SDE - Intern

To solve the problem of finding the maximum and minimum median of subsequences, the first step was to clearly understand the requirements. We are given an array of integers and an integer k, which represents the length of the subsequence. The goal is to efficiently determine the maximum and minimum median values among all possible subsequences of length k without generating every possible combination, as that would be computationally infeasible for large arrays.

The key insight was realizing that sorting the array provides a structured way to directly access the necessary elements for the answer. After sorting the array in ascending order, the minimum median corresponds to the middle element of the first k elements in the sorted array. This is because the smallest subsequence, in terms of element values, will yield the smallest median. On the other hand, the maximum median is obtained from the middle element of the last k elements in the sorted array. This subsequence consists of the largest elements, so its median is naturally the largest possible.

The median position is carefully calculated using zero-based indexing, taking the lower middle element when k is even to maintain consistency. Instead of generating all subsequences, which would have an exponential time complexity, we efficiently compute the result in O(n log n) time by just sorting the array once and performing simple index lookups.

For example, given the array [1, 3, 2, 5, 4] and k equal to 3, sorting the array gives [1, 2, 3, 4, 5]. The minimum median is the element at index one, which is 2, while the maximum median is the element at index three, which is 4. This approach guarantees correctness and performance, as it avoids unnecessary computations and focuses purely on sorted array properties.

To solve the problem of maximizing the number of packages where each package contains at most two items and all packages have the same total cost, I first recognized that a brute-force approach of trying all combinations would be too inefficient for large input sizes. Instead, I used a structured and efficient greedy strategy combined with sorting.

The first step was to sort the array of item costs in ascending order. Sorting helps because it places the smallest and largest elements next to each other, allowing us to efficiently pair items with the goal of forming equal-cost packages. After sorting, I used a two-pointer technique: one pointer starting at the beginning of the array (representing the cheapest item) and another pointer starting at the end of the array (representing the most expensive item).

The next step was to iterate through all possible target total costs, starting from the smallest possible (the cost of the cheapest item plus itself) up to the largest (the cost of the two most expensive items). For each target total cost, I attempted to form as many valid packages as possible using the two pointers. If the sum of the items at the two pointers matched the target total cost, it formed a valid package, and I moved both pointers inward. Otherwise, if the sum was less than the target cost, I moved the start pointer forward to consider a larger item. If the sum was greater, I moved the end pointer backward.

For each total cost attempt, I kept track of how many packages were successfully created. The solution was to return the maximum number of packages achieved for any total cost. This greedy and sorting-based method ensures that the solution runs efficiently in O(n log n) time, primarily due to sorting, and avoids the need to generate all possible subsequences.

Important considerations included handling edge cases where no valid packages are possible or where the number of items is odd, ensuring no item is used more than once, and carefully managing index boundaries to avoid out-of-range errors. This stepwise and logical approach guarantees both correctness and performance in solving the problem.

Tip 1: Decide Calmly & Logically: Analyze the situation step by step before choosing the best action.
Tip 2: Explain Your Reasoning: Communicate your thought process clearly to justify your decisions.
Tip 3: Stay Positive & Adaptive: Accept feedback, learn from others, and highlight the strengths of your approach.

Tip 1: Be Self-Aware: Clearly articulate your strengths, skills, and experiences.
Tip 2: Show Initiative: Highlight how you take decisions, solve problems, and learn from challenges.
Tip 3: Stay Positive & Collaborative: Demonstrate adaptability, openness to feedback, and teamwork.

Tip 1: Think Out Loud: Clearly explain your reasoning and what goes through your mind while approaching a problem.
Tip 2: Demonstrate Structured Problem-Solving: Break down problems into manageable steps, prioritize actions, and justify your decisions.
Tip 3: Be Self-Aware & Honest: Highlight your strengths, acknowledge limitations, and demonstrate adaptability.

Tip 1: Stay Calm & Analyze: Focus on logic, identify errors step by step.
Tip 2: Explain Clearly: Communicate your reasoning while fixing issues.
Tip 3: Be Positive & Confident: Highlight strengths, learn from others, stay composed.