Minimum Popping solution codechef

Minimum Popping solution codechef

You are given a double-ended queue QQ. Initially, it contains elements Q1,Q2,,QMQ1,Q2,…,QM in this order. Each of these elements is an integer between 11 and NN (inclusive) and each integer between 11 and NN (inclusive) occurs in the queue at least once.

We want to pop some (possibly zero) elements from the front of the queue and some (not necessarily the same number, possibly zero) elements from the back. Among all the popped elements, each integer between 11 and NN (inclusive) should appear at least once. Find the smallest possible total number of elements we need to pop.

Input Minimum Popping solution codechef

  • The first line of the 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 two space-separated integers NN and MM.
  • The second line contains MM space-separated integers Q1,Q2,,QMQ1,Q2,…,QM.

Output Minimum Popping solution codechef

For each test case, print a single line containing one integer — the minimum number of elements we need to pop.

Constraints Minimum Popping solution codechef

  • 1T101≤T≤10
  • 1N1051≤N≤105
  • NM2105N≤M≤2⋅105
  • for each ii (1iN1≤i≤N), there is at least one element equal to ii in the queue
  • the sum of NN over all test cases does not exceed 105105
  • the sum of MM over all test cases does not exceed 21052⋅105

Example Input Minimum Popping solution codechef

2 2
1 2
2 3
1 2 1
3 6
1 1 1 3 2 2

Example Output Minimum Popping solution codechef


Explanation Minimum Popping solution codechef

Example case 1: Since N=MN=M and all elements are pairwise distinct, we have to pop everything to get each value at least once.

Example case 2: We can pop the first 22 or the last 22 elements.

Example case 3: We can pop the first element and the last 33 elements, so the answer is 1+3=41+3=4.


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