3494 - Find the Minimum Amount of Time to Brew Potions.

Medium

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 <code>i^th</code> wizard on the <code>j^th</code> potion is <code>time_ij = skilli * manaj</code>.

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: 110

Explanation:

As an example for why wizard 0 cannot start working on the 1^st potion before time t = 52, consider the case where the wizards started preparing the 1^st potion at time t = 50. At time t = 58, wizard 2 is done with the 1^st potion, but wizard 3 will still be working on the 0^th potion till time t = 60.

Example 2:

Input: skill = 1,1,1, mana = 1,1,1

Output: 5

Explanation:

• Preparation of the 0^th potion begins at time t = 0, and is completed by time t = 3.

• Preparation of the 1^st potion begins at time t = 1, and is completed by time t = 4.

• Preparation of the 2^nd potion begins at time t = 2, and is completed by time t = 5.

Example 3:

Input: skill = 1,2,3,4, mana = 1,2

Output: 21

Constraints:

• n == skill.length

• m == mana.length

• 1 <= n, m <= 5000

• 1 <= mana[i], skill[i] <= 5000