C.cpp

#include "bits/stdc++.h"
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;

#define int long long
#define FOR(i, a, b) for (int i = (a), _##i = (b); i <= _##i; ++i)
#define FORD(i, a, b) for (int i = (a), _##i = (b); i >= _##i; --i)
#define REP(i, a) for (int i = 0, _##i = (a); i < _##i; ++i)
 
#define DEBUG(X) { auto _X = (X); cerr << "L" << __LINE__ << ": " << #X << " = " << (_X) << endl; }
#define PR(A, n) { cerr << "L" << __LINE__ << ": " << #A << " = "; FOR(_, 1, n) cerr << A[_] << ' '; cerr << endl; }
#define PR0(A, n) { cerr << "L" << __LINE__ << ": " << #A << " = "; REP(_, n) cerr << A[_] << ' '; cerr << endl; }
 
#define __builtin_popcount __builtin_popcountll
#define SZ(x) ((int)(x).size())
#define ALL(a) (a).begin(), (a).end()
inline int gcd(int a, int b) {int r; while (b) {r = a % b; a = b; b = r;} return a;}

const int MN = 444;
const int inf = 1000111000;
#define arg __arg
long long c[MN][MN];
long long fx[MN], fy[MN];
int mx[MN], my[MN];
int trace[MN], qu[MN], arg[MN];
long long d[MN];
int front, rear, start, finish;
int N;

void init() {
    FOR(i,1,N) {
        fy[i] = mx[i] = my[i] = 0;
        FOR(j,1,N) c[i][j] = inf;
    }
}

void addEdge(int i, int j, long long cost) {
    c[i][j] = min(c[i][j], cost);
}

inline long long getC(int i, int j) {
    return c[i][j] - fx[i] - fy[j];
}

void initBFS() {
    front = rear = 1;
    qu[1] = start;
    memset(trace, 0, sizeof trace);
    FOR(j,1,N) {
        d[j] = getC(start, j);
        arg[j] = start;
    }
    finish = 0;
}

void findAugPath() {
    while (front <= rear) {
        int i = qu[front++];
        FOR(j,1,N) if (!trace[j]) {
            long long w = getC(i, j);
            if (!w) {
                trace[j] = i;
                if (!my[j]) {
                    finish = j;
                    return ;
                }
                qu[++rear] = my[j];
            }
            if (d[j] > w) {
                d[j] = w;
                arg[j] = i;
            }
        }
    }
}

void subx_addy() {
    long long delta = inf;
    FOR(j,1,N)
        if (trace[j] == 0 && d[j] < delta) delta = d[j];

    // xoay
    fx[start] += delta;
    FOR(j,1,N)
        if (trace[j]) {
            int i = my[j];
            fy[j] -= delta;
            fx[i] += delta;
        }
        else d[j] -= delta;

    FOR(j,1,N)
        if (!trace[j] && !d[j]) {
            trace[j] = arg[j];
            if (!my[j]) { finish = j; return ; }
            qu[++rear] = my[j];
        }
}

void enlarge() {
    do {
        int i = trace[finish];
        int next = mx[i];
        mx[i] = finish;
        my[finish] = i;
        finish = next;
    } while (finish);
}

int mincost() {
    FOR(i,1,N) fx[i] = *min_element(c[i]+1, c[i]+N+1);
    FOR(j,1,N) {
        fy[j] = c[1][j] - fx[1];
        FOR(i,1,N) {
            fy[j] = min(fy[j], c[i][j] - fx[i]);
        }
    }
    FOR(i,1,N) {
        start = i;
        initBFS();
        while (finish == 0) {
            findAugPath();
            if (!finish) subx_addy();
        }
        enlarge();
    }
    int res = 0;
    FOR(i,1,N) res += c[i][mx[i]];
    return res;
}


int32_t main() {
    ios::sync_with_stdio(0);
    int ntest; cin >> ntest;
    while (ntest--) {
        int n; cin >> n;
        vector<int> a(n);
        for (auto& val : a) cin >> val;
        sort(ALL(a));

        N = 2*n;
        init();
        REP(i,n) FOR(j,1,N) {
            addEdge(i+1, j, llabs(a[i] - j));
        }
        int t = mincost();
        cout << t - n * inf << endl;
    }
    cerr << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n";
    return 0;
}