Visualize full Shell Sort passes

Here is the COMPLETE VISUALIZATION OF ENTIRE SHELL SORT

COMPLETE VISUALIZATION OF ENTIRE SHELL SORT

Here is the COMPLETE VISUALIZATION OF ENTIRE SHELL SORT
with your array:
45, 12, 78, 23, 56, 9, 67, 34, 89, 41

We use gap sequence: 5 → 2 → 1

FULL STEP-BY-STEP GRAPHICAL REPRESENTATION

Original Array
Index:  0   1   2   3   4   5   6   7   8   9
Value: 45  12  78  23  56   9  67  34  89  41
        ┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
        │45 │12 │78 │23 │56 │ 9 │67 │34 │89 │41 │
        └─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┘
          ↓   ↓   ↓   ↓   ↓   ↓   ↓   ↓   ↓   ↓
        Gap=5 groups → 0-5, 1-6, 2-7, 3-8, 4-9

PASS 1: GAP = 5

Groups being sorted (like mini insertion sort):

[45 ↔ 9]     → 9  < 45 → swap
[12 ↔ 67]    → already good
[78 ↔ 34]    → 34 < 78 → swap
[23 ↔ 89]    → already good
[56 ↔ 41]    → 41 < 56 → swap

After Gap=5:
 9  12  34  23  41  45  67  78  89  56
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
│ 9 │12 │34 │23 │41 │45 │67 │78 │89 │56 │
└───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘

PASS 2: GAP = 2

Now two long chains:

Chain 1 (even indices):  9, 34, 41, 67, 89   → already sorted ✓
Chain 2 (odd indices):  12, 23, 45, 78, 56

Focus on Chain 2:
12 → 23 → 45 → 78 → 56   ← 56 is out of order!

Insert 56 into correct position:
56 goes between 45 and 78 → shift 78 right

After Gap=2:
 9  12  34  23  41  45  67  56  89  78
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
│ 9 │12 │34 │23 │41 │45 │67 │56 │89 │78 │
└───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘

PASS 3: GAP = 1 (Final Insertion Sort)

Now normal insertion sort on nearly-sorted array:

 9  12  34  23  41  45  67  56  89  78
 ↑   ↑   ↑   ↑───────────────────────────→ sorted prefix grows

Step-by-step insertions:

1. Insert 23 → shifts 34 → becomes:  9 12 23 34 41 45 67 56 89 78
2. 41, 45, 67 → already in place
3. Insert 56 → shifts 67 → becomes:  9 12 23 34 41 45 56 67 89 78
4. 89 → already good
5. Insert 78 → shifts 89 → becomes:  9 12 23 34 41 45 56 67 78 89

FINAL SORTED ARRAY
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
│ 9 │12 │23 │34 │41 │45 │56 │67 │78 │89 │
└───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘

COMPLETE VISUAL SUMMARY (All Passes)

Pass     Gap     Array After Pass
────────────────────────────────────────────────────
0      Start    45  12  78  23  56   9  67  34  89  41
1        5      9  12  34  23  41  45  67  78  89  56
2        2      9  12  34  23  41  45  67  56  89  78
3        1      9  12  23  34  41  45  56  67  78  89   ← FINAL

Bar Graph Evolution (Draw this in exam!)

Initial:               After Gap 5:           After Gap 2:           Final (Gap 1):
89                                         89                     89
78     78                               78     78               78
67         67                           67         67           67
56             56                   56             56       56
45                 45               45                 45   45
41                     41           41                     41
34                         34       34                         34
23                             23   23                         23
12                                 12                             12
 9                                     9                           9
──────────────────────────────────────────────────────────────→
Original           Nearly grouped        Almost sorted        Fully sorted

Key Point: Only 3 major shifts happened in final pass because earlier gaps already moved elements close to their correct positions!

You can now draw this entire visualization on your answer sheet and impress your professor!
Want this as a printable image/PDF? Just say the word!

Last updated: Nov 28, 2025