135. Candy 考验逻辑能力的时候到了

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?

int candy(vector<int>& ratings) {
int len = ratings.size(), res = 0, i;
if (len>0)
{
vector<int> number(len, 0); // to save the number of candies for child[0:N-1]
number[0] = 1;
// forward scan to calculate how many candies needed for child i to make sure it has more candies than
//its left neighbor if it has a higher rate, otherwise, give one candy to it
for (i = 1; i<len; ++i) number[i] = ratings[i]>ratings[i - 1] ? number[i - 1] + 1 : 1;

// backward scan to calculate to make sure child i has more candies than its right neighbor if it has
//a higher rate, pick the bigger one from forward and backward scans as the final number for child i
for (i = len - 2, res = number[len - 1]; i >= 0; --i)
{
if ((ratings[i]>ratings[i + 1]) && number[i]<(number[i + 1] + 1)) number[i] = number[i + 1] + 1;
res += number[i];
}
}
return res;
}