Two codes in python should be giving the same result but they don't

Question

Description: The following codes recieves the coordinates of two dots with n dimensions. It calculates the manhanttan distance of theses two dots The codes:

def manhanttan( ponto1, ponto2 ):
    totalp1 = 0
    totalp2 = 0
    for x in range( 0, len( ponto1 ) ):
        totalp1 += ponto1[x]
        totalp2 += ponto2[x]
    return abs( totalp1 - totalp2 )

and

def manhanttan( ponto1, ponto2 ):
    total = 0
    for x in range( 0, len( ponto1 ) ):
        total += abs( ponto1[x] - ponto2[x] )
    return total

are giving different results and i don't know why. Can somebody help me?

PS: All values in the lists are positives

PS2: With the first one my classifications gets

K1: Expected Class: 6, Found Class: 0 K2: Expected Class: 6, Found Class: 0 K3: Expected Class: 6, Found Class: 0 K4: Expected Class: 6, Found Class: 0 K5: Expected Class: 6, Found Class: 0

and with the other i get K1: Expected Class: 6, Found Class: 6 K2: Expected Class: 6, Found Class: 6 K3: Expected Class: 6, Found Class: 6 K4: Expected Class: 6, Found Class: 6 K5: Expected Class: 6, Found Class: 6

( n.b.: your code-snippet mixed TABs and SPACEs, which it should not ) — user3666197, Oct 29 '14 at 16:31
Because they implement two different things.... Consider p1 = [-2, 2] p2 = [0,0] — igon, Oct 29 '14 at 16:32
The same input gets 12792 for the first one 27606 for the second — Victor, Oct 29 '14 at 16:52
unless you give a better description, we cannot guess. Mathematically are NOT the same, as @mgilson has already stated. — MariusSiuram, Oct 29 '14 at 16:52
But i'm using `abs()`to make it positive at the end. It is the same Look: ` (a - b) + (c - d) + (e - f) == (a + c + e) - (b + d + f)` — Victor, Oct 29 '14 at 16:55
But that's not the same as `abs(a-b)+abs(c-d)+abs(e-f)`, if `a — Yann Vernier, Oct 29 '14 at 17:03

score 3 · Answer 1 · answered Oct 29 '14 at 16:30

3

Why do you think they should be the same?

Consider summing only a single sequence of numbers:

a = [1, -1, 1, -1, 1, -1]

If you take the absolute value as you total, then you actually are summing the sequence:

a = [1, 1, 1, 1, 1, 1]

which will result in the total being reported as 6. But, if you wait until the end, to take the absolute value, you get the sum of a (0) and take the absolute value which is still 0.

^{*Note -- Just because all the values in each of the lists are positive doesn't mean that their differences are. e.g.
ponto1[x] - ponto2[x] could still be negative.}

answered Oct 29 '14 at 16:30

mgilson

300,191
65
633
696

All values are positives. I forgot to mention that – Victor Oct 29 '14 at 16:34
@user3624195 See my added note. – mgilson Oct 29 '14 at 16:34
But if i ` a = [1, 2, 3, 4, 5, 6] b = [3, 4, 5, 6, 7, 8] totalA == 21 totalB == 33 totalA - totalB == 12 ` and if i do the same for each value it gets the same result – Victor Oct 29 '14 at 16:36
That's why I use `abs()` – Victor Oct 29 '14 at 16:41

score 1 · Answer 2 · answered Oct 29 '14 at 17:03

It shouldn't give the save results.

Consider p1 = [0,1] and p2 = [1,0].

Then abs(sum(p1)-sum(p2)) gives 0, where sum(abs(p1-p2)) gives 2.

The distribution property of the summation gives you that abs(sum(p1)-sum(p2)) == abs(sum(p1-p2)), so you should only take the absolute value once you have calculated the total difference.

By the way, sum is a built-in python function that does exactly what you think it does.

score 0 · Accepted Answer · answered Oct 29 '14 at 16:54

Your second function is calculating Manhattan distance between two vectors, i.e. the sum of how far apart each individual dimension is. The first function reduces each vector to a single number before taking a difference; assuming all coordinates are positive, that means it takes the Manhattan distance from origo to each vector, then takes the difference of those. That's a very different function!

Consider this pair of 2D vectors:

y
5   a
4
3
2         b
1
0 o
  0 1 2 3 4 5 x

Here we have origo at (0,0), a at (1,5) and b at (4,2). To get from a to b, I need to move b-a=(4-1,2-5)=(3,-3), for a total of sum(map(abs,[3,-3]))=6 steps. But getting from o to a is 6 steps, and from o to b likewise, so the reduction first method considers a and b equal, even though they just happen to be on the same distance line running through (6,0) and (0,6) (because the Manhattan distance equivalent of a circle is actually a rhombus, a 45° rotated square).

Oh i see. That helped me a lot. Thanks. I hadn't see that mistake — Victor, Oct 29 '14 at 17:03

Two codes in python should be giving the same result but they don't

3 Answers3