Problem Description
You are entering a competition, and are given two positive integers initialEnergy and initialExperience denoting your initial energy and initial experience respectively. You are also given two 0-indexed integer arrays energy and experience, both of length n. You will face n opponents in order. The energy and experience of the i-th opponent is denoted by energy[i] and experience[i] respectively. When you face an opponent, you need to have both strictly greater experience and energy to defeat them and move to the next opponent if available. Defeating the i-th opponent increases your experience by experience[i], but decreases your energy by energy[i]. Before starting the competition, you can train for some number of hours. After each hour of training, you can either choose to increase your initial experience by one, or increase your initial energy by one. Return the minimum number of training hours required to defeat all n opponents.
Key Insights
- You must have strictly greater energy and experience than each opponent to win.
- Defeating an opponent modifies your energy and experience, which must be tracked.
- The goal is to determine the minimum training hours needed to meet the requirements for all opponents.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
The solution involves iterating through the opponents and checking if the current energy and experience levels are sufficient to win against each opponent. If not, calculate the deficit for both energy and experience, and accumulate the total training hours needed. This can be efficiently implemented using a single loop through the opponents, updating energy and experience after each victory.