LeetCode 135: Candy

Problem Description

LeetCode Problem 135

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 * 104
• 0 <= ratings[i] <= 2 * 104

Difficulty: Hard

Tags: array, greedy

Rating: 92.00%

Solution

Here’s my Python solution to this problem:

class Solution:
    def candy(self, ratings: List[int]) -> int:
        n = len(ratings)
        candies = [1] * n

        for i in range(1, n):
            if ratings[i] > ratings[i-1]:
                candies[i] = candies[i-1] + 1
        
        for i in range(n-2, -1, -1):
            if ratings[i] > ratings[i+1]:
                candies[i] = max(candies[i], candies[i+1] + 1)
        
        return sum(candies)

Complexity Analysis

The solution has the following complexity characteristics:

• Time Complexity: $O(n)$
• Space Complexity: $O(n)$

Note: This is an automated analysis and may not capture all edge cases or specific algorithmic optimizations.