Practice Time to Cross a Bridge

Move n boxes from the right warehouse to the left using k workers initially waiting left. Worker i has times [leftToRight,pick,rightToLeft,put]. Only one crosses at once; picking and putting can overlap other work. When free, the bridge first admits a waiting right-side worker, otherwise a waiting left-side worker if boxes remain unassigned. Within a side, prioritize larger leftToRight+rightToLeft, then larger worker index. Never dispatch more workers than remaining boxes. Return when the final box reaches the left bank, excluding its putting time. Practice approach: Use priority queues for waiting workers on each side and completion-time queues for workers picking or putting. Move every finished worker into a waiting queue before selecting a crossing. When nobody can cross, jump to the next completion time. Track boxes assigned separately from boxes delivered.