135. Candy

Hard

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There are n children standing in a line. Each child is assigned a rating value given in the integer array ratings.

You are giving candies to these children subjected to the following requirements:

• Each child must have at least one candy.

• Children with a higher rating get more candies than their neighbors.

Return the minimum number of candies you need to have to distribute the candies to the children.

Example 1:

Input: ratings = [1,0,2]
Output: 5
Explanation: You can allocate to the first, second and third child with 2, 1, 2 candies respectively.

Example 2:

Input: ratings = [1,2,2]
Output: 4
Explanation: You can allocate to the first, second and third child with 1, 2, 1 candies respectively.
The third child gets 1 candy because it satisfies the above two conditions.

Constraints:

• n == ratings.length

• 1 <= n <= 2 * 104

• 0 <= ratings[i] <= 2 * 104

class Solution:
    def candy(self, ratings: List[int]) -> int:
        length, ans = len(ratings), [1]*len(ratings)
        # Forward
        for index in range(length-1):
            if ratings[index] < ratings[index+1]:
                ans[index+1] = max(1+ans[index], ans[index+1])
        
        #Backward
        for index in range(length-2, -1 , -1):
            if ratings[index] > ratings[index+1]:
                ans[index] = max(1+ans[index+1], ans[index])
                
        return sum(ans)