How do you solve Maximize Value of Function in a Ball Passing Game on LeetCode?

Maximize Value of Function in a Ball Passing Game (LeetCode #2836) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log k) time complexity and O(n log k) space complexity. Key insight: Understanding the relationship between players and how the ball is passed is crucial for optimizing the solution.

What is the time complexity of Maximize Value of Function in a Ball Passing Game?

The optimal solution for Maximize Value of Function in a Ball Passing Game runs in O(n log k) time and uses O(n log k) space. The time complexity is O(n log k) because we preprocess the jump table in O(n log k) and then compute scores in O(n log k) as well, making it efficient even for large k.

What is the brute force solution for Maximize Value of Function in a Ball Passing Game?

The brute force approach for Maximize Value of Function in a Ball Passing Game is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves simulating the ball-passing game for each player and calculating the score for each starting position. This is straightforward but inefficient, as it checks every possible starting player and performs all passes for each. The optimal Optimal Solution approach improves this to O(n log k).

What algorithm or data structure is used to solve Maximize Value of Function in a Ball Passing Game?

Maximize Value of Function in a Ball Passing Game uses the following concepts: Array, Dynamic Programming, Bit Manipulation. The recommended patterns to study are: Dynamic Programming, Binary Lifting, Graph Traversal.

What are the interview tips for Maximize Value of Function in a Ball Passing Game?

Always start with a brute force solution to understand the problem before optimizing. Explain your thought process clearly during the interview, especially when transitioning to more complex solutions. Practice building and using data structures like jump tables or binary lifting techniques.

What are common mistakes when solving Maximize Value of Function in a Ball Passing Game?

Not considering the case where k is very large, leading to inefficient brute force solutions. Failing to understand how to build and use the jump table for binary lifting.

#2836

Maximize Value of Function in a Ball Passing Game

Hard

ArrayDynamic ProgrammingBit ManipulationDynamic ProgrammingBinary LiftingGraph Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n log k)Space O(n log k)

The optimal solution uses a technique called binary lifting to efficiently compute the score after k passes. Instead of simulating each pass, we can jump directly to the player who would receive the ball after a certain number of passes, reducing the time complexity significantly.

⚙️

Algorithm

3 steps

1Step 1: Precompute the next player for each player using binary lifting.
2Step 2: For each player, calculate the total score for k passes using the precomputed values.
3Step 3: Return the maximum score found.

solution.py20 lines

1def maxScore(receiver, k):
2    n = len(receiver)
3    max_score = 0
4    log_k = k.bit_length()
5    jump = [[0] * log_k for _ in range(n)]
6    for i in range(n):
7        jump[i][0] = receiver[i]
8    for j in range(1, log_k):
9        for i in range(n):
10            jump[i][j] = jump[jump[i][j-1]][j-1]
11    for i in range(n):
12        current_score = 0
13        current_player = i
14        for j in range(log_k):
15            if k & (1 << j):
16                current_score += current_player
17                current_player = jump[current_player][j]
18        current_score += current_player
19        max_score = max(max_score, current_score)
20    return max_score

ℹ

Complexity note: The time complexity is O(n log k) because we preprocess the jump table in O(n log k) and then compute scores in O(n log k) as well, making it efficient even for large k.

1Understanding the relationship between players and how the ball is passed is crucial for optimizing the solution.
2Binary lifting allows us to efficiently compute the result without simulating every pass.

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