Is Maximum Total Area Occupied by Pistons easy or hard?

Maximum Total Area Occupied by Pistons is classified as a Hard problem. The difficulty comes from recognizing that direct simulation is too slow and that prefix sums combined with counting techniques can compress the computation into a linear-time scan.

Maximum Total Area Occupied by Pistons Python/Java solution

Most implementations simulate piston movement by converting characters to numeric increments and maintaining a running prefix height. Python solutions typically use dictionaries for counting heights, while Java implementations use HashMap. Both versions achieve O(n) time complexity and O(n) space complexity.

How to solve Maximum Total Area Occupied by Pistons in O(n)?

Convert piston movements into numeric changes and compute a prefix sum representing the piston height at every step. While iterating through the string, maintain a hash map that tracks occurrences of each height level. This allows you to quickly determine spans that contribute to the maximum total occupied area, completing the computation in a single pass.

What is the best approach for Maximum Total Area Occupied by Pistons?

The most efficient approach combines prefix sum height tracking with a hash table for counting height occurrences. Each piston movement is converted into a +1 or -1 change, and prefix sums track the cumulative height at each step. A hash map stores previously seen height levels, allowing the algorithm to compute the maximum total area in O(n) time with O(n) space.

Is Maximum Total Area Occupied by Pistons asked at Google/Amazon/Meta?

Problems involving prefix sums, simulation, and hash-table counting are common in interviews at companies like Google, Amazon, and Meta. Variants of movement simulation and cumulative height tracking frequently appear in hard-level algorithm rounds, especially when combined with prefix-sum optimization.

What data structure is used in Maximum Total Area Occupied by Pistons?

The main data structures are arrays for prefix sums and a hash table for counting or tracking previously seen height states. These structures enable constant-time updates and quick lookups while iterating through the movement sequence.

What is the time complexity of Maximum Total Area Occupied by Pistons?

The optimal solution runs in O(n) time where n is the length of the movement string. Each character is processed once to update the prefix height and perform constant-time hash map operations. Space complexity is O(n) due to storing prefix sums or frequency counts of height states.

Description Hints 4 Solution Video 21:29

3279. Maximum Total Area Occupied by Pistons

Hard41.3% acceptancePremium elsewhere, free here

There are several pistons in an old car engine, and we want to calculate the maximum possible area under the pistons.

You are given:

An integer height, representing the maximum height a piston can reach.
An integer array positions, where positions[i] is the current position of piston i, which is equal to the current area under it.
A string directions, where directions[i] is the current moving direction of piston i, 'U' for up, and 'D' for down.

Each second:

Every piston moves in its current direction 1 unit. e.g., if the direction is up, positions[i] is incremented by 1.
If a piston has reached one of the ends, i.e., positions[i] == 0 or positions[i] == height, its direction will change.

Return the maximum possible area under all the pistons.

Example 1:

Input: height = 5, positions = [2,5], directions = "UD"

Output: 7

Explanation:

The current position of the pistons has the maximum possible area under it.

Example 2:

Input: height = 6, positions = [0,0,6,3], directions = "UUDU"

Output: 15

Explanation:

After 3 seconds, the pistons will be in positions [3, 3, 3, 6], which has the maximum possible area under it.

Constraints:

1 <= height <= 10⁶
1 <= positions.length == directions.length <= 10⁵
0 <= positions[i] <= height
directions[i] is either 'U' or 'D'.

Topics

Hints open one at a time

Hint 1

Simulate the process.

Hint 2

We only need to keep track of the times when a piston reaches one end and let’s call these critical points.

Hint 3

For each piston, find the first time it reaches one end and sort these times (these times are critical points).

Hint 4

Find a way to calculate the area difference between two consecutive critical points in constant time.

21:29

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1class Solution:
  def solve(self):
      pass


Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

5
[2,5]
"UD"

Input

6
[0,0,6,3]
"UUDU"

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