Minimum Hours of Training to Win a Competition

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class Solution:
    def minNumberOfHours(self, initialEnergy: int, initialExperience: int, energy: List[int], experience: List[int]) -> int:
        # Prepare a list of tuples, each containing (energy, experience) of each opponent
        opponents = sorted(zip(energy, experience))

        hours = 0  # Initialize hours for training

        for e, exp in opponents:
            # Calculate needed hours for energy and experience
            need_hours_for_energy = max(0, e - initialEnergy)
            need_hours_for_experience = max(0, exp - initialExperience)

            # Select the maximum of the needed hours
            need_hours = max(need_hours_for_energy, need_hours_for_experience)

            # Add the need_hours to the total hours
            hours += need_hours

            # Increase the initial energy and experience
            initialEnergy += need_hours
            initialExperience += need_hours

            # Decrease energy by e and increase experience by exp after defeating an opponent
            initialEnergy -= e
            initialExperience += exp

        return hours

The function minNumberOfHours calculates the minimum number of training hours required to defeat all opponents in a competition. Here’s a step-by-step explanation:

1. Prepare a list of opponents: First, the function creates a list of tuples, where each tuple consists of the energy and experience of each opponent. The zip function combines the energy and experience lists into a list of tuples, and sorted sorts this list. This ensures that you face the opponents in increasing order of their energy and experience.

2. Initialization: The variable hours is initialized to 0. This variable keeps track of the total training hours.

3. Iteration through opponents: The function then iterates over each opponent.

   • For each opponent, it calculates the training hours needed for energy (need_hours_for_energy) and experience (need_hours_for_experience) to defeat the opponent. If the initial energy or experience is greater than the opponent’s energy or experience, no training hours are needed for that aspect, hence the use of max(0, ...).

   • The need_hours is calculated as the maximum of need_hours_for_energy and need_hours_for_experience, because you need to have both energy and experience greater than the opponent to defeat them. The larger of the two values is chosen, to ensure that both energy and experience are at least equal to the opponent’s.

   • The need_hours is then added to hours, and also added to both initialEnergy and initialExperience, indicating that you’ve spent these hours training and increasing both your energy and experience.

   • After defeating the opponent, your energy decreases by the energy of the opponent (e), and your experience increases by the experience of the opponent (exp).

4. Return result: Finally, the function returns the total training hours (hours) needed to defeat all opponents.

The function uses a greedy approach, always spending the necessary hours to just barely defeat the next opponent, which ensures the minimum total hours.