[LintCode] 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?

Example

Given ratings = [1, 2], return 3.

Given ratings = [1, 1, 1], return 3.

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

class Solution {
public:
    int candy(vector<int> &ratings) 
    {
        int num = ratings.size();
        if(0 == num) return 0;
        vector<int> candies(num, 1);
        
        for(int i=1;i<num;i++)
        {
            if(ratings[i]>ratings[i-1])
                candies[i] = candies[i-1]+1;
        }
        
        for(int i=num-2;i>=0;i--)
        {
            if(ratings[i] > ratings[i+1] && candies[i] <= candies[i+1])
            {
                candies[i] = candies[i+1] + 1;
            }
        }
        int sum = 0;
        for(int i=0;i<num;i++) sum += candies[i];
        
        return sum;
    }
};