How do you solve Sell Diminishing-Valued Colored Balls on LeetCode?

Sell Diminishing-Valued Colored Balls (LeetCode #1648) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n + orders log n) time complexity and O(n) space complexity. Key insight: Greedily sell the highest valued balls first.

What is the time complexity of Sell Diminishing-Valued Colored Balls?

The optimal solution for Sell Diminishing-Valued Colored Balls runs in O(n log n + orders log n) time and uses O(n) space. The complexity is O(n log n) for building the max-heap and O(orders log n) for processing each order, making it efficient for larger inputs.

What is the brute force solution for Sell Diminishing-Valued Colored Balls?

The brute force approach for Sell Diminishing-Valued Colored Balls is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves selling balls one by one, always choosing the ball with the highest current value. This method is straightforward but inefficient, especially with large inventories and high order counts. The optimal Optimal Solution approach improves this to O(n log n + orders log n).

What algorithm or data structure is used to solve Sell Diminishing-Valued Colored Balls?

Sell Diminishing-Valued Colored Balls uses the following concepts: Array, Math, Binary Search, Greedy, Sorting, Heap (Priority Queue). The recommended patterns to study are: Heap, Greedy.

What are the interview tips for Sell Diminishing-Valued Colored Balls?

Explain your thought process clearly when discussing the greedy approach. Be prepared to discuss time and space complexity. Practice implementing heaps and understand their operations.

What are common mistakes when solving Sell Diminishing-Valued Colored Balls?

Not using a max-heap and trying to sort repeatedly. Overcomplicating the logic instead of focusing on the greedy approach.

#1648

Sell Diminishing-Valued Colored Balls

Medium

ArrayMathBinary SearchGreedySortingHeap (Priority Queue)HeapGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n + orders log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n + orders log n)Space O(n)

The optimal solution uses a greedy approach combined with a priority queue (max-heap) to efficiently sell the highest valued balls first while keeping track of the remaining orders. This significantly reduces the time complexity.

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Algorithm

4 steps

1Step 1: Use a max-heap to store the inventory counts.
2Step 2: While there are orders to fulfill, extract the maximum value from the heap.
3Step 3: Calculate how many balls can be sold at that value and update the total value accordingly.
4Step 4: If there are remaining balls of that value, push the new value back into the heap.

solution.py13 lines

1import heapq
2
3def maxProfit(inventory, orders):
4    inventory = [-x for x in inventory]
5    heapq.heapify(inventory)
6    total_value = 0
7    while orders > 0:
8        max_value = -heapq.heappop(inventory)
9        total_value += max_value
10        orders -= 1
11        if max_value - 1 > 0:
12            heapq.heappush(inventory, -(max_value - 1))
13    return total_value % (10**9 + 7)

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Complexity note: The complexity is O(n log n) for building the max-heap and O(orders log n) for processing each order, making it efficient for larger inputs.

1Greedily sell the highest valued balls first.
2Using a max-heap allows efficient retrieval of the maximum value.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.