Alice and Bob take turns playing a game, with Alice starting first.
Initially, there is a number n on the chalkboard. On each player's turn, that player makes a move consisting of:
Also, if a player cannot make a move, they lose the game.
Return true if and only if Alice wins the game, assuming both players play optimally.
Examples
Example 1
Input: n = 2
Output: true
Explanation: Alice chooses 1, and Bob has no more moves.
Example 2
Input: n = 3
Output: false
Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.
Constraints
1 <= n <= 1000
1025. Divisor Game
Easy
10 Points
Math
Dynamic Programming
Brainteaser
Game Theory
Alice and Bob take turns playing a game, with Alice starting first.
Initially, there is a number n on the chalkboard. On each player's turn, that player makes a move consisting of:
Also, if a player cannot make a move, they lose the game.
Return true if and only if Alice wins the game, assuming both players play optimally.
Examples
Example 1
Input: n = 2
Output: true
Explanation: Alice chooses 1, and Bob has no more moves.
Example 2
Input: n = 3
Output: false
Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.