The problem of integer operation taking ceiling in "turn" C language

Original: http://blog.csdn.net/laciqs/article/details/6662472

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This topic from: "Linux C Programming One-stop learning"

Assuming that the variables x and n are two positive integers, we know that the result of the x/n expression is to take the floor, for example, if X is 17,n 4, then the result is 4. How do you write an expression if you want the result to be ceiling? For example X is 17,n is 4, then the result is 5;x is 16,n is 4, then the result is 4.

The answer to this question on the Internet only and proof, although we can prove the correctness of the answer is not know how to draw, this article fills this gap.

The derivation of a master (according to his original text):

Set X=kn+b,b∈ (0, N) and B∈z, when B=0,

(x+z)/n=k, namely (KN+Z)/n=k, according to the title, z Maximum is n-1;

When B≠0, (x+z)/n=k+1, that is (kn+b+z)/n=k+1, that is (b+z)/n=1, because b∈ (0, N) and b∈z, so B has a minimum value of 1, at this time Z is n-1, when B takes 2 o'clock, Z is n-2 ... When the b=n-1, Z=1, can be seen regardless of special circumstances, Z maximum is n-1, and when the b=n-1, z if the n-1, then (b+z)/n=2-2/n<2, that is (kn+b+z)/n<k+2, is still able to take ceiling. So no matter how z can be n-1, that is, z=n-1.

∈[1, n-1],∵[

So this expression should be written as: (x+n-1)/n

And from the above deduction process can be seen, for x%n=n-1 situation, as long as The X plus a 1 can take ceiling, such as 19%4=3, (19+1)/4=5.

The problem of integer operation taking ceiling in "turn" C language