#3279 - Maximum Total Area Occupied by Pistons

Problem Description

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.

Solution

/**
 * @param {number} height
 * @param {number[]} positions
 * @param {string} directions
 * @return {number}
 */
var maxArea = function(height, positions, directions) {
  const n = directions.length;
  let upCount = directions.split('').filter(dir => dir === 'U').length;
  let result = positions.reduce((sum, pos) => sum + pos, 0);
  let currentArea = result;
  const vertices = new Map();
  vertices.set(0, 0);

  for (let i = 0; i < n; i++) {
    const direction = directions[i];
    const position = positions[i];

    if (direction === 'U') {
      vertices.set(height - position, (vertices.get(height - position) || 0) - 1);
      vertices.set(2 * height - position, (vertices.get(2 * height - position) || 0) + 1);
    } else {
      vertices.set(height + position, (vertices.get(height + position) || 0) - 1);
      vertices.set(position, (vertices.get(position) || 0) + 1);
    }
  }

  const sortedTimes = Array.from(vertices.keys()).sort((a, b) => a - b);
  for (let i = 0; i < sortedTimes.length - 1; i++) {
    const leftTime = sortedTimes[i];
    const rightTime = sortedTimes[i + 1];

    currentArea += (rightTime - leftTime) * (2 * upCount - n);
    if (currentArea > result) {
      result = currentArea;
    }
    upCount += vertices.get(rightTime) || 0;
  }

  return result;
};