135. Candy
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)
class Solution {
public:
int candy(const vector<int> &ratings) {
const int n = ratings.size();
vector<int> candy_for_student(n, 1);
for (int i = 1; i < n; ++i) {
if (ratings[i] > ratings[i - 1]) {
candy_for_student[i] = candy_for_student[i - 1] + 1;
}
}
int candy_count = candy_for_student.back();
for (int i = n - 2; i >= 0; --i) {
if (ratings[i] > ratings[i + 1]) {
candy_for_student[i] = max(candy_for_student[i], candy_for_student[i + 1] + 1);
}
candy_count += candy_for_student[i];
}
return candy_count;
}
};
Single Iteration && Greedy
n = ratings.size()
Time complexity: O(n)
Space complexity: O(1)
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;
}
};