3279. Maximum Total Area Occupied by Pistons

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
• An integer array positions, where positions[i] is the current position of piston i
• 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.

class Solution {
public:
    long long maxArea(int height, vector<int>& positions, string directions) {
        long long res = 0, now = 0, cnt = 0;
        vector<int> A(2 * height + 1);
        for(int i = 0; i < positions.size(); i++) {
            now += positions[i];
            if(positions[i] == 0) directions[i] = 'U';
            if(positions[i] == height) directions[i] = 'D';
            if(directions[i] == 'U') {
                int mi = height - positions[i];
                A[mi] -= 1;
                A[mi+height] += 1;
                cnt++;
            } else {
                A[positions[i]] += 1;
                A[positions[i] + height] -= 1;
            }
        }
        res = max(res, now);
        for(int i = 0; i <= 2 * height; i++) {
            cnt += A[i];
            now = now + cnt - (positions.size() - cnt);
            res = max(res, now);
        }
        return res;
    }
};