Candy

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?

class Solution {
public:
//two pass, one from the left, other from the right. the left one find the least number of candy that needed according the the left side
//right one find the least number of candy that needed according to the right side.
    int candy(vector<int>& ratings) {
        if (ratings.empty())
            return 0;
        if (ratings.size() == 1)
            return 1;
        int n = ratings.size();
        vector<int> candy(n,1);
        for(int i=1; i < n; i++){
            if (ratings[i] > ratings[i-1])
                candy[i] = candy[i-1] + 1;
        }
        int total = candy[n-1];
        for(int i=n-2; i>=0; i--){
            if (ratings[i] > ratings[i+1])
                candy[i] = max(candy[i], candy[i+1]+1);
            total += candy[i];
        }
        return total;
    }
};