List of Lists solution codechef December Long Challenge

Contents

• List of Lists solution codechef
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  • • List of Lists solution codechef Input Format
    • Output Format
    • Constraints List of Lists solution codechef
    • Subtasks
    • Sample Input 1 
    • List of Lists solution codechef Sample Output 1 
    • Explanation
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List of Lists solution codechef

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You are given a positive integer NN and an array AA of size NN. There are NN lists L1,L2…LNL1,L2…LN. Initially, Li=[Ai]Li=[Ai].

You can perform the following operation any number of times as long as there are at least 22 lists:

• Select 22 (non-empty) lists LiLi and LjLj (i≠ji≠j)
• Append LjLj to LiLi and remove the list LjLj. Note that this means LjLj cannot be chosen in any future operation.

Find the minimum number of operations required to obtain a set of lists that satisfies the following conditions:

• The first element and last element of each list are equal.
• The first element of all the lists is the same.

Print −1−1 if it is not possible to achieve this via any sequence of operations.

List of Lists solution codechef Input Format

• The first line of input contains a single integer TT, denoting the number of test cases. The description of TT test cases follows.
• The first line of each test case contains an integer NN.
• The second line of each test case contains NN space-separated integers A1,A2,…,ANA1,A2,…,AN.

Output Format

For each test case, print a single line containing one integer: the minimum number of operations required to obtain an array of lists that satisfies the given conditions.

Print −1−1 if it is impossible to achieve such an array of lists.

Constraints List of Lists solution codechef

• 1≤T≤1051≤T≤105
• 1≤N≤2⋅1051≤N≤2⋅105
• 1≤Ai≤N1≤Ai≤N
• Sum of NN over all test cases doesn’t exceed 2⋅1052⋅105

Subtasks

Subtask 1(100 points): Original constraints

Sample Input 1 

3
1
1
2
1 2
3
1 1 2

List of Lists solution codechef Sample Output 1 

0
-1
2

Explanation

Test case 11: There is only one list [1][1], and it trivially satisfies the condition so no operations are required.

Test case 22: There are only 22 ways to do an operation – either take list [1][1] and append it to list [2][2] or take list [2][2] and append it to list [1][1]. In both cases, it is not possible to satisfy both given conditions at the same time. Hence, the answer is −1−1.

Test case 33: Here is one possible order of operations:

• Select the 33rd list [2][2] and append it to the 11st list [1][1].
• Then, select the 22nd list [1][1] and append it to the 11st list [1,2][1,2].

Finally, we are left with the single list [1,2,1][1,2,1] which satisfies the given conditions. It can be verified that it is impossible to do this using less than 22 operations.

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