Maximum Spending After Buying Items

Maximum Spending After Buying Items

1. What is this problem about?

The Maximum Spending After Buying Items coding problem presents you with an m x n matrix of item prices, where each row represents a shop and the items in each shop are sorted in non-increasing order. You must buy all items over m * n days, one item per day. On day d, the cost of an item is price * d. In each shop, you can only buy the rightmost available item. The goal is to maximize your total spending.

2. Why is this asked in interviews?

This "Hard" problem is popular at TikTok and Zomato because it tests a candidate's ability to apply greedy strategies to matrix-based data. It evaluates whether you can identify the optimal "buying schedule"—realizing that to maximize spending, you should save the most expensive items for the later days (when the multiplier d is largest). It also tests your ability to efficiently manage multiple sorted lists.

3. Algorithmic pattern used

This problem utilizes the Heap (Priority Queue) and Greedy interview pattern. Since you want to buy the cheapest items first (on days 1, 2, etc.) and save expensive ones for later, the greedy choice is to always pick the smallest available item among the rightmost items of all shops. A Min-Heap is perfect for this, as it allows you to efficiently find and extract the minimum price across m shops in O(log m) time.

4. Example explanation

Shops: Shop 1: [10, 8, 2] Shop 2: [9, 5, 3]

1. Available rightmost: {2, 3}. Min is 2. Day 1: 2 * 1 = 2.
2. Available: {8, 3}. Min is 3. Day 2: 3 * 2 = 6.
3. Available: {8, 5}. Min is 5. Day 3: 5 * 3 = 15.
4. Available: {8, 9}. Min is 8. Day 4: 8 * 4 = 32.
5. Available: {10, 9}. Min is 9. Day 5: 9 * 5 = 45.
6. Available: {10}. Min is 10. Day 6: 10 * 6 = 60. Total Spending: 2+6+15+32+45+60 = 160.

5. Common mistakes candidates make

A common error is not realizing that the problem can be simplified. Since you can eventually buy any item as long as you buy the ones to its right first, and you want to buy all of them, you are essentially just sorting all items in the matrix in non-decreasing order and multiplying them by day 1, 2, 3, etc. Failing to see this "global sort" optimization might lead to a more complex and slower implementation.

6. Interview preparation tip

For "Matrix, Greedy interview pattern" problems, always ask: "Does the local constraint (rightmost item only) actually prevent me from picking the global minimum?" In this case, since the rows are already sorted, the global minimum is guaranteed to be one of the rightmost items. This insight simplifies the problem from a complex multi-list management task to a simple sorting task.