Monsters (easy version) (Codeforces 1784A)
Tags: Greedy, brute force

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:  Deal $$$1$$$ damage to any single alive monster of your choice.  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?

Input: 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 $$$2 \cdot 10^5$$$.

Output: 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.

Note: 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.

Sample Inputs:
2
3
3 1 2
6
4 1 5 4 1 1

Sample Outputs:
0
4

Solution (Python):
def monsters():
    n = int(input())
    lst = sorted(list(map(int, input().split())))
    res = 0
    i = 1
    for itm in lst:
        if itm < i:
            continue
        if itm > i:
            res += itm - i
        i += 1
    return res
for _ in range(int(input())):
    print(monsters())

Solution (Python):
for _ in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    a.sort()
    j = 1
    ans = 0
    for i in a:
        if i >= j:
            ans += i - j
            j += 1
    print(ans)

Solution (Python):
for _ in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    a.sort()
    j = 1
    ans = 0
    for i in a:
        if i >= j:
            ans += i - j
            j += 1
    print(ans)