Introduction

In this blog post, we will explore how to solve the LeetCode problem "2212" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

Alice and Bob are opponents in an archery competition. The competition has set the following rules: Alice first shoots numArrows arrows and then Bob shoots numArrows arrows. The points are then calculated as follows: The target has integer scoring sections ranging from 0 to 11 inclusive. For each section of the target with score k (in between 0 to 11), say Alice and Bob have shot ak and bk arrows on that section respectively. If ak >= bk, then Alice takes k points. If ak < bk, then Bob takes k points. However, if ak == bk == 0, then nobody takes k points. For example, if Alice and Bob both shot 2 arrows on the section with score 11, then Alice takes 11 points. On the other hand, if Alice shot 0 arrows on the section with score 11 and Bob shot 2 arrows on that same section, then Bob takes 11 points. You are given the integer numArrows and an integer array aliceArrows of size 12, which represents the number of arrows Alice shot on each scoring section from 0 to 11. Now, Bob wants to maximize the total number of points he can obtain. Return the array bobArrows which represents the number of arrows Bob shot on each scoring section from 0 to 11. The sum of the values in bobArrows should equal numArrows. If there are multiple ways for Bob to earn the maximum total points, return any one of them. Example 1: Input: numArrows = 9, aliceArrows = [1,1,0,1,0,0,2,1,0,1,2,0] Output: [0,0,0,0,1,1,0,0,1,2,3,1] Explanation: The table above shows how the competition is scored. Bob earns a total point of 4 + 5 + 8 + 9 + 10 + 11 = 47. It can be shown that Bob cannot obtain a score higher than 47 points. Example 2: Input: numArrows = 3, aliceArrows = [0,0,1,0,0,0,0,0,0,0,0,2] Output: [0,0,0,0,0,0,0,0,1,1,1,0] Explanation: The table above shows how the competition is scored. Bob earns a total point of 8 + 9 + 10 = 27. It can be shown that Bob cannot obtain a score higher than 27 points. Constraints: 1 <= numArrows <= 105 aliceArrows.length == bobArrows.length == 12 0 <= aliceArrows[i], bobArrows[i] <= numArrows sum(aliceArrows[i]) == numArrows

Explanation

Here's the breakdown of the solution:

• Maximize Points using Bitmasking/Backtracking: Iterate through all possible combinations of target sections Bob can win using bitmasking. Each bit in the mask represents whether Bob wins a particular section.
• Calculate Score and Arrows Used: For each combination, calculate the points Bob scores and the number of arrows required.

• Track Optimal Solution: Keep track of the combination that yields the maximum score while ensuring the total arrows used doesn't exceed the available numArrows.

• Runtime Complexity: O(2¹²), where 12 is the number of scoring sections (0-11). Storage Complexity: O(1), as the space used is constant irrespective of input size.

Code

    def maximumBobPoints(numArrows: int, aliceArrows: list[int]) -> list[int]:
    max_score = -1
    best_bob_arrows = []

    for i in range(1 << 12):
        current_score = 0
        current_arrows = 0
        bob_arrows = [0] * 12

        for j in range(12):
            if (i >> j) & 1:
                required_arrows = aliceArrows[j] + 1
                if current_arrows + required_arrows <= numArrows:
                    current_score += j
                    current_arrows += required_arrows
                    bob_arrows[j] = required_arrows
                else:
                    current_score = -1  # Invalid combination
                    break

        if current_score > max_score:
            max_score = current_score
            best_bob_arrows = bob_arrows[:]
            remaining_arrows = numArrows - current_arrows
            best_bob_arrows[0] += remaining_arrows

    return best_bob_arrows