Is Maximum Calories Burnt from Jumps easy or hard?

The problem is typically classified as Medium. The brute force idea is straightforward, but recognizing that sorting and greedily pairing extremes maximizes adjacent differences requires algorithmic insight.

Maximum Calories Burnt from Jumps Python/Java solution

Implement the greedy approach by sorting the array and using two pointers to build the sequence. This logic works the same across Python, Java, C++, Go, and TypeScript because it only requires array sorting, pointer movement, and absolute difference calculations.

How to solve Maximum Calories Burnt from Jumps in O(n log n)?

First sort the jump heights. Then use two pointers at the start and end of the array to alternately select the smallest and largest elements, creating a sequence that maximizes adjacent differences. Finally compute the total calories by summing absolute differences between neighboring values.

What is the best approach for Maximum Calories Burnt from Jumps?

The most efficient method uses a greedy strategy after sorting the array. By arranging the smallest and largest remaining values next to each other using a two-pointer technique, you maximize the absolute difference between consecutive jumps. Sorting takes O(n log n) time and the arrangement step runs in O(n).

Is Maximum Calories Burnt from Jumps asked at Google/Amazon/Meta?

Problems involving maximizing adjacent differences or arranging numbers using greedy ordering appear frequently in interviews at companies like Amazon, Google, and Meta. The exact problem title may vary, but the underlying pattern of sorting plus greedy arrangement is common.

What data structure is used in Maximum Calories Burnt from Jumps?

The primary data structure is a simple array. The algorithm relies on sorting the array and then using the two-pointer technique to pick elements from both ends efficiently while constructing the optimal order.

What is the time complexity of Maximum Calories Burnt from Jumps?

The optimal solution runs in O(n log n) time due to sorting the jump heights. After sorting, building the alternating sequence with two pointers and calculating the total calories both take linear O(n) time. Space complexity is typically O(n) for storing the rearranged order.

Description Hints 3 Solution Video 6:05

3730. Maximum Calories Burnt from Jumps

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You are given an integer array heights of size n, where heights[i] represents the height of the i^th block in an exercise routine.

You start on the ground (height 0) and must jump onto each block exactly once in any order.

The calories burned for a jump from a block of height a to a block of height b is (a - b)².
The calories burned for the first jump from the ground to the chosen first block heights[i] is (0 - heights[i])².

Return the maximum total calories you can burn by selecting an optimal jumping sequence.

Note: Once you jump onto the first block, you cannot return to the ground.

Example 1:

Input: heights = [1,7,9]

Output: 181

Explanation:

The optimal sequence is [9, 1, 7].

Initial jump from the ground to heights[2] = 9: (0 - 9)² = 81.
Next jump to heights[0] = 1: (9 - 1)² = 64.
Final jump to heights[1] = 7: (1 - 7)² = 36.

Total calories burned = 81 + 64 + 36 = 181.

Example 2:

Input: heights = [5,2,4]

Output: 38

Explanation:

The optimal sequence is [5, 2, 4].

Initial jump from the ground to heights[0] = 5: (0 - 5)² = 25.
Next jump to heights[1] = 2: (5 - 2)² = 9.
Final jump to heights[2] = 4: (2 - 4)² = 4.

Total calories burned = 25 + 9 + 4 = 38.

Example 3:

Input: heights = [3,3]

Output: 9

Explanation:

The optimal sequence is [3, 3].

Initial jump from the ground to heights[0] = 3: (0 - 3)² = 9.
Next jump to heights[1] = 3: (3 - 3)² = 0.

Total calories burned = 9 + 0 = 9.

Constraints:

1 <= n == heights.length <= 10⁵
1 <= heights[i] <= 10⁵

Asked at 1 company

Amazon

Topics

Hints open one at a time

Hint 1

Sort heights and greedily distribute the values.

Hint 2

Place larger values from the back of the sorted heights in non-increasing order at the even indices.

Hint 3

Place smaller values from the front of the sorted heights in non-decreasing order at the odd indices.

6:05

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  def solve(self):
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Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[1,7,9]

Input

[5,2,4]

Input

[3,3]

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