reducing-dishes

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1402. Reducing Dishes (Hard)

A chef has collected data on the satisfaction level of his n dishes. Chef can cook any dish in 1 unit of time.

Like-time coefficient of a dish is defined as the time taken to cook that dish including previous dishes multiplied by its satisfaction level i.e. time[i] * satisfaction[i].

Return the maximum sum of like-time coefficient that the chef can obtain after dishes preparation.

Dishes can be prepared in any order and the chef can discard some dishes to get this maximum value.

 

Example 1:

Input: satisfaction = [-1,-8,0,5,-9]
Output: 14
Explanation: After Removing the second and last dish, the maximum total like-time coefficient will be equal to (-1*1 + 0*2 + 5*3 = 14).
Each dish is prepared in one unit of time.

Example 2:

Input: satisfaction = [4,3,2]
Output: 20
Explanation: Dishes can be prepared in any order, (2*1 + 3*2 + 4*3 = 20)

Example 3:

Input: satisfaction = [-1,-4,-5]
Output: 0
Explanation: People do not like the dishes. No dish is prepared.

 

Constraints:

• n == satisfaction.length
• 1 <= n <= 500
• -1000 <= satisfaction[i] <= 1000

Related Topics

[Array] [Dynamic Programming] [Greedy] [Sorting]

Hints

Hint 1

Use dynamic programming to find the optimal solution by saving the previous best like-time coefficient and its corresponding element sum.

Hint 2

If adding the current element to the previous best like-time coefficient and its corresponding element sum would increase the best like-time coefficient, then go ahead and add it. Otherwise, keep the previous best like-time coefficient.