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?

Example1

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

Example2

Input: [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.

Solution

class Solution {
public:
    vector<int> f;
    vector<int> w;
    int n;

    int candy(vector<int>& ratings) {
        n = ratings.size();
        w = ratings;
        f.resize(n, -1);

        int res = 0;
        for (int i = 0; i < n; i ++ ) res += dp(i);
        return res;
    }

    int dp(int x) {
        if (f[x] != -1) return f[x];
        f[x] = 1;
        if (x && w[x - 1] < w[x]) f[x] = max(f[x], dp(x - 1) + 1);
        if (x + 1 < n && w[x + 1] < w[x]) f[x] = max(f[x], dp(x + 1) + 1);
        return f[x];
    }
};