How do you solve Maximum Coins From K Consecutive Bags on LeetCode?

Maximum Coins From K Consecutive Bags (LeetCode #3413) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n + m) time complexity and O(m) space complexity. Key insight: The segments are non-overlapping, allowing us to efficiently calculate the coins in a straightforward manner.

What is the brute force solution for Maximum Coins From K Consecutive Bags?

The brute force approach for Maximum Coins From K Consecutive Bags is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every possible starting position for k consecutive bags and sums the coins in those bags. This is straightforward but inefficient, especially for large inputs. The optimal Optimal Solution approach improves this to O(n + m).

What are the interview tips for Maximum Coins From K Consecutive Bags?

Always start with a brute force approach to understand the problem deeply. Look for patterns in the problem that can lead to optimization, such as sliding windows or prefix sums. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Maximum Coins From K Consecutive Bags?

Not considering the boundaries of the segments correctly when summing coins. Failing to optimize the approach and sticking to a brute force method even when a better solution exists.

#3413

Maximum Coins From K Consecutive Bags

Medium

ArrayBinary SearchGreedySliding WindowSortingPrefix SumSliding WindowPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n + m)Space O(m)

The optimal solution leverages the fact that the segments are non-overlapping and allows us to efficiently calculate the maximum coins by focusing on valid starting positions based on the segments.

⚙️

Algorithm

3 steps

1Step 1: Create an array to store the number of coins at each bag position based on the segments provided.
2Step 2: For each segment [l_i, r_i], update the corresponding positions in the array with the number of coins c_i.
3Step 3: Use a sliding window of size k to find the maximum sum of coins in any k consecutive bags.

solution.py12 lines

1def maxCoins(coins, k):
2    max_position = max(r for _, r, _ in coins)
3    coin_count = [0] * (max_position + 1)
4    for l, r, c in coins:
5        for i in range(l, r + 1):
6            coin_count[i] += c
7    max_coins = sum(coin_count[1:k + 1])
8    current_sum = max_coins
9    for i in range(2, max_position + 1 - k + 1):
10        current_sum = current_sum - coin_count[i - 1] + coin_count[i + k - 1]
11        max_coins = max(max_coins, current_sum)
12    return max_coins

ℹ

Complexity note: The time complexity is O(n + m) where n is the number of segments and m is the maximum r_i. We iterate through the segments once and then through the coinCount array.

1The segments are non-overlapping, allowing us to efficiently calculate the coins in a straightforward manner.
2Using a sliding window technique helps us optimize the search for k consecutive bags.

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