## 03 Jan Aurora Saturday 14:30 Python Practice 22.01.01.

**Question 1: **

Some of the secret doors contain a very interesting word puzzle. The team of archaeologists has to solve it to open that doors. Because there is no other way to open the doors, the puzzle is very important for us.

There is a large number of magnetic plates on every door. Every plate has one word written on it. The plates must be arranged into a sequence in such a way that every word begins with the same letter as the previous word ends. For example, the word ‘acm’ can be followed by the word ‘motorola’. Your task is to write a computer program that will read the list of words and determine whether it is possible to arrange all of the plates in a sequence (according to the given rule) and consequently to open the door.

**Input**

The input consists of T test cases. The number of them (T) is given on the first line of the input file.

Each test case begins with a line containing a single integer number N that indicates the number of plates (1 ≤ N ≤ 100000). Then exactly N lines follow, each containing a single word. Each word contains at least two and at most 1000 lowercase characters, that means only letters ‘a’ through ‘z’ will appear in the word. The same word may appear several times in the list.

**Output**

Your program has to determine whether it is possible to arrange all the plates in a sequence such that the first letter of each word is equal to the last letter of the previous word. All the plates from the list must be used, each exactly once. The words mentioned several times must be used that number of times.

If there exists such an ordering of plates, your program should print the sentence ‘Ordering is possible.’. Otherwise, output the sentence ‘The door cannot be opened.’

Sample Input3 2 acm ibm 3 acm malform mouse 2 ok okSample OutputThe door cannot be opened. Ordering is possible. The door cannot be opened.

**Methods to consider:** Graph/DFS

**Question 2:**

Farmer Kenn has been informed of the location of a fugitive cow and wants to catch her immediately. He starts at a point *N* (0 ≤ *N* ≤ 100,000) on a number line and the cow is at a point *K* (0 ≤ *K* ≤ 100,000) on the same number line. Farmer Kenn has two modes of transportation: walking and teleporting.

* Walking: Farmer Kenn can move from any point *X* to the points *X *– 1 or *X *+ 1 in a single minute

* Teleporting: Farmer Kenn can move from any point *X* to the point 2 × *X* in a single minute.

If the cow, unaware of its pursuit, does not move at all, how long does it take for Farmer Kenn to retrieve it?

Input

Line 1: Two space-separated integers: *N* and *K*

Output

Line 1: The least amount of time, in minutes, it takes for Farmer Kenn to catch the fugitive cow.

Sample Input5 17Sample Output4HintThe fastest way for Farmer Kenn to reach the fugitive cow is to move along the following path: 5-10-9-18-17, which takes 4 minutes.

**Methods to consider:** BFS

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