## Insertion Sort Algorithm

1. Algorithm Description

Insertion Sort is one of the simplest, but less effective, sorting algorithms . It works very similar to the way (us humans) sort a hard of playing cards:

 1. At first none of our cards are sorted . So we start with an “empty” space in our hand were we are going to insert cards one at a time . 2. We take a card from our hand and we put it in the “special place” were we planned to keep our cards sorted . We do this for every card in our initial hand, until we finish them off . 3. Finding the right position for the insertion is not hard . At this point we can apply two tactics : We compare the card we are planning to insert with all the cards that are already in sorted state O(n); We use binary search to determine the right position (O(logn)) .

In our case that “special place” were we are going to insert cards one at a time, is not an additional array, but the array itself . We know for sure that an array of size 1 is always sorted, so we consider that first sorted sub-array, is the block composed by the first element .

For example, we want to sort the following array (with bold, are the elements already sorted):

 8 0 3 11 5 -1 14 10 1 1 -2 Array is unsorted . 8 0 3 11 5 -1 14 10 1 1 -2 The first sorted block is {8} . 0 8 3 11 5 -1 14 10 1 1 -2 We compare {0} with {8} we move {0} at the new position, we shift {8} . 0 3 8 11 5 -1 14 10 1 1 -2 We compare {3} with {8}, {0}, we move {3} at the new position, we shift {8} . 0 3 8 11 5 -1 14 10 1 1 -2 We compare {11} with {8}, {11} remains at the same position . 0 3 5 8 11 -1 14 10 1 1 -2 We compare {5} with {11}, {8} and {3}, we move {5} at the new position, we shift {8}, {11} . -1 0 3 5 8 11 14 10 1 1 -2 We compare {-1} with {11}, {8}, …, {0}, we move {-1} at the new position, we shift {0}, {3}, … {11} . -1 0 3 5 8 11 14 10 1 1 -2 We compare {14} with {11}, we move {11} at the new position . -1 0 3 5 8 10 11 14 1 1 -2 We compare {10} with {14}, {11}, {8}, we move {10} at the new position, we shift {11}, {14}. -1 0 1 3 5 8 10 11 14 1 -2 We compare {1} with {14}, {11}, …, {0}, we move {1} at the new position, we shift {3}, {5}, …, {14} . -1 0 1 1 3 5 8 10 11 14 -2 We compare {1} with {14}, {11}, …, {1}, we move {1} at the new position, we shift {3}, {5}, …, {14} . -2 -1 0 1 1 3 5 8 10 11 14 We compare {-2} with {14}, {11}, …, {-1}, we move {-2} at the new position, we shift {-1}, {0}, …, {14} .

The pseudo-code for the algorithm can be easily written as follows:

```FUNCTION SORT(A, length)
// The array is 0-indexed
FOR i:=1 TO length DO
key := A[i]
j := i - 1

// COMPARE
WHILE j >= 0 AND A[j] > key DO
// SHIFT
A[j+1] := A[j]
j := j - 1

// MOVE
A[j+1] = key
```

2. Algorithm Implemenation in Java

The Java implementation of the algorithm is pretty straight-forward (follow the comments):