• Introduction
• Key Insight
• Code
• Conclusion

Codeforces Problem 1875A - Jellyfish and Undertale

Introduction

The bomb has a timer initially set to b. Every second, the timer decreases by 1. When it reaches 0, the bomb explodes. You have n tools, each increasing the timer by x_i when used. However, due to a bug, the timer is capped at a if it exceeds this value. The goal is to maximize the explosion time by using the tools optimally.

problem link: Codeforces Problem 1875A - Jellyfish and Undertale from Codeforces.

Optimal Tool Usage

To maximize the delay, the best strategy is to use tools when the timer reaches 1 second. Using a tool at this point ensures the bomb doesn’t explode and provides the maximum possible delay.

Key Insights

• Initial Timer Delay: The initial timer alone delays the explosion by its value.
• Tool Efficiency: A tool adds its value to the timer unless it exceeds a.
• Maximum Contribution: Any tool with x ≥ a contributes a maximum delay of a - 1, regardless of its value.

Step-by-Step Breakdown

Example Considered:

• Maximum Timer Value (a) = 4
• Initial Timer Value (b) = 3
• Tools Available (x) = {1, 3, 4, 5}

1. Initial Timer Behavior Without Tools

Total time before explosion: 3 seconds

Second	Timer
1st	2
2nd	1
3rd	0 (Explosion)

2. Using Tools to Add Delays

Step 1: Using Tool with Value 1

At Timer = 1, apply tool 1 → Timer becomes 2

Total time before explosion: 3 + 1 = 4 seconds

Second	Timer
1st	2
2nd	2
3rd	1
4th	0 (Explosion)

Step 2: Using Tool with Value 3

At Timer = 1, apply tool 3 → Timer becomes 4

Total time before explosion: 4 + 3 = 7 seconds

Second	Timer
1st	2
2nd	2
3rd	4
4th	3
5th	2
6th	1
7th	0 (Explosion)

Step 3: Using Tool with Value 4

At Timer = 1, apply tool 4 → Timer becomes 5, but is capped at 4

Total time before explosion: 7 + 3 = 10 seconds

Second	Timer
1st	2
2nd	2
3rd	4
4th	3
5th	2
6th	4
7th	3
8th	2
9th	1
10th	0 (Explosion)

Step 4: Using Tool with Value 5

At Timer = 1, apply tool 5 → Timer becomes 6, but is capped at 4

Total time before explosion: 10 + 3 = 13 seconds

Second	Timer
1st	2
2nd	2
3rd	4
4th	3
5th	2
6th	4
7th	3
8th	2
9th	4
10th	3
11th	2
12th	1
13th	0 (Explosion)

Code Implementations

Below are the implementations in Java and C++.

C++

#include <iostream>
#include <vector>

using namespace std;

int main() {
    int testCases;
    cin >> testCases; // Number of test cases

    while (testCases-- > 0) {
        long long maxTimerValue, initialTimerValue, numberOfTools;
        cin >> maxTimerValue >> initialTimerValue >> numberOfTools; // Read inputs

        long long currentTimerValue = initialTimerValue;

        while (numberOfTools-- > 0) {
            long long toolEffect;
            cin >> toolEffect;
            currentTimerValue += min(toolEffect, maxTimerValue - 1); // Apply tool effect, capped at maxTimerValue - 1
        }

        cout << currentTimerValue << endl; // Output the maximum possible timer value
    }

    return 0;
}
        

JAVA

import java.util.*;

public class JellyfishAndUndertale {

    public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);
        int testCases = scn.nextInt(); // Number of test cases

        while (testCases-- > 0) {
            long maxTimerValue = scn.nextInt(); // Maximum value of the bomb's timer
            long initialTimerValue = scn.nextInt(); // Initial value of the bomb's timer
            long numberOfTools = scn.nextInt(); // Number of tools available

            long currentTimerValue = initialTimerValue;

            while (numberOfTools-- > 0) {
                long toolEffect = scn.nextInt();
                currentTimerValue += Math.min(toolEffect, maxTimerValue - 1); // Apply tool effect, capped at maxTimerValue - 1
            }

            System.out.println(currentTimerValue); // Output the maximum possible timer value
        }

        scn.close();
    }
}
        

Conclusion

By applying the tools optimally, we achieve the maximum delay possible. The key takeaway is that using tools when the timer reaches 1 second ensures the bomb doesn’t explode immediately and allows for maximum extension of the countdown. Additionally, tools with values ≥ a contribute at most a - 1 extra seconds.