Digit Wood

This problem is worth 50 points.

Let �A denote a permutation of length �N.

Define �(�)=∑�=1�min⁡(��,��+1)f(A)=∑i=1N​min(Ai​,Ai+1​), where ��+1=�1AN+1​=A1​.

Find the minimum value of �(�)f(A) over all permutations of length �N.

Note that a permutation of length �N consists of all integers from 11 to �N exactly once.

Input Format

• The first line of input will contain a single integer �T, denoting the number of test cases.
• Each test case consists of a single line of input containing �N, the size of the permutation.

Output Format

For each test case, output on a new line, the minimum value of �(�)f(A).

Note : The answer may not fit in a 32-bit integer. You are recommended to use 64-bit integers.

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

long long minFunction(vector<int>& perm) {
    int N = perm.size();
    long long result = 0;
    for (int i = 0; i < N; ++i) {
        result += min(perm[i], perm[(i + 1) % N]);
    }
    return result;
}

int main() {
    int T;
    cin >> T;
    
    while (T--) {
        int N;
        cin >> N;
        
        vector<int> permutation(N);
        for (int i = 0; i < N; ++i) {
            permutation[i] = i + 1;
        }
        
        long long minVal = minFunction(permutation);
        cout << minVal << endl;
    }
    
    return 0;
}