Overview

This problem asks you to find the difference between the theoretical value and the actual balance R, where the activity fund starts with an initial balance of S yen and two types of events—membership fee deposits and beverage purchases—are processed in order.

Analysis

The essence of the problem is very simple: process the given events in order to compute the final theoretical value, then find the difference from the actual balance R. Although the number of events M can be as large as 200,000, each event involves only simple addition or subtraction, so a straightforward simulation is sufficiently fast.

Since the constraint “theoretical value ≥ R” is guaranteed, there is no concern about the result becoming negative. Additionally, since it is guaranteed that the balance never becomes negative after processing each event, there is no need to worry about errors such as overflow.

Algorithm

1. Set the initial balance S as the initial theoretical value
2. Process each event in order:
   • For a membership event (\(e_i = 1\)): add \(v_i\) to the theoretical value
   • For a purchase event (\(e_i = 2\)): subtract \(v_i \times P\) from the theoretical value
3. After processing all events, subtract the actual balance R from the theoretical value and output the difference

Complexity

• Time complexity: \(O(M)\) (each of the M events is processed in constant time)
• Space complexity: \(O(M)\) (memory usage for storing the event information)

Implementation Notes

• Read all data from standard input at once and process it efficiently

• Perform the appropriate calculation depending on the event type (\(e_i\))

• Each event is processed with simple addition or subtraction only; no complex data structures are needed

• Correctly compute the difference between the theoretical value and the actual balance R

  Source Code

def main():
    import sys
    data = sys.stdin.read().split()
    if not data:
        return
    
    S = int(data[0])
    P = int(data[1])
    R = int(data[2])
    M = int(data[3])
    
    index = 4
    events = []
    for i in range(M):
        e = int(data[index])
        v = int(data[index+1])
        index += 2
        events.append((e, v))
        
    total = S
    for e, v in events:
        if e == 1:
            total += v
        else:
            total -= v * P
            
    result = total - R
    print(result)

if __name__ == "__main__":
    main()

This editorial was generated by deepseekv3.