item2[1] - item2[2]): # W[1] > W[2]
        return 1
    elif (item1[1] - item1[2]) < (item2[1] - item2[2]):
        return -1
    
    if min(item1[2], item2[2]) > max(item1[1], item2[1]): # k2 > k1
        if item1[2] < item2[2]:
            return 1
        elif item1[2] > item2[2]:
            return -1
        else: # k2 > k1 but z2 = z1
            if item1[1] > item2[1]:
                return 1
            elif item1[1] < item2[1]:
                return -1
            else:
                return 0
    elif min(item1[2], item2[2]) > max(item1[1], item2[1]): # k1 > k2
        if item1[1] > item1[2]:
            return 1
        elif item1[2] < item2[1]:
            return -1
        else: # k1 > k2 but y1 = y2
            if item1[2] < item2[2]:
                return 1
            elif item1[2] > item2[2]:
                return -1
            else:
                return 0
    else: # k1 = k2
        if item1[2] < item2[2]: # Z1 < Z2
            return 1
        elif item1[2] > item2[2]:
            return -1
        elif item1[1] > item2[1]: # Z1 = Z2, Y1 > Y2
            return 1
        elif item1[1] < item2[1]:
            return -1
        else:
            return 0

Now you could use this comparator as

from functools import cmp_to_key
sorted(zip(X,Y,Z), key=cmp_to_key(comparator), reverse=True)

This would return

[('d', 16, 10), ('a', 10, 5), ('b', 1, 6), ('c', 2, 7)]
Answered By: Dmitri Chubarov

Here from my point of view the actual right answer which tests for the condition according to which list the sub-sorting in case W-values are the same should be done.

To accomplish the sub-sorting W-values are now extended to a tuple with an index of item in X. After sorting the extended W the itertools.groupby() is used to put together items with same W-value and the indices of items in X are used to find the max-value in Y and min-value in Z required to decide about the key to sub-sorting in case of same W-values. Then the indices are further used to put the right items of X together in fully sorted order.

Here the code which accomplishes this:

X    = ["a", "b", "c", "d"]
Y    = [10 ,  2,   1 , 16 ] # positive list
Z    = [ 5 ,  7,   6 , 10 ] # negative list
Wsorted = sorted([ (Y[i]-Z[i], i) for i in range(len(X)) ])
Xsorted = []
import itertools
for _, g in itertools.groupby(Wsorted, lambda w: w[0]):
    lg = list(g)
    if len(lg) == 1:
        Xsorted += X[lg[0][1]]
    else:
        maxY = max([Y[i] for _,i in lg])
        minZ = min([Z[i] for _,i in lg])
        if maxY  > minZ: lg.sort(key=lambda lgitem: Y[lgitem[1]])
        if maxY  < minZ: lg.sort(key=lambda lgitem: Z[lgitem[1]])
        if maxY == minZ: pass # no preferred sub-sorting
        Xsorted += [ X[lgitem[1]] for lgitem in lg ]
Xsorted.reverse()
print(f'{Xsorted=}') # gives: Xsorted=['d', 'a', 'b', 'c']

The above code covers a general case of sorting condition based on comparison of maximum of values in Y and minimum of values in Z for same W-values to decide about sub-sorting according to Y or to Z.

The general case does not take into consideration that when W values are Y values minus Z values it doesn’t actually matter for the sub-sorting after which, Y or Z values, the sub-sorting has to be done.

It doesn’t actually matter as the order of Y values for same W values is always the same as the order of Z values because of the equal difference.

So a search for a maximum value in Y and minimum value in Z is not necessary in this special case of W and the sorting can be made much easier just using only Y values ( or Z values which gives same result ) for the sub-sorting.

Below the one liner performing such a sort for the case of the simple W being the difference between Y and Z values:

Xsorted = [ X[i] for i in sorted( 
    list(range(len(X))),key=lambda i: (Y[i]-Z[i],Y[i]),reverse=True)]
print(Xsorted) # gives ['d', 'a', 'b', 'c']
Answered By: Claudio
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