difference between int( (n+1)/2 ) and (n+1)//2?

Question

In python for a problem https://www.spoj.com/problems/APM i used

t = int(input())
while t > 0:
    n= int(input())

    if n%2 == 0:
        print(-1)
    else:
        n = int((n+1)/2)
        print(n,n-1)
    t -= 1

this code and rejected,

but for this :

t = int(input())

while t > 0:
    n= int(input())

    if n%2 == 0:
        print(-1)
    else:
        n = (n+1)//2
        print(n,n-1)
    t -= 1

accepted, my question is why int((n+1)/2) gives different ans then (n+1)//2 at large number n< 10^18?

Does this answer your question? [Is floating point math broken?](https://stackoverflow.com/questions/588004/is-floating-point-math-broken) — Gabriel Devillers, May 09 '20 at 12:33

score 4 · Accepted Answer · answered May 09 '20 at 12:43

4

Even though for small n, it is true that int(n*(n-1)/2) == n*(n-1)//2, that can fail for large n. The reason why is that / is floating point division, which can result in loss of information, information that int() can't recover:

>>> n = 10**18 - 1
>>> n*(n-1)
999999999999999997000000000000000002
>>> n*(n-1)//2
499999999999999998500000000000000001
>>> n*(n-1)/2
5e+35
>>> int(n*(n-1)/2)
500000000000000021210318687008980992

The loss of information can be seen in 5e+35 vs. 499999999999999998500000000000000001

answered May 09 '20 at 12:43

John Coleman

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1

@gaurav It is integer division. Mathematically, it is the same as `int( / )` but is guaranteed to work for all integers, even ones with hundreds of digits. This is because the computation involves only integers, and doesn't compute an intermediate float. – John Coleman May 10 '20 at 11:12

score 1 · Answer 2 · answered May 09 '20 at 13:04

Consider:

import sys

print(sys.float_info)

i=(10**17+2)/2
j=(10**16+2)/2

print(i,j)
print(type(i), type(j))

i,j=int(i),int(j)

print(i,j)
print(type(i), type(j))

Although you're far from reaching float limits - you reached limit of digits that float can store - so everything after this limit will just get truncated in the exponential notation - so it will be the same magnitude of values, yet all the excessive numbers from the back will be 0.

Conclusion:

Converting types requires great care to detail - just use \\ instead.

score 0 · Answer 3 · answered May 09 '20 at 12:35

The double slash in Python performs integer division, whereas the single slash performs regular old division which may yield a float.

I don't see anywhere in the question you linked to that requires you to have an integer answer, but I imagine the author wanted it to be this way to prevent any floating point precision errors preventing the automated test cases from being successful.

difference between int( (n+1)/2 ) and (n+1)//2?

3 Answers3