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give short and optimal cpp soultion in a given tem...

Created on: November 2, 2025

Answered using GPT-5 Thinking by Chat01

Question

give short and optimal cpp soultion in a given template
Question 2

A company buys fragile components that are shipped in costly containers. The seller offers a promotion: customers receive a free container of components if they return a specific number of empty containers.

Calculate the maximum number of containers a customer can obtain given:

  1. A fixed budget

  2. The cost per container

  3. The number of empty containers required for a free container

Each container is assumed to be emptied and returned for credit immediately.

Example

n=4

cost = 1

m=2

Start with a budget n = 4 units of currency to buy containers at cost = 1 unit each. The number of empty containers to return for a free full container is m = 2. First, buy 4 containers with the entire budget. Turn in those 4 containers for 2 more containers. Turn in those 2 containers for one more. At this point, there are not enough funds or containers to receive another. In total, 4+2+1=7 containers were obtained.

Function Description

Complete the function maximumContainers in the editor with the following

parameter(s):

string scenarios[n]: Each string contains three space-separated integers, starting budget, cost, and the number of containers to return for a full container.

Print

For each test case, the function must print an integer: the maximum number of containers the manufacturer can obtain, each on a new line. No return value is expected.

Constraints

Isns 103

2 s starting budget s 105

1s cost of a container in money s starting budget

2 s number of empty containers to return s starting budget

Input Format for Custom Testing

Input from stdin will be processed as follows and passed to the function.

The first line contains an integer n, the size of scenarios or the number of test cases.

Each of the next n lines contains three space-separated integers, original budget, cost in dollars, and cost in empty containers. These are read as a single string by the code stub.

Sample Case O

Sample Input O

STDIN

Function

3

→ size of scenarios[] n = 3

10 25 scenarios = ['10 25', '12 44', '62 2']

12 4 4

622

Sample Output O

6

3

5
Explanation O

There are 3 test cases:

  1. Spend 10 units of currency on 5 containers at 2 units each. Turn in 5 containers for another one for a total of 6.

  2. Spend 12 units on 3 containers at 4 units. There are not enough containers to turn in, so the total is 3.

  3. Spend 6 units on 3 containers at 2 units. Turn in 2 of the containers for a 4th container leaving 7 old and 7 new container. Turn those 2 in for 1 more container making the total 5.

▼Sample Case 1

Sample Input 1

STDIN

Function

2 scenarios[] size n = 2

842

→ scenarios = ['842', '72 3']

723

Sample Output 1

3

Explanation 1

There are 2 test cases:

  1. Spend 8 units of currency on 2 containers at 4 units each. Turn in 2 containers for another one.

  2. Spend ó units on 3 containers at 2 units. Turn in 3 containers for another one. 1 unit of currency is left over.

Code snippet. void maximumContainers (vector<string> scenarios) (

}

Thought

Creating C++ solution for chocolate feast

I need to provide a C++ function that calculates the maximum containers someone can get based on their budget, cost, and wrappers/containers. After calculating the initial purchase, I’ll handle the wrapper exchange. The logic includes checking if wrappers are enough to get additional containers and summing them until we can't trade more.

Creating a minimal C++ function

The user wants a short and optimal C++ solution. I'll focus on providing just the maximumContainers function implementation, ensuring it's clean and minimal. It looks like no browsing is needed, and I’ll avoid adding extra explanations or unnecessary code. I'll include the necessary headers and keep it simple.

Writing final C++ solution

I’ll finalize the code with the maximumContainers function. It processes each scenario, calculating total containers based on initial purchase and wrapper exchanges. I’ll include the necessary imports like iostream, sstream, and vector. While I could optimize the formula, I’ll go with a more readable iterative approach for now.

Considering loop vs. closed-form

I’m thinking the loop is safe here since the worst-case for wrappers isn't too large, but I’m also considering using a closed-form formula for the wrapper exchange. The formula seems correct, but I’ll test it with examples to confirm that extra wrappers and total containers line up as expected.

Verifying formula vs. loop for optimization

I’m refining the formula for wrapper exchanges and testing different values to check for consistency. The formula for extras appears valid for all cases, but I’m still questioning the "borrow rule." For the specific "no borrow" case, the formula works fine. In various tests, the loop confirms the same result, concluding the formula is optimal.

Thought for 38s

Answer

Here’s a short, O(1) per test case solution using the known closed-form for wrapper exchanges:

cpp
#include <bits/stdc++.h>
using namespace std;

void maximumContainers(vector<string> scenarios) {
    for (const string& s : scenarios) {
        long long n, cost, m;
        istringstream in(s);
        in >> n >> cost >> m;

        long long bought = n / cost;                 // initial containers
        if (bought == 0) { cout << 0 << '\n'; continue; }

        // Total = bought + extra from exchanges.
        // For m >= 2, extras = floor((bought - 1) / (m - 1))
        long long total = bought + (bought - 1) / (m - 1);
        cout << total << '\n';
    }
}

(Uses the standard “chocolate feast” formula; constraints guarantee m ≥ 2.)

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