标签:stones stone 博弈 removes your 动态 规划 Your friend
292. Nim GameYou are playing the following Nim Game with your friend:
- Initially, there is a heap of stones on the table.
- You and your friend will alternate taking turns, and you go first.
- On each turn, the person whose turn it is will remove 1 to 3 stones from the heap.
- The one who removes the last stone is the winner.
Given n
, the number of stones in the heap, return true
if you can win the game assuming both you and your friend play optimally, otherwise return false
.
Example 1:
Input: n = 4 Output: false Explanation: These are the possible outcomes: 1. You remove 1 stone. Your friend removes 3 stones, including the last stone. Your friend wins. 2. You remove 2 stones. Your friend removes 2 stones, including the last stone. Your friend wins. 3. You remove 3 stones. Your friend removes the last stone. Your friend wins. In all outcomes, your friend wins.
Example 2:
Input: n = 1 Output: true
Example 3:
Input: n = 2 Output: true
Constraints:
1 <= n <= 231 - 1
class Solution { public boolean canWinNim(int n) { Boolean[] status = new Boolean[n+1]; return helper(n,status); } private boolean helper(int n,Boolean[] status){ if(n<=0) return false;//如果没有剩余的石头了,那么我就输了 if(status[n]!=null) return status[n]; for(int i=1;i<4;i++){//我可以取1,2,3个石头 if(!helper(n-i,status)) return true; //如果我拿i个,剩下的如果对手能赢(true),那我就输了,对手输了(false) 我就能赢 } return status[n]=false; } }
标签:stones,stone,博弈,removes,your,动态,规划,Your,friend 来源: https://www.cnblogs.com/cynrjy/p/15670672.html
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