135. Candy

• Difficulty: Hard

• Topics: Greedy

• Similar Questions:

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?

Example 1:

Input: [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: [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.

Solutions:

class Solution {
public:
    int candy(vector<int>& ratings) { // pay attention to the condition that two adjecent ratings are equal
        int n = ratings.size();
        vector<int> candyCount (n, 0);

        vector<pair<int, int>> ratingWithIndex;

        for (int i = 0; i < n; ++i) {
            ratingWithIndex.push_back({ratings[i], i});
        }

        sort(ratingWithIndex.begin(), ratingWithIndex.end());
        int sum = 0;

        for (int i = 0; i < n; ++i) {
            int index = ratingWithIndex[i].second;
            candyCount[index] = 1;
            if (index - 1 >= 0 && ratings[index] > ratings[index - 1]) {
                candyCount[index] = max(candyCount[index], candyCount[index - 1] + 1);
            }

            if (index + 1 < n && ratings[index] > ratings[index + 1]) {
                candyCount[index] = max(candyCount[index], candyCount[index + 1] + 1);
            }

            sum += candyCount[index];
        }

        return sum;

    }
};