HDU-6709 Fishing Master

Description

Heard that eom is a fishing MASTER, you want to acknowledge him as your mentor. As everybody knows, if you want to be a MASTER's apprentice, you should pass the trial. So when you find fishing MASTER eom, the trial is as follow:

There are n fish in the pool. For the i - th fish, it takes at least ti minutes to stew(overcook is acceptable). To simplify this problem, the time spent catching a fish is kminutes. You can catch fish one at a time and because there is only one pot, only one fish can be stewed in the pot at a time. While you are catching a fish, you can not put a raw fish you have caught into the pot, that means if you begin to catch a fish, you can't stop until after k minutes; when you are not catching fish, you can take a cooked fish (stewed for no less than ti) out of the pot or put a raw fish into the pot, these two operations take no time. Note that if the fish stewed in the pot is not stewed for enough time, you cannot take it out, but you can go to catch another fish or just wait for a while doing nothing until it is sufficiently stewed.

Now eom wants you to catch and stew all the fish as soon as possible (you definitely know that a fish can be eaten only after sufficiently stewed), so that he can have a satisfying meal. If you can complete that in the shortest possible time, eom will accept you as his apprentice and say "I am done! I am full!". If you can't, eom will not accept you and say "You are done! You are fool!".

So what's the shortest time to pass the trial if you arrange the time optimally?

Input

The first line of input consists of a single integer T(1≤T≤20), denoting the number of test cases.

For each test case, the first line contains two integers n(1≤n≤105),k(1≤k≤109), denoting the number of fish in the pool and the time needed to catch a fish.

the second line contains n integers, t1,t2,…,tn(1≤ti≤109) ,denoting the least time needed to cook the i - th fish.

Output

For each test case, print a single integer in one line, denoting the shortest time to pass the trial.

Sample Input

2
3 5
5 5 8
2 4
3 3

Sample Output

23
11

题解

对于每条鱼，我们肯定要花费把它煮熟的时间，另外，我们肯定要花费钓上第一条鱼的时间。之后我们考虑每条鱼的烹饪时间，如果在这段时间内能钓上鱼，那就钓，如果都不能钓且还有鱼没钓，那就依次找需要等待时间最少的钓鱼。我们在减去钓上去的鱼的时间后，剩下的时间排个序，选最大的时间，即等待时间最少，依次钓完鱼即可。

AC代码

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1e5 + 50;
ll a[N];
int main() {
    int t;
    scanf("%d", &t);
    while (t--) {
        ll n, k;
        scanf("%lld%lld", &n, &k);
        for (int i = 1; i <= n; i++) scanf("%lld", &a[i]);
        ll cnt = 0;
        ll ans = 0;
        for (int i = 1; i <= n; i++) {
            ans += a[i];
            cnt += a[i] / k;
            a[i] %= k;
        }
        sort(a + 1, a + n + 1);
        for (int i = n; i >= 1; i--) {
            if (cnt >= n - 1) break;
            cnt++; ans += k - a[i];
        }
        printf("%lld\n", ans + k);
    }
    return 0;
}