Proper way to count down with unsigned

Question

I am reading Carnegie Mellon slides on computer systems for my quiz. In the slide page 49 :

Counting Down with Unsigned
Proper way to use unsigned as loop index

unsigned i; 
for (i = cnt-2; i < cnt; i--) 
a[i] += a[i+1]; 

Even better

size_t i; 
for (i = cnt-2; i < cnt; i--) 
a[i] += a[i+1];   

I don't get why it's not going to be infinite loop. I am decrementing i and it is unsigned so it should be always less than cnt. Please explain.

Answer 1

This appears to be an alternative expression of the established idiom for implementing the same thing

for (unsigned i = N; i != -1; --i) 
   ...;

They simply replaced the more readable condition of i != -1 with a slightly more cryptic i < cnt. When 0 is decremented in the unsigned domain it actually wraps around to the UINT_MAX value, which compares equal to -1 (in the unsigned domain) and which is greater than or equal to cnt. So, either i != -1 or i < cnt works as a condition for continuing iterations.

Why would they do it that way specifically? Apparently because they start from cnt - 2 and the value of cnt can be smaller than 2, in which case their condition does indeed work properly (and i != -1 doesn't). Aside from such situations there's no reason to involve cnt into the termination condition. One might say that an even better idea would be to pre-check the value of cnt and then use the i != -1 idiom

if (cnt >= 2)
  for (unsigned i = cnt - 2; i != -1; --i) 
     ...;

Note, BTW, that as long as the starting value of i is known to be non-negative, the implementation based on the i != -1 condition works regardless of whether i is signed or unsigned.