P2953 [USACO09OPEN]牛的数字游戏Cow Digit Game
Posted 心之所向 素履以往
tags:
篇首语:本文由小常识网(cha138.com)小编为大家整理,主要介绍了P2953 [USACO09OPEN]牛的数字游戏Cow Digit Game相关的知识,希望对你有一定的参考价值。
P2953 [USACO09OPEN]牛的数字游戏Cow Digit Game
题目描述
Bessie is playing a number game against Farmer John, and she wants you to help her achieve victory.
Game i starts with an integer N_i (1 <= N_i <= 1,000,000). Bessie goes first, and then the two players alternate turns. On each turn, a player can subtract either the largest digit or the smallest non-zero digit from the current number to obtain a new number. For example, from 3014 we may subtract either 1 or 4 to obtain either 3013 or 3010, respectively. The game continues until the number becomes 0, at which point the last player to have taken a turn is the winner.
Bessie and FJ play G (1 <= G <= 100) games. Determine, for each game, whether Bessie or FJ will win, assuming that both play perfectly (that is, on each turn, if the current player has a move that will guarantee his or her win, he or she will take it).
Consider a sample game where N_i = 13. Bessie goes first and takes 3, leaving 10. FJ is forced to take 1, leaving 9. Bessie takes the remainder and wins the game.
贝茜和约翰在玩一个数字游戏.贝茜需要你帮助她.
游戏一共进行了G(1≤G≤100)场.第i场游戏开始于一个正整数Ni(l≤Ni≤1,000,000).游
戏规则是这样的:双方轮流操作,将当前的数字减去一个数,这个数可以是当前数字的最大数码,也可以是最小的非0数码.比如当前的数是3014,操作者可以减去1变成3013,也可以减去4变成3010.若干次操作之后,这个数字会变成0.这时候不能再操作的一方为输家. 贝茜总是先开始操作.如果贝茜和约翰都足够聪明,执行最好的策略.请你计算最后的赢家.
比如,一场游戏开始于13.贝茜将13减去3变成10.约翰只能将10减去1变成9.贝茜再将9减去9变成0.最后贝茜赢.
输入输出格式
输入格式:
-
Line 1: A single integer: G
- Lines 2..G+1: Line i+1 contains the single integer: N_i
输出格式:
- Lines 1..G: Line i contains ‘YES‘ if Bessie can win game i, and ‘NO‘ otherwise.
输入输出样例
2
9
10
YES
NO
说明
For the first game, Bessie simply takes the number 9 and wins. For the second game, Bessie must take 1 (since she cannot take 0), and then FJ can win by taking 9.
博弈论 用到了sg函数和sg定理 然而我一开始并没有看出来
乱搞拿了40 ,这数据是要多水啊
1 #include <cstdio> 2 #include <cctype> 3 4 const int MAXN=1000010; 5 6 int n,t; 7 8 int sg[MAXN]; 9 10 inline void read(int&x) { 11 int f=1;register char c=getchar(); 12 for(x=0;!isdigit(c);c==‘-‘&&(f=-1),c=getchar()); 13 for(;isdigit(c);x=x*10+c-48,c=getchar()); 14 x=x*f; 15 } 16 17 int hh() { 18 read(n); 19 for(int mn,mx,t,i=1;i<MAXN-1;++i) { 20 mn=9;mx=0;t=i; 21 while(t) { 22 int b=t%10; 23 if(b) {mx=mx<b?b:mx;mn=mn>b?b:mn;} 24 t/=10; 25 } 26 sg[i]=(sg[i-mx]&sg[i-mn])^1; 27 } 28 for(int t,i=1;i<=n;++i) { 29 read(t); 30 sg[t]?printf("YES\n"):printf("NO\n"); 31 } 32 return 0; 33 } 34 35 int sb=hh(); 36 int main(int argc,char**argv) {;}
以上是关于P2953 [USACO09OPEN]牛的数字游戏Cow Digit Game的主要内容,如果未能解决你的问题,请参考以下文章
洛谷 P2909 [USACO08OPEN]牛的车Cow Cars
洛谷P2906 [USACO08OPEN]牛的街区Cow Neighborhoods