135. Candy

/*
 * @lc app=leetcode id=135 lang=cpp
 *
 * [135] Candy
 *
 * https://leetcode.com/problems/candy/description/
 *
 * algorithms
 * Hard (43.78%)
 * Likes:    8018
 * Dislikes: 683
 * Total Accepted:    610.6K
 * Total Submissions: 1.4M
 * Testcase Example:  '[1,0,2]'
 *
 * There are n children standing in a line. Each child is assigned a rating
 * value given in the integer array ratings.
 *
 * 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.
 *
 *
 * Return the minimum number of candies you need to have to distribute the
 * candies to the children.
 *
 *
 * Example 1:
 *
 *
 * Input: ratings = [1,0,2]
 * Output: 5
 * Explanation: You can allocate to the first, second and third child with 2,
 * 1, 2 candies respectively.
 *
 *
 * Example 2:
 *
 *
 * Input: ratings = [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.
 *
 *
 *
 * Constraints:
 *
 *
 * n == ratings.length
 * 1 <= n <= 2 * 10^4
 * 0 <= ratings[i] <= 2 * 10^4
 *
 *
 */

// @lc code=start
class Solution {
public:
    int candy(vector<int>& ratings)
    {
        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;
            }
        }

        for (int i = n - 2; i >= 0; --i)
        {
            if (ratings[i] > ratings[i + 1])
            {
                candy[i] = max(candy[i], candy[i + 1] + 1);
            }
        }
        return accumulate(candy.begin(), candy.end(), 0);
    }
};
// @lc code=end

• T: $O(n)$
• S: $O(n)$