Plus-Minus Split(Codeforces)
date
Jan 9, 2024
slug
codeforces-plus-minus
status
Published
tags
CODEFORCES
summary
type
Post
Problem
You're given a string consisting of '+' and '-' characters, representing an array. Your task is to split this array into subarrays in such a way that the sum of penalties for all subarrays is minimized. The penalty for a subarray is calculated as the absolute sum of its elements multiplied by its length.
My Approach
In solving the problem, I chose to take a different route by simulating the process of forming subarrays without actually creating them. This simulation was achieved using a deque, which acted like a stack.
My Thought Process
- Recognizing Patterns:
- I noticed that the penalties depend on the arrangement of '+' and '-' elements within the array. This observation guided my approach.
- Simulating Subarray Formation:
- Instead of forming subarrays directly, I decided to simulate their formation using a deque This allowed me to understand how the penalties would be influenced by the arrangement of elements.
- Dealing with Contradictory Elements:
- I paid special attention to how I should handle adjacent '+' and '-' characters within the array. By making specific adjustments to the deque based on these pairs, I aimed to minimize the penalties.
- Goal was to add as many pairs of (+,-) to a subarray because they would cancel out each other thus making penalty 0 of the subarray.
- Achieving Minimum Penalty:
- My ultimate goal was to find a configuration where the total penalties for all subarrays would be minimized. By using the deque to simulate the formation of subarrays and adjusting it based on the '+' and '-' pairs, I worked towards achieving this goal effectively.
- If such pair is not possible we just make that individual character a single array and add 1 penaltiy to whole penalty value. For example, for array [+,+,+] it is optimal to make it [+],[+],[+] which has total penalty 3 compared to [+,+,+] which has penaltiy 9.
Simply Put
I approached the problem with the idea of minimizing penalties by cleverly simulating subarray formations using a deque. By making smart choices about which elements to group together, I aimed to achieve the lowest possible total penalty.
Code(Rust)
NOTE: println!("{}", stack.len() - 1) cause last element contains “\n” character.