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When it does, the invariant becomes "the subarray a[0:n-1] is sorted," which is the goal of the loop. " Describing the loop invariants in program comments is often very useful documentation; we could, for example, write for (i = 1; i < n; ++i) { /* a[0:i-1] => sorted */ insert a[i] into its correct place } /* a[0:n-1] => sorted */ 46 47 To insert a[i] into the correct place, we copy it into a temporary (t), thus freeing up the location a[i]. Then, for each element of a[0:i-1] which is greater than t, we move it one position to the right, then insert t into its ordered position.
One simple way to prevent fussy overflows is to perform the operation in unsigned arithmetic, since overflow checking is explicitly disabled for unsigned operations. A more precise way, in the case of atopi, would be to parenthesize the problematic expression like this: n = 10 * n + (s[i] - '0'); If the operator inside the parentheses were a "plus," the technique would not work, because the compiler is free to re-arrange commutative-associative operators, even across parentheses. Since, however, it is a "minus," the subtraction is guaranteed to be performed before the addition (unless the compiler has a bug in this delicate area, that is).
The pointer itself can be undefined, or defined. It can be NULL, or it can point to valid storage. The array object being accessed through the pointer has its own properties: It could be complete or incomplete. It could be a multiset array (either sorted or unsorted). It could be a string. Or it could have any other property that we have defined for arrays. In order to talk sensibly about the object being referenced we will need some new terminology. Because of the way C references arrays through pointers, the array being accessed is not simply the "indirect object" of the pointer (*p), because *p is just the individual array element pointed to by the pointer.