How do you solve Maximum Fruits Harvested After at Most K Steps on LeetCode?

Maximum Fruits Harvested After at Most K Steps (LeetCode #2106) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The optimal path can only turn once, which simplifies the problem significantly.

What is the time complexity of Maximum Fruits Harvested After at Most K Steps?

The optimal solution for Maximum Fruits Harvested After at Most K Steps runs in O(n) time and uses O(1) space. The time complexity is O(n) because we only traverse the fruits array once with the two pointers, making it efficient.

What is the brute force solution for Maximum Fruits Harvested After at Most K Steps?

The brute force approach for Maximum Fruits Harvested After at Most K Steps is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves exploring all possible paths you can take within the allowed steps. This means calculating the total fruits harvested for every possible combination of left and right movements. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Fruits Harvested After at Most K Steps?

Maximum Fruits Harvested After at Most K Steps uses the following concepts: Array, Binary Search, Sliding Window, Prefix Sum. The recommended patterns to study are: Sliding Window, Two Pointers.

What are the interview tips for Maximum Fruits Harvested After at Most K Steps?

Always clarify the constraints and edge cases before jumping into coding. Think about the problem's structure — can you break it down into smaller parts? Practice explaining your thought process out loud as you code.

What are common mistakes when solving Maximum Fruits Harvested After at Most K Steps?

Not considering the boundaries of k when moving left or right. Failing to update the total fruits correctly when moving the left pointer.

#2106

Maximum Fruits Harvested After at Most K Steps

Hard

ArrayBinary SearchSliding WindowPrefix SumSliding WindowTwo Pointers

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(1)

The optimal solution leverages the observation that the best path can only turn once. We can use a sliding window approach to efficiently calculate the maximum fruits harvested by considering all possible left and right movements.

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Algorithm

4 steps

1Step 1: Initialize two pointers, one for the leftmost position and one for the rightmost position, starting from the initial position.
2Step 2: Expand the right pointer to include fruits within the allowed steps, updating the total fruits harvested.
3Step 3: If the total steps exceed k, move the left pointer to reduce the steps, adjusting the total fruits harvested accordingly.
4Step 4: Keep track of the maximum fruits harvested during this process.

solution.py21 lines

1def maxFruits(fruits, startPos, k):
2    left = 0
3    right = 0
4    max_fruits = 0
5    total_fruits = 0
6    n = len(fruits)
7    while right < n:
8        # Move right pointer
9        while right < n and (fruits[right][0] <= startPos + k):
10            total_fruits += fruits[right][1]
11            right += 1
12        # Check if we need to move left pointer
13        while left < right and (startPos - fruits[left][0] > k):
14            total_fruits -= fruits[left][1]
15            left += 1
16        max_fruits = max(max_fruits, total_fruits)
17        # Move left pointer if necessary
18        if left < right:
19            total_fruits -= fruits[left][1]
20            left += 1
21    return max_fruits

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Complexity note: The time complexity is O(n) because we only traverse the fruits array once with the two pointers, making it efficient.

1The optimal path can only turn once, which simplifies the problem significantly.
2Using a sliding window approach allows us to efficiently calculate the maximum fruits harvested.

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