How do you solve Can I Win on LeetCode?

Can I Win (LeetCode #464) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding the state of the game is crucial; knowing which integers have been used helps determine possible outcomes.

What is the brute force solution for Can I Win?

The brute force approach for Can I Win is Brute Force, with O(n²) time complexity and O(1) space complexity. We can simulate every possible move for both players to see if the first player can guarantee a win. This involves recursively checking all combinations of choices until we reach the desired total or exhaust all options. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Can I Win?

Can I Win uses the following concepts: Math, Dynamic Programming, Bit Manipulation, Memoization, Game Theory, Bitmask. The recommended patterns to study are: Dynamic Programming, Bit Manipulation.

What are the interview tips for Can I Win?

Always explain your thought process clearly; it helps the interviewer understand your approach. Consider edge cases, such as when the desired total is 0 or when the maximum choosable integer is very small. Practice recursive problems with memoization to build confidence in dynamic programming techniques.

What are common mistakes when solving Can I Win?

Assuming the first player always has a winning strategy without considering the opponent's optimal moves. Not using memoization effectively, leading to redundant calculations.

#464

Can I Win

Medium

MathDynamic ProgrammingBit ManipulationMemoizationGame TheoryBitmaskDynamic ProgrammingBit Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

We can use dynamic programming with memoization to avoid recalculating results for the same state. This allows us to efficiently determine if the first player can force a win by checking possible moves and their outcomes.

⚙️

Algorithm

3 steps

1Step 1: Create a memoization table to store results for each state (used integers).
2Step 2: Use a recursive function to explore each possible move, checking if the opponent can win from the resulting state.
3Step 3: If the opponent cannot win from any of their possible moves, the first player can win from that state.

solution.py19 lines

1def canIWin(maxChoosableInteger, desiredTotal):
2    if desiredTotal <= 0:
3        return True
4    if (maxChoosableInteger * (maxChoosableInteger + 1)) // 2 < desiredTotal:
5        return False
6    memo = {}
7    def canWin(remainingTotal, used):
8        if remainingTotal <= 0:
9            return False
10        if used in memo:
11            return memo[used]
12        for i in range(1, maxChoosableInteger + 1):
13            if not (used & (1 << i)):
14                if not canWin(remainingTotal - i, used | (1 << i)):
15                    memo[used] = True
16                    return True
17        memo[used] = False
18        return False
19    return canWin(desiredTotal, 0)

ℹ

Complexity note: The time complexity is O(n) since we are using memoization to store results for each state, significantly reducing the number of recursive calls needed.

1Understanding the state of the game is crucial; knowing which integers have been used helps determine possible outcomes.
2Optimal play means anticipating the opponent's moves and countering them effectively.

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