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
Solutions
Solution 1: Two traversals
We initialize two arrays $left$ and $right$, where $left[i]$ represents the minimum number of candies the current child should get when the current child's score is higher than the left child's score, and $right[i]$ represents the minimum number of candies the current child should get when the current child's score is higher than the right child's score. Initially, $left[i]=1$, $right[i]=1$.
We traverse the array from left to right once, and if the current child's score is higher than the left child's score, then $left[i]=left[i-1]+1$; similarly, we traverse the array from right to left once, and if the current child's score is higher than the right child's score, then $right[i]=right[i+1]+1$.
Finally, we traverse the array of scores once, and the minimum number of candies each child should get is the maximum of $left[i]$ and $right[i]$, and we add them up to get the answer.
Time complexity $O(n)$, space complexity $O(n)$. Where $n$ is the length of the array of scores.