Intern

Brute Force Approach (Online Test):

Step 1: I initially attempted a brute force approach by trying all possible combinations of adding or subtracting K to each stick's height.

• I calculated the difference between the maximum and minimum heights for each configuration and recorded the smallest difference.

Step 2: During the online test, I realized the inefficiency of this approach and considered optimizing it by sorting the array to focus on boundary values.

• Sorting allowed me to systematically explore the extremes of the array, reducing the spread between the smallest and largest heights.

Step 3: After sorting the array, I applied the following logic:

• Increase the smallest value by K and decrease the largest value by K.
• Adjust the intermediate values to explore potential minimum differences based on the sorted boundaries.
• This optimization reduced the time complexity to O(NlogN), making the solution efficient within the constraints of the test.

Conclusion: By implementing the optimized, sorting-based approach, I successfully passed the test cases and minimized the maximum difference effectively. This solution was significantly faster than the brute force method.

Approach:

1. Understand the cost function:
The cost of the box is defined as the sum of the squares of the frequencies of each letter in the string. To minimize the cost, we should remove candles corresponding to the letter with the highest frequency. This is because reducing the highest frequency has the most significant impact on lowering the cost.

2. Steps to solve:

• Compute the frequency of each character in the string.
• Use a max-heap (priority queue) to repeatedly remove M candles from the most frequent letter.
• Recompute the cost using the remaining frequencies.