Insertion Sort

(referrence: GeeksforGeeks)

Insertion sort is a simple sorting algorithm that works the way we sort playing cards in our hands.

Algorithm
// Sort an arr[] of size n
insertionSort(arr, n)
Loop from i = 1 to n-1.
……a) Pick element arr[i] and insert it into sorted sequence arr[0…i-1]

Example: 
12, 11, 13, 5, 6

Let us loop for i = 1 (second element of the array) to 5 (Size of input array)

i = 1. Since 11 is smaller than 12, move 12 and insert 11 before 12
11, 12, 13, 5, 6

i = 2. 13 will remain at its position as all elements in A[0..I-1] are smaller than 13
11, 12, 13, 5, 6

i = 3. 5 will move to the beginning and all other elements from 11 to 13 will move one position ahead of their current position.
5, 11, 12, 13, 6

i = 4. 6 will move to position after 5, and elements from 11 to 13 will move one position ahead of their current position.
5, 6, 11, 12, 13

class Solution {
    public static void insertionSort(int[] nums) {
        for (int i = 1; i < nums.length; i++) {
            key = nums[i];
            int j = i - 1;

            while (j >= 0 && nums[j] > key) {
                nums[j + 1] = arr[j]
                j--;
            }
            nums[j + 1] = key;
        }
    }
}

Time complexity O(n^2), space cost O(1), and it's in-place sorting.