C. Great Graphs Codeforces Solution

C. Great Graphs

Farmer John has a farm that consists of nn pastures connected by one-directional roads. Each road has a weight, representing the time it takes to go from the start to the end of the road. The roads could have negative weight, where the cows go so fast that they go back in time! However, Farmer John guarantees that it is impossible for the cows to get stuck in a time loop, where they can infinitely go back in time by traveling across a sequence of roads. Also, each pair of pastures is connected by at most one road in each direction.

Unfortunately, Farmer John lost the map of the farm. All he remembers is an array dd, where didi is the smallest amount of time it took the cows to reach the ii-th pasture from pasture 11 using a sequence of roads. The cost of his farm is the sum of the weights of each of the roads, and Farmer John needs to know the minimal cost of a farm that is consistent with his memory.Input

The first line contains one integer tt (1≤t≤1041≤t≤104) — the number of test cases. Then tt cases follow.

The first line of each test case contains a single integer nn (1≤n≤1051≤n≤105) — the number of pastures.

The second line of each test case contains nn space separated integers d1,d2,…,dnd1,d2,…,dn (0≤di≤1090≤di≤109) — the array dd. It is guaranteed that d1=0d1=0.

It is guaranteed that the sum of nn over all test cases does not exceed 105105.Output

For each test case, output the minimum possible cost of a farm that is consistent with Farmer John’s memory.



0 2 3
0 1000000000




In the first test case, you can add roads

  • from pasture 11 to pasture 22 with a time of 22,
  • from pasture 22 to pasture 33 with a time of 11,
  • from pasture 33 to pasture 11 with a time of −3−3,
  • from pasture 33 to pasture 22 with a time of −1−1,
  • from pasture 22 to pasture 11 with a time of −2−2.

The total cost is 2+1+−3+−1+−2=−32+1+−3+−1+−2=−3.

In the second test case, you can add a road from pasture 11 to pasture 22 with cost 10000000001000000000 and a road from pasture 22 to pasture 11 with cost −1000000000−1000000000. The total cost is 1000000000+−1000000000=01000000000+−1000000000=0.

In the third test case, you can’t add any roads. The total cost is 00.


#include <bits/stdc++.h>

using namespace std;

const int maxn = 200005;
long long a[maxn], a1, a2;
map<int, int> v;

int main()
    int T, n, m, k, x, r;
    cin >> T;
    long long ans, p;
        cin >> n;
        ans = p = 0ll;
        for(register int i = 1; i <= n; i += 1)
            cin >> a[i];
        sort(a+1, a+n+1);
        for(register int i = 1; i < n; i += 1)
            p += a[n] - a[i];
        ans = p;
        for(register int i = n; i > 2; i -= 1)
            p -= (a[i]-a[i-1])*(i-1ll);
            ans += p;
        cout << -(ans-a[n]) << endl;
    return 0;

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