Understanding ShellSort Code from K & R on page 62

Question

I am trying to understand ShellSort code in the K & R book on page 62. But there is one part that I'm not sure about.

So, here is the source code from the book:

void shellsort(int* v, int n) {
    int gap, i, j, temp;
    for (gap = n / 2; gap > 0; gap /= 2) {
        for (i = gap; i < n; i++) {
            for (j = i - gap; j >= 0 && v[j] > v[j + gap]; j -= gap) {
                temp = v[j];
                v[j] = v[j + gap];
                v[j + gap] = temp;
            }
        }
    }
}

And I'm trying to understand why there is a third cycle. It can only be if he could not?

The code version has been changed here (the one that I think might work):

void shellsort(int* v, int n) {
    int gap, i, j, temp;
    for (gap = n / 2; gap > 0; gap /= 2) {
        for (i = gap; i < n; i++) {
            j = i - gap;
            if (v[j] > v[j + gap]) {
                temp = v[j];
                v[j] = v[j + gap];
                v[j + gap] = temp;
            }
        }
    }
}

And when I run the code, and it outputs the same as the first code:

Conclusion:

12345679

But, of course, there is some reason using forthere. And I can not find the reason. So I thought someone could clean this up?

Answer 1

, , , . :

void shellsort(int* v, int n) {
    int gap, i, j, temp;
    for (gap = n / 2; gap > 0; gap /= 2) {
        printf("enter outer loop with gap = %d\n", gap);
        for (i = gap; i < n; i++) {
            printf("- enter second loop with i = %d\n", i);
            for (j = i - gap; j >= 0 && v[j] > v[j + gap]; j -= gap) {
                temp = v[j];
                v[j] = v[j + gap];
                v[j + gap] = temp;
            }
            printf("- after innermost loop:");
            print_array(v, n);
        }
    }
}

( print_array.)

{ 5, 4, 3, 2, 1 }, , :

 5 4 3 2 1
enter outer loop with gap = 2
- enter second loop with i = 2
- after innermost loop: 3 4 5 2 1
- enter second loop with i = 3
- after innermost loop: 3 2 5 4 1
- enter second loop with i = 4
- after innermost loop: 1 2 3 4 5
enter outer loop with gap = 1
- enter second loop with i = 1
- after innermost loop: 1 2 3 4 5
- enter second loop with i = 2
- after innermost loop: 1 2 3 4 5
- enter second loop with i = 3
- after innermost loop: 1 2 3 4 5
- enter second loop with i = 4
- after innermost loop: 1 2 3 4 5
 1 2 3 4 5

, , if for:

 5 4 3 2 1
enter outer loop with gap = 2
- enter second loop with i = 2
- after swap: 3 4 5 2 1
- enter second loop with i = 3
- after swap: 3 2 5 4 1
- enter second loop with i = 4
- after swap: 3 2 1 4 5
enter outer loop with gap = 1
- enter second loop with i = 1
- after swap: 2 3 1 4 5
- enter second loop with i = 2
- after swap: 2 1 3 4 5
- enter second loop with i = 3
- after swap: 2 1 3 4 5
- enter second loop with i = 4
- after swap: 2 1 3 4 5
 2 1 3 4 5

, 1 . . gap = 2 i = 4 5 1 ; 3 1 , , (1, 3, 5) . . gap = 1, 1 (3), 2.

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