Overview

This is a problem about neighborhood association activity funds. You need to calculate the theoretical final balance by applying all events (addition of membership fees and subtraction of beverage purchases) in order to the initial balance, then compute the difference from the actual balance \(R\).

Analysis

What we need to find in this problem can be broken down into two steps:

1. Calculate the theoretical value: Process \(M\) events sequentially starting from the initial balance \(S\) to determine the final balance.
2. Calculate the difference: Subtract the actual balance \(R\) from the theoretical value.

Each event is processed as follows:

• Membership event (\(e_i = 1\)): The membership fee of \(v_i\) yen is directly added.
• Purchase event (\(e_i = 2\)): \(v_i\) bottles of drinking water are purchased, so \(v_i \times P\) yen is subtracted.

For example, suppose \(S = 10000\), \(P = 150\), \(R = 9000\), with the following events:

The theoretical value is \(13500\) yen, and the difference is \(13500 - 9000 = 4500\) yen.

No special algorithm is needed — simply simulating the process as described in the problem statement will give the correct answer. However, you need to be careful about the range of values.

Algorithm

1. Initialize a variable balance with the initial balance \(S\).
2. Read and process each of the \(M\) events in order as follows:
   • If \(e_i = 1\), then balance += v_i (add membership fee)
   • If \(e_i = 2\), then balance -= v_i * P (subtract beverage purchase cost)
3. The final balance is the theoretical value, so output balance - R.

Complexity

• Time complexity: \(O(M)\) — We simply process each event once.
• Space complexity: \(O(1)\) — Only a variable to hold the balance is needed; there is no need to store event information.

Implementation Notes

• Beware of overflow: \(S\) can be up to \(10^9\), membership fees can also be up to \(10^9\), and \(M\) can be up to \(2 \times 10^5\), so the theoretical value can reach approximately \(10^9 + 2 \times 10^5 \times 10^9 = 2 \times 10^{14}\). Also, \(R\) can be up to \(10^{18}\). In languages like C++, you need to use the long long type, but in Python, there is no integer overflow, so you can compute directly.

• Purchase event calculation: You need to multiply the number of bottles \(v_i\) by the unit price \(P\). Be careful not to overlook that \(v_i\) is not the monetary amount itself.

  Source Code

S, P, R = map(int, input().split())
M = int(input())
balance = S
for _ in range(M):
    e, v = map(int, input().split())
    if e == 1:
        balance += v
    else:
        balance -= v * P
print(balance - R)

This editorial was generated by claude4.6opus-thinking.