A15746 | Monsters (easy version)
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题目描述
This is the easy version of the problem. In this version, you only need to find the answer once. In this version, hacks are not allowed.
In a computer game, you are fighting against $n$ monsters. Monster number $i$ has $a_i$ health points, all $a_i$ are integers. A monster is alive while it has at least $1$ health point.
You can cast spells of two types:
1. Deal $1$ damage to any single alive monster of your choice.
2. Deal $1$ damage to all alive monsters. If at least one monster dies (ends up with $0$ health points) as a result of this action, then repeat it (and keep repeating while at least one monster dies every time).
Dealing $1$ damage to a monster reduces its health by $1$ .
Spells of type 1 can be cast any number of times, while a spell of type 2 can be cast at most once during the game.
What is the smallest number of times you need to cast spells of type 1 to kill all monsters?
In a computer game, you are fighting against $n$ monsters. Monster number $i$ has $a_i$ health points, all $a_i$ are integers. A monster is alive while it has at least $1$ health point.
You can cast spells of two types:
1. Deal $1$ damage to any single alive monster of your choice.
2. Deal $1$ damage to all alive monsters. If at least one monster dies (ends up with $0$ health points) as a result of this action, then repeat it (and keep repeating while at least one monster dies every time).
Dealing $1$ damage to a monster reduces its health by $1$ .
Spells of type 1 can be cast any number of times, while a spell of type 2 can be cast at most once during the game.
What is the smallest number of times you need to cast spells of type 1 to kill all monsters?
输入格式
Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 10^4$ ). The description of the test cases follows.
Each test case consists of two lines. The first line contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the number of monsters.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le n$ ) — monsters' health points.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .
Each test case consists of two lines. The first line contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the number of monsters.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le n$ ) — monsters' health points.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .
输出格式
For each test case, print a single integer — the smallest number of times you need to cast spells of type 1 to kill all monsters.
输入输出样例
输入 #1
2 3 3 1 2 6 4 1 5 4 1 1
输出 #1
0 4
In the first test case, the initial health points of the monsters are $[3, 1, 2]$ . It is enough to cast a spell of type 2:
- Monsters' health points change to $[2, 0, 1]$ . Since monster number $2$ dies, the spell is repeated.
- Monsters' health points change to $[1, 0, 0]$ . Since monster number $3$ dies, the spell is repeated.
- Monsters' health points change to $[0, 0, 0]$ . Since monster number $1$ dies, the spell is repeated.
- Monsters' health points change to $[0, 0, 0]$ .
Since it is possible to use no spells of type 1 at all, the answer is $0$ .
In the second test case, the initial health points of the monsters are $[4, 1, 5, 4, 1, 1]$ . Here is one of the optimal action sequences:
- Using a spell of type 1, deal $1$ damage to monster number $1$ . Monsters' health points change to $[3, 1, 5, 4, 1, 1]$ .
- Using a spell of type 1, deal $1$ damage to monster number $4$ . Monsters' health points change to $[3, 1, 5, 3, 1, 1]$ .
- Using a spell of type 1, deal $1$ damage to monster number $4$ again. Monsters' health points change to $[3, 1, 5, 2, 1, 1]$ .
- Use a spell of type 2:
- Monsters' health points change to $[2, 0, 4, 1, 0, 0]$ . Since monsters number $2$ , $5$ , and $6$ die, the spell is repeated.
- Monsters' health points change to $[1, 0, 3, 0, 0, 0]$ . Since monster number $4$ dies, the spell is repeated.
- Monsters' health points change to $[0, 0, 2, 0, 0, 0]$ . Since monster number $1$ dies, the spell is repeated.
- Monsters' health points change to $[0, 0, 1, 0, 0, 0]$ .
- Using a spell of type 1, deal $1$ damage to monster number $3$ . Monsters' health points change to $[0, 0, 0, 0, 0, 0]$ .
Spells of type 1 are cast $4$ times in total. It can be shown that this is the smallest possible number.
- Monsters' health points change to $[2, 0, 1]$ . Since monster number $2$ dies, the spell is repeated.
- Monsters' health points change to $[1, 0, 0]$ . Since monster number $3$ dies, the spell is repeated.
- Monsters' health points change to $[0, 0, 0]$ . Since monster number $1$ dies, the spell is repeated.
- Monsters' health points change to $[0, 0, 0]$ .
Since it is possible to use no spells of type 1 at all, the answer is $0$ .
In the second test case, the initial health points of the monsters are $[4, 1, 5, 4, 1, 1]$ . Here is one of the optimal action sequences:
- Using a spell of type 1, deal $1$ damage to monster number $1$ . Monsters' health points change to $[3, 1, 5, 4, 1, 1]$ .
- Using a spell of type 1, deal $1$ damage to monster number $4$ . Monsters' health points change to $[3, 1, 5, 3, 1, 1]$ .
- Using a spell of type 1, deal $1$ damage to monster number $4$ again. Monsters' health points change to $[3, 1, 5, 2, 1, 1]$ .
- Use a spell of type 2:
- Monsters' health points change to $[2, 0, 4, 1, 0, 0]$ . Since monsters number $2$ , $5$ , and $6$ die, the spell is repeated.
- Monsters' health points change to $[1, 0, 3, 0, 0, 0]$ . Since monster number $4$ dies, the spell is repeated.
- Monsters' health points change to $[0, 0, 2, 0, 0, 0]$ . Since monster number $1$ dies, the spell is repeated.
- Monsters' health points change to $[0, 0, 1, 0, 0, 0]$ .
- Using a spell of type 1, deal $1$ damage to monster number $3$ . Monsters' health points change to $[0, 0, 0, 0, 0, 0]$ .
Spells of type 1 are cast $4$ times in total. It can be shown that this is the smallest possible number.
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评测结果：Accepted