Problem

There are N children standing in a line. Each child is assigned a rating value.

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.

What is the minimum candies you must give?

Example

Given ratings = [1, 2], return 3.

Given ratings = [1, 1, 1], return 3.

Given ratings = [1, 2, 2], return 4. ([1,2,1]).

Note

保证rating高的小朋友拿到的糖果更多，我们建立一个分糖果数组A。小朋友不吃糖果，考试拿A也是可以的。
首先，分析边界条件：如果没有小朋友，或者只有一个小朋友，分别对应没有糖果，和有一个糖果。
然后我们用两个for循环来更新分糖果数组A。
排排坐，吃果果。先往右，再往左。右边高，多一个。左边高，吃得多。
这样，糖果数组可能就变成了类似于[0, 1, 0, 1, 2, 3, 0, 2, 1, 0]，小朋友们一定看出来了，这个不是真正的糖果数，而是根据考试级别ratings给高分小朋友的bonus。
好啦，每个小朋友至少要有一个糖果呢。
bonus总和加上小朋友总数n，就是要准备糖果的总数啦。

Solution

public class Solution {
    public int candy(int[] ratings) {
        int n = ratings.length;
        if (n < 2) return n;
        int[] A = new int[n];
        for (int i = 1; i < n; i++) {
            if (ratings[i] > ratings[i-1]) A[i] = A[i-1]+1;
        }
        for (int i = n-2; i >= 0; i--) {
            if (ratings[i] > ratings[i+1]) A[i] = Math.max(A[i], A[i+1]+1);
        }
        int res = n;
        for (int a: A) res += a;
        return res;
    }
}