How do you solve Maximize Happiness of Selected Children on LeetCode?

Maximize Happiness of Selected Children (LeetCode #3075) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Greedily selecting the largest happiness values maximizes the total happiness.

What is the time complexity of Maximize Happiness of Selected Children?

The optimal solution for Maximize Happiness of Selected Children runs in O(n log n) time and uses O(1) space. The time complexity is O(n log n) due to the sorting step, and the space complexity is O(1) since we are using a constant amount of extra space.

What is the brute force solution for Maximize Happiness of Selected Children?

The brute force approach for Maximize Happiness of Selected Children is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we will consider all possible combinations of selecting k children from the array. For each combination, we calculate the total happiness after the decrements and keep track of the maximum happiness found. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximize Happiness of Selected Children?

Maximize Happiness of Selected Children uses the following concepts: Array, Greedy, Sorting. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Maximize Happiness of Selected Children?

Always consider edge cases, such as when k equals n or when all happiness values are the same. Explain your thought process clearly while coding; it helps interviewers understand your approach. Practice similar problems to recognize patterns and improve your problem-solving speed.

What are common mistakes when solving Maximize Happiness of Selected Children?

Not accounting for the decrements correctly when calculating total happiness. Overlooking the importance of sorting the happiness values.

#3075

Maximize Happiness of Selected Children

Medium

ArrayGreedySortingGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

💡

Intuition

Time O(n log n)Space O(1)

In the optimal approach, we sort the happiness values in descending order and select the top k values. We account for the decrements based on the order of selection, which allows us to maximize the total happiness efficiently.

⚙️

Algorithm

3 steps

1Step 1: Sort the happiness array in descending order.
2Step 2: Select the top k happiness values.
3Step 3: For each selected happiness value, subtract the appropriate decrements based on its position in the selection.

solution.py6 lines

1def maxHappiness(happiness, k):
2    happiness.sort(reverse=True)
3    max_happiness = 0
4    for i in range(k):
5        max_happiness += max(0, happiness[i] - i)
6    return max_happiness

ℹ

Complexity note: The time complexity is O(n log n) due to the sorting step, and the space complexity is O(1) since we are using a constant amount of extra space.

1Greedily selecting the largest happiness values maximizes the total happiness.
2Decrementing the happiness values based on the order of selection is crucial.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.