Candy
Problem 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.
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
Solve it on LeetCode
Approaches
1. Brute Force
Intuition:
The problem can be approached with a brute-force method where we repeatedly iterate over the array to ensure all conditions are satisfied: each child gets at least one candy, and children with a higher rating than their neighbors get more candy than their neighbors. This involves iteratively adjusting the candy values until we reach a stable state.
Code:
- Time Complexity: O(n^2) in the worst case due to the repeated iteration over the array.
- Space Complexity: O(n) for the
candiesarray.
2. Two-pass Linear Greedy
Intuition:
This approach improves upon the brute force by using a two-pass linear greedy strategy. We handle conditions in a more organized manner:
- Make one pass from left to right, ensuring children with a higher rating than the previous one get more candies.
- Make a second pass from right to left, doing similar adjustments but also ensuring not to disturb what was established in the first pass.
Code:
- Time Complexity: O(n), where n is the number of children, because each array is traversed twice.
- Space Complexity: O(n) for the
candiesarray.