135. Candy

2024, Apr 12 2 mins read

1. Description

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.

2. Example

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.

3. Constraints

n == ratings.length
1 <= n <= 2 * 10$^{4}$
0 <= ratings[i] <= 2 * 10$^{4}$

4. Solutions

Two Iterations && Greedy

n = ratings.size()
Time complexity: O(n)
Space complexity: O(n)

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class Solution {
public:
    int candy(vector<int> &ratings) {
        const 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]);
            }
        }

        return accumulate(candy.begin(), candy.end(), 0);
    }
};

Single Iteration && Greedy

n = ratings.size()
Time complexity: O(n)
Space complexity: O(1)

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class Solution {
public:
    int candy(const vector<int> &ratings) {
        const int n = ratings.size();
        int candy_count = 1, up = 0, down = 0, peak = 0;
        for (int i = 1; i < n; ++i) {
            if (ratings[i] > ratings[i - 1]) {
                ++up;
                peak = up;
                down = 0;

                candy_count += 1 + up;
            } else if (ratings[i] == ratings[i - 1]) {
                up = down = peak = 0;
                candy_count += 1;
            } else {
                ++down;
                up = 0;

                candy_count += 1 + down;

                if (down <= peak) {
                    --candy_count;
                }
            }
        }

        return candy_count;
    }
};

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