Rotated List

Given a list of numbers obtained by rotating a sorted list in ascending order,determine the minimum number of times the original list was rotated to obtain the current list.Rotating a list is defined as removing the last element of the list and adding it before the first element in the list.

Problem Statement

Find the minimum number of times a list sorted in ascending order is rotated to obtain current version of list.

Input

Numbers: A rotated listed i.e [9,10,11,5,6,7,8]

Output

Rotation: Number of times original list was rotated to get current list i.e 3 for list above.

Test Cases

Possible cases

1. An empty list.

2. A listed sorted 3 times i.e [12, 13, 15, 0, 3, 5, 7]

3. A list rotated n times i.e [0, 3, 5, 7, 12, 13, 15] where n is the size of the list

4. A list rotated 1 i.e [15, 3, 5, 7, 8, 11]

5. A list rotated 0 times i.e [14, 16, 17, 19, 21]

6. A list with one element i.e [4]

7. A list with negative integers rotated 4 times i.e [-5, -4, -3, -1, -7, -9, -10]

8. A list with negative and positive integers rotated 5 times i.e [-12,-10, 0, 4, 6, -24, -20, -18, -14]

9. A rotated list with repeated numbers [16, 19, 19, 20, 20, 0, 4, 4, 6, 6, 8, 10]

Tests

tests =[

        {
            "input":[],
            "output":-1
        },

        {
            "input": [12, 13, 15, 0, 3, 5, 7],
            "output": 3
        },

        {
            "input": [4],
            "output": 0
        },

        {
            "input": [0, 3, 5, 7, 12, 13, 15],
            "output": 0
        },

        {
            "input": [15, 3, 5, 7, 8, 11],
            "output": 1
        },

        {
            "input": [-5, -4, -3, -1, -7, -9, -10],
            "output": 4
        },

        {
            "input": [12, 14, 16, 18, 0, 1, 2, 3, 4, 6, 7, 8, 9, 10],
            "output": 4
        }

]