# W2202 Insertion Sort

Within these castle walls be forged Mavens of Computer Science ...
— Merlin, The Coder

## Algorithm

Unlike Bubble Sort, which compares only two elements at a time, insertion sort works by looking at each element and finding where it belongs in the sorted array. At its base, insertion sort is more complicated than bubble sort, but not by much:

• Iterate over the array
• For each element at index i, loop back through the array starting at i to 0.
• Similar to bubble sort, if the element on the left is larger than the element on the right, swap them.
• Because this starts by comparing i and i - 1, if the current element is not in place, it will get swapped to i - 1. If it is still not in place in the next iteration, it will be swapped to i - 2, and so on until it is in the correct place.
• After each iteration, all the elements up to i + 1 will be in the correct order, although not necessarily sorted in the context of the full array.
• Unlike bubble sort, you need to iterate through the array only once. Once you reach the end, the array is sorted.

### Swap

You can use the same swap function as in bubble sort because you need to be able to swap only two adjacent elements at a time.

### Performance Considerations

Similar to bubble sort, consider passing the array by reference into the swap function (if you have one) instead of by value to avoid copying the entire array for each swap.

Additionally, in insertion sort, you can stop/break the inner loop once you reach two sorted elements. In other words, you need to swap only until the element on the left is smaller than the element on the right, at which point, you can exit the loop.

### Example

Here is an example with an array of 5 elements: Note: The Array contents are shown, directly after each pass of the insertion sort.

```Array: [95, 47, 62, 33, 89] | Initial
|
// The algorithm first looks at the element at index 1: 47. Since 47 < 95, the two elements are swapped.

Array: [47, 95, 62, 33, 89] | Swaps: 1, Pass: 1   <- Result immediately after the first pass
|
// The algorithm then looks at the element at index 2: 62. Since 62 < 95, the two elements are swapped
// The algorithm then checks if 62 < 47, this is not true, so the pass is completed.

Array: [47, 62, 95, 33, 89] | Swaps: 1, Pass: 2
|
// The algorithm then looks at the element at index 3: 33. Since 33 < 95, the two elements are swapped.
// This is repeated until 33 is at the beginning of the list

Array: [33, 47, 62, 95, 89] | Swaps: 3, Pass: 3
|
// The algorithm now looks at the element at index 4: 89. Since 89 < 95, the two elements are swapped.
// 89 is swapped only once because, after the first swap, 89 !< 62.

Array: [33, 47, 62, 89, 95] | Swaps: 1, Pass: 4  <- Result after 4 passes
```

## Quiz

1 Insertion Sort is an algorithm that selects the smallest element from an unsorted list in each iteration and places that element at the beginning of the unsorted list.

 True False

2 In which case does an insertion sort perform best?

 If the array was in a random order If the array was sorted in reverse order These will all perform equally well If the array was already sorted

3 One advantage of insertion sort is that it requires only one comparison.

 False True

4 Insertion sort is recommended for large arrays.

 True False

5 Insertion sort is useful when the array is close to being sorted.

 True False

6 Elements can move toward the beginning of the list very quickly.

 True False

7 Consider the list: 10, -59, 511, 831, -982
After the first insertion, the list will be:

 -982, 10, -59, 511, 831 -59, 511, 10, 831, -982 -982, -59, 10, 511, 831 -59, 10, 511, 831, -982

8 Consider the list: 10, -59, 511, 831, -982
After the second insertion, the list will be:

 -982, 10, -59, 511, 831 -59, 10, 511, 831, -982 -982, -59, 10, 511, 831 -59, 10, 511, 831, -932

9 Consider the list: 10, -59, 511, 831, -982
After the third insertion, the list will be:

 -59, 10, 511, 831, -982 -982, 10, -59, 511, 831 -982, -59, 10, 511, 831 -59, 10, 511, 831, -932

10 Consider the list: 10, -59, 511, 831, -982
After the first pass, the list will be:

 -59, 10, 511, 831, -982 -982, 10, -59, 511, 831 -982, -59, 10, 511, 831 -59, 511, 10, 831, -982

11 Consider the list: 10, -59, 511, 831, -982
After the fourth pass, the list will be:

 -59, 10, 511, 831, -982 -982, -59, 10, 511, 831 -59, 10, 511, 831, -982 -982, 10, -59, 511, 831

12 Consider the list: -365, -894, 638, 678, -41
How many passes are required before the algorithm terminates?

 Two Three Four Five

## References

Insertion Sort (Wikipedia)