Hello everyone,↵
↵
I'm currently facing an optimization problem related to server requests and would greatly appreciate your assistance. To explain the issue more clearly:↵
↵
Problem Statement:↵
We need to send multiple tickets to a server, and our goal is to minimize the number of requests made.↵
↵
Here's an example to illustrate the problem:↵
↵
~~~~~↵
Request Amount↵
1+3 2↵
1+2 1↵
1+4 3↵
2+3 4↵
2+4 1↵
2+5 2↵
3+4 1↵
3+5 2↵
3+6 5↵
~~~~~↵
↵
In this example, each request combines specific tickets with corresponding amounts. For instance, the first request (1+3) means we are attempting to send ticket 1 and ticket 3, with a total amount of 2 for each.↵
↵
We have two methods to reduce the number of requests:↵
↵
**1. Banker Method:**↵
↵
Combine multiple requests into one request.↵
For example, 1>2,3,4,5 corresponds to sending (1+2), (1+3), (1+4), (1+5).↵
↵
**2. Permutation Method:**↵
↵
Send all possible pairs of tickets as one request.↵
For example, 1+2+3+4 corresponds to sending (1,2), (1,3), ... (3,4).↵
In the example provided, here's one possible solution:↵
↵
~~~~~↵
Request Amount↵
1>2,3,4 1↵
1>3,4 1↵
2>3,5 2↵
3>5,6 2↵
1+4 1↵
2+3+4 1↵
3+6 3↵
2+3 1↵
~~~~~↵
↵
This solution achieves the same total amount, preserves the amount of each ticket, and uses only 8 requests instead of 9.↵
↵
However, I'm seeking the optimal solution, which in this case is:↵
↵
~~~~~↵
Request Amount↵
3>1,2,5,6 1↵
3>1,2,4,5 1↵
1+2+3+4+6 1↵
2+3+5 1↵
~~~~~↵
↵
I've attempted a greedy solution using graphs and also explored a constraint-satisfaction approach, but neither has provided the optimal solution. I believe dynamic programming might hold the key, but I'm uncertain about how to think and implement it.↵
↵
If you have any ideas or insights to help solve this challenge, please share them with me. Your assistance is greatly appreciated.↵
↵
For more details, the constraint is relatively small. 1<= Ticket <=10. Number of initial requests <=30. Amount <= 1k. ↵
↵
Thank you very much for your support.↵
↵
↵
I'm currently facing an optimization problem related to server requests and would greatly appreciate your assistance. To explain the issue more clearly:↵
↵
Problem Statement:↵
We need to send multiple tickets to a server, and our goal is to minimize the number of requests made.↵
↵
Here's an example to illustrate the problem:↵
↵
~~~~~↵
Request Amount↵
1+3 2↵
1+2 1↵
1+4 3↵
2+3 4↵
2+4 1↵
2+5 2↵
3+4 1↵
3+5 2↵
3+6 5↵
~~~~~↵
↵
In this example, each request combines specific tickets with corresponding amounts. For instance, the first request (1+3) means we are attempting to send ticket 1 and ticket 3, with a total amount of 2 for each.↵
↵
We have two methods to reduce the number of requests:↵
↵
**1. Banker Method:**↵
↵
Combine multiple requests into one request.↵
For example, 1>2,3,4,5 corresponds to sending (1+2), (1+3), (1+4), (1+5).↵
↵
**2. Permutation Method:**↵
↵
Send all possible pairs of tickets as one request.↵
For example, 1+2+3+4 corresponds to sending (1,2), (1,3), ... (3,4).↵
In the example provided, here's one possible solution:↵
↵
~~~~~↵
Request Amount↵
1>2,3,4 1↵
1>3,4 1↵
2>3,5 2↵
3>5,6 2↵
1+4 1↵
2+3+4 1↵
3+6 3↵
2+3 1↵
~~~~~↵
↵
This solution achieves the same total amount, preserves the amount of each ticket, and uses only 8 requests instead of 9.↵
↵
However, I'm seeking the optimal solution, which in this case is:↵
↵
~~~~~↵
Request Amount↵
3>1,2,5,6 1↵
3>1,2,4,5 1↵
1+2+3+4+6 1↵
2+3+5 1↵
~~~~~↵
↵
I've attempted a greedy solution using graphs and also explored a constraint-satisfaction approach, but neither has provided the optimal solution. I believe dynamic programming might hold the key, but I'm uncertain about how to think and implement it.↵
↵
If you have any ideas or insights to help solve this challenge, please share them with me. Your assistance is greatly appreciated.↵
↵
For more details, the constraint is relatively small. 1<= Ticket <=10. Number of initial requests <=30. Amount <= 1k. ↵
↵
Thank you very much for your support.↵
↵
