How do you solve Maximum Number of Coins You Can Get on LeetCode?

Maximum Number of Coins You Can Get (LeetCode #1561) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: You can maximize your coins by allowing Bob to take the smallest pile.

What is the time complexity of Maximum Number of Coins You Can Get?

The optimal solution for Maximum Number of Coins You Can Get runs in O(n log n) time and uses O(1) space. The complexity is O(n log n) due to the sorting step, which is efficient for large inputs compared to the brute force approach.

What is the brute force solution for Maximum Number of Coins You Can Get?

The brute force approach for Maximum Number of Coins You Can Get is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we will try every possible combination of selecting 3 piles at a time and simulate the game to see how many coins we can collect. This is simple but inefficient. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Number of Coins You Can Get?

Maximum Number of Coins You Can Get uses the following concepts: Array, Math, Greedy, Sorting, Game Theory. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Maximum Number of Coins You Can Get?

Always think about the implications of each player's choices. Practice sorting and selecting elements efficiently. Explain your thought process clearly during the interview.

What are common mistakes when solving Maximum Number of Coins You Can Get?

Not considering the impact of Bob's choice on your own coins. Overcomplicating the selection of piles instead of using a systematic approach.

#1561

Maximum Number of Coins You Can Get

Medium

ArrayMathGreedySortingGame TheoryGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n log n)Space O(1)

In the optimal approach, we sort the piles and strategically select piles to maximize our coins while minimizing what Bob gets. By always allowing Bob to take the smallest pile, we can ensure we get the maximum possible coins.

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Algorithm

3 steps

1Step 1: Sort the piles in ascending order.
2Step 2: Select the last n piles for yourself, skipping every third pile from the end (which Bob will take).
3Step 3: Sum the coins from the selected piles to get the maximum coins you can collect.

solution.py5 lines

1# Full working Python code
2
3def maxCoins(piles):
4    piles.sort()
5    return sum(piles[len(piles)//3:len(piles)//3*2:2])

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Complexity note: The complexity is O(n log n) due to the sorting step, which is efficient for large inputs compared to the brute force approach.

1You can maximize your coins by allowing Bob to take the smallest pile.
2Sorting the piles helps in easily selecting the optimal coins.

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