How do you solve Predict the Winner on LeetCode?

Predict the Winner (LeetCode #486) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n²) time complexity and O(n²) space complexity. Key insight: Player 1 can win if they can ensure a non-negative score difference against Player 2.

What is the brute force solution for Predict the Winner?

The brute force approach for Predict the Winner is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we explore all possible ways players can choose numbers from the ends of the array. We simulate the game recursively, checking every possible outcome to see if Player 1 can win. The optimal Optimal Solution approach improves this to O(n²).

What algorithm or data structure is used to solve Predict the Winner?

Predict the Winner uses the following concepts: Array, Math, Dynamic Programming, Recursion, Game Theory. The recommended patterns to study are: Dynamic Programming, Game Theory.

What are the interview tips for Predict the Winner?

Clearly explain your thought process and how you arrived at your solution. Discuss the time and space complexities of your approach. Be prepared to optimize your solution if asked, showing your understanding of dynamic programming.

What are common mistakes when solving Predict the Winner?

Not considering both players play optimally, leading to incorrect assumptions about score outcomes. Failing to properly implement the recursive structure or DP table, missing edge cases.

#486

Predict the Winner

Medium

ArrayMathDynamic ProgrammingRecursionGame TheoryDynamic ProgrammingGame Theory

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n²)Space O(n²)

In the optimal approach, we use dynamic programming to store results of subproblems, avoiding redundant calculations. This allows us to efficiently determine the maximum score difference Player 1 can achieve over Player 2.

⚙️

Algorithm

4 steps

1Step 1: Create a DP table where dp[i][j] represents the maximum score difference Player 1 can achieve over Player 2 from nums[i] to nums[j].
2Step 2: Initialize the table for single elements, where dp[i][i] = nums[i].
3Step 3: Fill the table for subarrays of increasing lengths, calculating the score difference based on choices from either end.
4Step 4: Return true if dp[0][n-1] >= 0, indicating Player 1 can win.

solution.py12 lines

1# Full working Python code
2
3def predict_the_winner(nums):
4    n = len(nums)
5    dp = [[0] * n for _ in range(n)]
6    for i in range(n):
7        dp[i][i] = nums[i]
8    for length in range(2, n + 1):
9        for left in range(n - length + 1):
10            right = left + length - 1
11            dp[left][right] = max(nums[left] - dp[left + 1][right], nums[right] - dp[left][right - 1])
12    return dp[0][n - 1] >= 0

ℹ

Complexity note: The time complexity is O(n²) due to filling the DP table, which requires iterating through all pairs of indices. The space complexity is also O(n²) because we store results for all subarrays in the DP table.

1Player 1 can win if they can ensure a non-negative score difference against Player 2.
2Optimal play means both players will always choose the option that maximizes their score difference.

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