Find the Minimum Amount of Time to Brew Potions
You are given two integer arrays, skill and mana, of length n and m, respectively.
In a laboratory, n wizards must brew m potions in order. Each potion has a mana capacity mana[j] and must pass through all the wizards sequentially to be brewed properly. The time taken by the i^th wizard on the j^th potion is time_i_j = skill[i] * mana[j].
Since the brewing process is delicate, a potion must be passed to the next wizard immediately after the current wizard completes their work. This means the timing must be synchronized so that each wizard begins working on a potion exactly when it arrives.
Return the minimum amount of time required for the potions to be brewed properly.
Example 1
Input
skill = [1,5,2,4], mana = [5,1,4,2]Output
110With the required synchronization, the four potions finish after wizard 3 completes the last potion at time 110.
Example 2
Input
skill = [1,1,1], mana = [1,1,1]Output
5The three potions can begin at times 0, 1, and 2, so the last potion is completed by time 5.
Constraints
- n == skill.length
- m == mana.length
- 1 <= n, m <= 5000
- 1 <= mana[i], skill[i] <= 5000