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zydgyy
Posts: **13**Member

in Algorithms

As the following picture:

It's a circle that is consist of the numbers,how can i simply calculate the distance between some tow numbers,for example,5 and 8 is 3;22 and 2 is 4 ???????????

0 1 2 3 4 5

23 6

22 7

21 8

20 9

19 10

18 11

17 16 15 14 13 12

It's a circle that is consist of the numbers,how can i simply calculate the distance between some tow numbers,for example,5 and 8 is 3;22 and 2 is 4 ???????????

0 1 2 3 4 5

23 6

22 7

21 8

20 9

19 10

18 11

17 16 15 14 13 12

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## Comments

39Memberlambda a, b, size: min((a - b) % size, (b - a) % size)

where a and b are inputs and size is the number of elements (24 for this case).

The slightly longer answer is

SIZE = 24

def dis(a, b):

d1 = (a - b) % size

d2 = (b - a) % size

return min(d1, d2)

And, if you don't like modular arithmetic,

SIZE = 24

def dis2(a, b):

high = max(a, b)

low = min(a, b)

dis1 = high - low

dis2 = SIZE - dis1

return min(dis1, dis2)

That one only works for values of a and b in range(0, 24), but it saves you the trouble of having to understand modular arithmetic.

13MemberSIZE = 24

def dis(a, b):

d1 = (a - b) % size

d2 = (b - a) % size

return min(d1, d2)

-----------------------

It dosen't work:

a=22,b=2

d1=(22-2)%24 = 20

d2=(2-22)%24 = -20

min(d1,d2)=20 is not the right answer 4?!!!!!??!!?!

39Member-20 % 24 = 4

Bear in mind that % returns the remainder of the division of its arguments.

13Member39Member-20 % 24 is equivalent to -20 mod 24 (in psuedo code).

If you are questioning the math behind it, here is the complicated answer: http://en.wikipedia.org/wiki/Modular_arithmetic

Consider:

52 % 24 = 4

28 % 24 = 4

4 % 24 = 4

-20 % 24 = 4

52 = 2 * 24 +4

28 = 1 * 24 + 4

4 = 0 * 24 + 4

-20 = -1 * 24 + 4