How do you solve Maximum Value of K Coins From Piles on LeetCode?

Maximum Value of K Coins From Piles (LeetCode #2218) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * k) time complexity and O(k) space complexity. Key insight: Dynamic programming allows us to build solutions incrementally.

What is the time complexity of Maximum Value of K Coins From Piles?

The optimal solution for Maximum Value of K Coins From Piles runs in O(n * k) time and uses O(k) space. The complexity is O(n * k) because we iterate through each pile and for each pile, we potentially update the DP array for k coins.

What is the brute force solution for Maximum Value of K Coins From Piles?

The brute force approach for Maximum Value of K Coins From Piles is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying every possible combination of coins we can take from the piles. This is straightforward but inefficient, as it doesn't leverage any optimal strategies. The optimal Optimal Solution approach improves this to O(n * k).

What algorithm or data structure is used to solve Maximum Value of K Coins From Piles?

Maximum Value of K Coins From Piles uses the following concepts: Array, Dynamic Programming, Prefix Sum. The recommended patterns to study are: Dynamic Programming, Prefix Sum.

What are the interview tips for Maximum Value of K Coins From Piles?

Explain your thought process clearly when discussing dynamic programming. Practice writing out the state transition equations before coding. Be mindful of edge cases, such as when k exceeds the total number of coins.

What are common mistakes when solving Maximum Value of K Coins From Piles?

Not initializing the DP array correctly. Forgetting to iterate backwards when updating the DP array.

#2218

Maximum Value of K Coins From Piles

Hard

ArrayDynamic ProgrammingPrefix SumDynamic ProgrammingPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n * k)Space O(k)

The optimal solution uses dynamic programming to efficiently calculate the maximum value of coins we can collect by considering the best choices from each pile incrementally.

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Algorithm

3 steps

1Step 1: Initialize a DP array where dp[j] represents the maximum value we can obtain with j coins.
2Step 2: Iterate through each pile and for each pile, update the DP array from the back to avoid overwriting previous results.
3Step 3: For each pile, consider taking 0 to min(k, number of coins in the pile) coins and update the DP array accordingly.

solution.py9 lines

1def maxCoins(piles, k):
2    dp = [0] * (k + 1)
3    for pile in piles:
4        current_sum = 0
5        for j in range(min(len(pile), k)):
6            current_sum += pile[j]
7            for x in range(k, j, -1):
8                dp[x] = max(dp[x], dp[x - j - 1] + current_sum)
9    return dp[k]

ℹ

Complexity note: The complexity is O(n * k) because we iterate through each pile and for each pile, we potentially update the DP array for k coins.

1Dynamic programming allows us to build solutions incrementally.
2Understanding how to manage state transitions in DP is crucial.

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