How do you solve Sum Game on LeetCode?

Sum Game (LeetCode #1927) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Alice can always win if she can create a situation where Bob cannot balance the sums.

What is the brute force solution for Sum Game?

The brute force approach for Sum Game is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute-force approach, we will try all possible combinations of replacing '?' with digits from '0' to '9'. This means simulating every possible game state until we find a configuration where Alice wins or all '?' are replaced. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Sum Game?

Sum Game uses the following concepts: Math, String, Greedy, Game Theory. The recommended patterns to study are: Game Theory, Greedy Algorithms.

What are the interview tips for Sum Game?

Always clarify the rules of the game and how players can make moves. Discuss your thought process and reasoning as you explore solutions. Consider edge cases, such as strings with no '?' or all '?' characters.

What are common mistakes when solving Sum Game?

Not considering the impact of '?' characters on both sides equally. Assuming that the game can only end in a draw without exploring all options.

#1927

Sum Game

Medium

MathStringGreedyGame TheoryGame TheoryGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

In the optimal approach, we focus on the difference between the sums of the two halves and the number of '?' characters. By strategically replacing '?' characters, we can ensure Alice wins if she can create a situation where Bob cannot balance the sums.

⚙️

Algorithm

4 steps

1Step 1: Calculate the sum of digits in both halves, ignoring '?' characters.
2Step 2: Count the number of '?' in both halves.
3Step 3: Determine the difference between the two sums and the total '?' characters.
4Step 4: Check if Alice can create an imbalance by replacing '?' optimally.

solution.py15 lines

1def sumGame(num):
2    n = len(num)
3    half = n // 2
4    left_sum = sum(int(num[i]) for i in range(half) if num[i] != '?')
5    right_sum = sum(int(num[i]) for i in range(half, n) if num[i] != '?')
6    left_q = num[:half].count('?')
7    right_q = num[half:].count('?')
8
9    total_q = left_q + right_q
10    diff = abs(left_sum - right_sum)
11
12    if diff % 9 == 0 and total_q == 0:
13        return False
14    return True
15

ℹ

Complexity note: The time complexity is O(n) because we only traverse the string a couple of times to compute sums and counts, making it efficient.

1Alice can always win if she can create a situation where Bob cannot balance the sums.
2The difference in sums can be manipulated using '?' characters.

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