1025. Divisor Game.md

1025. Divisor Game

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leetcode-cn Daily Challenge on July 24th, 2020.

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Difficulty : Easy

Related Topics : Math、Dynamic Programming

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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:

• Choosing any x with 0 < x < N and N % x == 0.
• Replacing the number N on the chalkboard with N - x.

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.

Example 1:

Input: 2
Output: true
Explanation: Alice chooses 1, and Bob has no more moves.

Example 2:

Input: 3
Output: false
Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.

Note:

• 1 <= N <= 1000

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Solution

• mine
  • Java
    • Runtime: 0 ms, faster than 100.00%, Memory Usage: 35.9 MB, less than 84.88% of Java online submissions

      // O(1)time
      // O(1)space
      
      //if you want to win, you will make the last you face is 2.
      // when N is odd, whatever your choose, N will be even.
      // if N is even, you just make N change to odd. so your next N is also even. 
      // final you will got 2, and you choose 1, and you win.
      public boolean divisorGame(int N) {
        return N % 2 == 0;
      }
      

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